Wikipedia talk:WikiProject Mathematics/Archive/2023

Jan 2023

Tensor versus tensor field

There is a Tensor article and also a Tensor field article. The Tensor article contains a good deal of material on tensor fields. The two articles should either be cleanly separated into separate articles or merged; I'm not sure which option is better. Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:06, 23 December 2022 (UTC)

I think I would lean to a merge, or more precisely that the main tensor article should be primarily about tensor fields. It would be reasonable to have a subsidiary article on the sparer concept from abstract algebra. --Trovatore (talk) 22:57, 23 December 2022 (UTC)

I lean against a merge. Based on my experience both on Wikipedia and in the real world, the material covered by the current Tensor article is difficult and confusing for a lot of people, even without bringing in a bunch of calculus and other stuff needed for tensor fields. If we rewrote Tensor to be primarily about tensor fields, then I would want there to still be an article (maybe named Tensor at a point, but hopefully something much better!) that covers the current material well. Mgnbar (talk) 23:19, 23 December 2022 (UTC)

Tensors are algebraic entities in their own right: the name Tensor at a point is inappropriate for anything but tensors on the tangent space at a point of a differentiable manifold. Tensor (algebra) would be more appropriate. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:52, 25 December 2022 (UTC)

Under no circumstances should the Tensor article be changed to be primarily about tensor fields. Tensors are used in many contexts which are not "evaluate a tensor field at a point on a manifold" including in: functional analysis, abstract algebra, multilinear algebra, etc.

As much as physicists who don't know the proper words for mathematical objects might disagree, the notion of tensor field is different and secondary to the notion of tensor.

The two articles should be properly separated. Tazerenix (talk) 01:21, 24 December 2022 (UTC)

I believe that, despite the existence of a Tensor field article, Tensor is currently mostly about tensor fields, which I believe should be corrected. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:52, 25 December 2022 (UTC)

Your belief is one thing, the reality is another thing. The section Tensor#Definitition has 5 subsections, and only the last one is about tensor fields. In this section, a tensor field is defined as a function whose components are tensors, or equivalently as a tensor-valued function (so, a tensor field cannot be correctly defined without the primary concept of a tensor). So, tensor fields is a (very important) application of tensors, but there are other important applications that have nothing to do with tensor fields. One of these important applications is the use of the rank of a tensor in computational complexity theory, in particular for matrix multiplication. Another fundamental application of tensors, which is independent from any tensor field, is geometric algebra.

I do not know what supports your belief that "Tensor is currently mostly about tensor fields". Either, you have read only the article introduction, or the content of the introduction and the article are biased by the knowledge and the preferences of the authors of the article. In any case, the merge that you suggest is a mathematical nonsense. D.Lazard (talk) 14:44, 25 December 2022 (UTC)

The problem is that Tensor#applications et al give applications of Tensor fields. Also, your belief that I support a merge is bizarre, and, in fact, what I support is moving the tensor-field examples to Tensor field. I mention a merge only because it would be better than having two different articles giving examples of tensor fields; that's why I wrote cleanly separated. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:15, 25 December 2022 (UTC)

OK D.Lazard (talk) 21:26, 25 December 2022 (UTC)

better than having two different articles giving examples of tensor fields Why is this a problem? It seems entirely fine to me if both of these articles give examples of tensor fields, as long as the prose is clear about it. (The problem here IMO is the bullet list format for the "Other examples from physics" section, which is rigid and hard to modify or extend, makes it difficult to group different examples together or provide unified context, etc.) –jacobolus (t) 21:07, 27 December 2022 (UTC)

At a minimum, shouldn't the tensor article give substantially more examples of thensors than of tensor fields? --Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:14, 28 December 2022 (UTC)

Why don’t you add some more examples then? –jacobolus (t) 04:48, 29 December 2022 (UTC)

It seems to me that the origin of the notion of tensor is almost inextricably connected with tensor fields. The name "tensor" comes from the stress tensor in a substance, which is pretty much always going to be a field, and the first serious usages beyond that were in differential geometry and general relativity.

On the other hand the purely algebraic notion is hard to separate out as its own thing. As I understand it, an algebraic tensor is a linear transformation from a vector space to another vector space, particularly when the domain and range are tensor products of simpler spaces. We have articles on linear transformations and tensor products. Shouldn't the main content on algebraic tensors be at tensor product rather than at tensor? What is there really to say about algebraic tensors that wouldn't fit naturally at tensor product? --Trovatore (talk) 22:57, 2 January 2023 (UTC)

Tensor

@Alexmov: has been repeatedly vandalizing Tensor, replacing standard terminology with infantile expressions, e.g. "Multidimenional maps" with " M-way array". Please help. JRSpriggs (talk) 17:44, 22 December 2022 (UTC)

I'll keep an eye on Tensor and revert/warn/block as needed.

Perhaps a knowledgeable editor could review Multilinear principal component analysis as well; a recent edit by Alexmov removed 2k including several types/applications of MPCA.

CRGreathouse (t | c) 18:31, 22 December 2022 (UTC)

It's counterproductive to refer to well-intentioned edits as vandalism (even when, as here, they are obvious disimprovements). --JBL (talk) 22:10, 22 December 2022 (UTC)

Pinging @JayBeeEll: @JRSpriggs:@CRGreathouse::

@JRSpriggs: is vandelising well informed corrections to Tensor, and gaslighting everyone by decreeing those corrections as vandelism or juvenille without any evidence or argument. I've explained that "Multidimensional arrays" are an informal terminology that refers to multi-way array or M-way arrays. Using Profesor Scrotum's terminolgy to which JRSpriggs reverts creates confusion. For example, saying that a 3 dimensional vector is a 1 dimensional array with 3 dimensions creates confusion. Do you see the problem with this informal terminology? Please help. Alexmov (talk) 17:44, 22 December 2022 (UTC)

Pinging @JayBeeEll: @JRSpriggs:@CRGreathouse:

These are not disimprovements. They are correct and well-established terminpology in CS/ML. See

• J.B. Kruskal. Rank, decomposition, and uniqueness for 3-way and n-way arrays. In R. Coppi and S. Bolasco, editors, Multiway Data Analysis, pages 7–18, Amsterdam, 1989. North Holland.
• DeLathauwer etal or https://alterlab.org/teaching/BME6780/papers+patents/De_Lathauwer_2000.pdf
• Kolda and Bader, https://www.kolda.net/publication/TensorReview.pdf

The terminology dimensionality, order and mode are closely related but refer to different properties.

In CS/ML, the information of a 3 dimensional vector is stored (as opposed to represented) in a 1-way array data structure with 3 dimensions. Saying that 3 dimensional vecor is a 1 dimensional array with 3 dimensions or even 3 number creates unnecessary confusion. Here is an example of the words order, mode and dimension used for tensors and the words M-way and dimension used for arrays:

• The information of a 3rd order tensor, ${\mathcal {A}}$, of dimensionality $I_{1}\times I_{2}\times I_{3}$ is stored in 3-way array array with the same dimensions. The dimensionality of the 2nd mode of the third-order tensor ${\mathcal {A}}$ is $I_{2}$.
• The word rank in physics was normally used to refer to the order of a tensor, but it is my understanding that rank is being used in physics the same way it is being used in mathematics.

Alexmov (talk) 18:34, 22 December 2022 (UTC)

My view is that the CS/ML usages are not what the main tensor article is or should be mostly about, and those fields should not unduly influence the terminology. It's a convenient word for computer scientists but it's not exactly the same concept. A tensor is not an array; it's a linear transformation between vector spaces that don't necessarily have a preferred basis. We should emphasize the "coordinate-free" approach, and I don't quite see how that applies to ML; in my limited experience ML models have a coordinate system defined by the problem. --Trovatore (talk) 22:43, 23 December 2022 (UTC)

I agree with you 100%!!! JRSpriggs completely misrepresented the edit I was trying to make. Alexmov (talk) 20:25, 1 January 2023 (UTC)

CS/ML was a "slip of the toungue", I meant computational mathematics. I used articles from statistics, psychometrics, economerics and chemometrics that go back to 1960s to substantiate the terminology change. Alexmov (talk) 23:49, 2 January 2023 (UTC)

Just because computer scientists discovered the concept of a tensor in the last 10 years and invented all their own names for the terminology doesn't mean we should go rewrite a century of mathematical language to use their new words. Tazerenix (talk) 01:18, 24 December 2022 (UTC)

I was referring to about 40+ years worth of in statistics, psychometrics, economerics and chemometrics. CS/ML was a "slip of he toungue", I meant computational mathematics. Alexmov (talk) 12:44, 1 January 2023 (UTC)

Your statement does not address the issue under discussion. The second sentence in the section called Multidimensional Array is using the phrase "a vector in an n-dimensional space is represented by a one-dimensional array with n components" uses two discrepant definitions of the word dimensional. I argue that it needs to be edited and I had suggested a compromise similar to the one used in Kruskal's work which uses replace "multidimensional array" with "multiway array (multidimensional array)".

• (4326 citations) Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31(3), 279–311. https://doi.org/10.1007/BF02289464
• (1815 citations) Joseph B. Kruskal, (1977) Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics, Linear Algebra and its Applications, Volume 18, Issue 2, 1977, Pages 95-138,ISSN 0024-3795, https://doi.org/10.1016/0024-3795(77)90069-6

Alexmov (talk) 12:57, 1 January 2023 (UTC)

Multidimensional arrays are useful things. Basis-free tensors are also useful things. But they are not the same thing, and the mathematical tensor article should not be converted into something about multidimensional arrays by editors who do not appreciate the distinction. —David Eppstein (talk) 05:40, 25 December 2022 (UTC)

Your statement does not address the issue under discussion.

The second sentence in the section called Multidimensional Array is using the phrase "a vector in an n-dimensional space is represented by a one-dimensional array with n components" uses two different definitions of the word dimensional. Mgnbar thought that it needs to be edited. I suggested a compromise similar to the one used in Kruskal's work which uses replace "multidimensional array" with "multiway array (multidimensional array)".

• (4326 citations) Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31(3), 279–311. https://doi.org/10.1007/BF02289464
• (1815 citations) Joseph B. Kruskal, (1977) Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics, Linear Algebra and its Applications, Volume 18, Issue 2, 1977, Pages 95-138,ISSN 0024-3795, https://doi.org/10.1016/0024-3795(77)90069-6

Alexmov (talk) 12:51, 1 January 2023 (UTC)

I have edited the article, and, now, the two meanings of "dimension" are linked. D.Lazard (talk) 13:08, 1 January 2023 (UTC)

To be clear JRSpriggs has misrepresented the edit I was trying to make to the second sentence in the Multidimensional Array Section.

• In statistics, psychometrics, econometrics, and chemometrics, which have been working on tensor factor analysis since the 1960s, the term "multidimensional array" was deprecated in favor of the term "multiway array" since it clashes with the traditional mathematical meaning of multidimensional. At one point, I suggested Kruskal's compromise which could fix the dual use of the word dimensional and keeps both terms. Six (6) instances of "multidimensional array" could be replaced with "multiway array (multidimensional array)". Thus, deprecating the term multidimensional. Alexmov (talk) 19:52, 1 January 2023 (UTC)

Poincaré lemma

Hi all,

I don't know if this matter has been discussed before (if so, let me know) but I am thinking of splitting off the materials on Poincaré lemma from Closed and exact differential forms to its own article. I think the result is important enough for a separate article. Also, it is a bit awkward to have a discussion of relative Poincare lemma or del-bar Poincare lemma (Grothendieck?) in the closed and exact article. What do the others think? If there is no objection, I will carry out the splitting. -- Taku (talk) 14:04, 8 January 2023 (UTC)

I agree it should probably be its own article. Tazerenix (talk) 20:46, 8 January 2023 (UTC)

It's certainly important historically, but in the context of Homology theory it's a trivial result, since De Rham cohomology satisfies the Eilenberg–Steenrod axioms and an open ball in Rⁿ is simply connected. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:51, 9 January 2023 (UTC)

The result is certainly not trivial. It is required to prove that de Rham satisfies the axioms in the first place. Axioms/universal properties do not specify existence!! Tazerenix (talk) 23:06, 10 January 2023 (UTC)

References

Well, it still requires that we prove the homotopy invariance of de Rham cohomology (to know the axioms are satisfied). That basically amounts to proving Poincaré lemma, since a typical proof is a proof of the homotopy invariance by constructing a homotopy operator (e.g., by integration along fibers.) —- Taku (talk) 10:07, 10 January 2023 (UTC)

Twice more

Would a few of you please check User:WhatamIdoing/Sandbox 3 (permalink) and comment here if anything needs to be fixed? I hope this will help editors who are trying to figure out whether "doubling" is the same as "a 200% increase". WhatamIdoing (talk) 04:02, 12 January 2023 (UTC)

It is better for everyone to avoid this kind of ambiguity in Wiki articles, because there are many readers who will be confused and interpret it to mean the wrong thing. –jacobolus (t) 04:21, 12 January 2023 (UTC)

By the way, this is not the best venue for this question. You may want to try Wikipedia:Reference desk/Mathematics instead. –jacobolus (t) 04:25, 12 January 2023 (UTC)

Question about volume

I'm trying to improve this very-broad but extremely important article about the volume, that volume with liters. While at least I have a clue on how to improve the history and measurement section, I have absolutely no idea on how to rewrite the calculation section to make it more encyclopedic. Do you have any ideas on how to do so? CactiStaccingCrane (talk) 13:26, 12 January 2023 (UTC)

I suggest removing the formulae of volumes of geometric shapes. There is already a link to List of formulas in elementary geometry and each shape has its own article anyway — Martin (MSGJ · talk) 14:16, 12 January 2023 (UTC)

@MSGJ Done, and I've moved the image montage to that list instead. CactiStaccingCrane (talk) 14:40, 12 January 2023 (UTC)

This seems like a regression. Calculating the volume of various shapes seems entirely in scope for the article as it stands (though perhaps a separate volume (mathematics) article would be helpful. The page List of formulas in elementary geometry is frankly terrible, with very unclear purpose and scope. –jacobolus (t) 18:38, 12 January 2023 (UTC)

Would mension of Measure theory be TMI? --Shmuel (Seymour J.) Metz Username:Chatul (talk) 19:51, 12 January 2023 (UTC)

RD nomination for Yuri Manin

In case anyone here is interested: Wikipedia:In the news/Candidates#RD: Yuri Manin. — MarkH₂₁^talk 22:20, 12 January 2023 (UTC)

Also, Wikipedia:In the news/Candidates#RD:Mikio Sato. Mikio Sato might benefit from the attention of more algebraic analysis sources. — MarkH₂₁^talk 15:45, 14 January 2023 (UTC)

Regarding lists of properties/examples in mathematics articles

I have a disagreement with editor Mgkrupa regarding the article Dense-in-itself, but it's a more general issue actually. In the previous version (https://en.wikipedia.org/w/index.php?title=Dense-in-itself&oldid=1131194770) the list of properties were presented in a bullet format. Mgkrupa changed it to this (https://en.wikipedia.org/w/index.php?title=Dense-in-itself&oldid=1132822549), which I have since reverted. His comment was " Reorganized, reworded, and copy editing". Apart from the fact that I don't agree with his particular reorganization of the topics in the article, which we can ignore here, I'd like to focus on the use of lists here. Mgkrupa says in Talk:Dense-in-itself that bullet lists are not encyclopedic and goes against Wikipedia's manual of style, and that it violates MOS:LISTBULLET and Wikipedia:Manual of Style/Lists.

I'd like to ask guidance from the community on this topic. In many articles (in topology for example, which I am more familiar with: Baire space, Countably compact space, etc) we need to present a list of properties or examples, mostly independent of each other, and each of them one line with maybe an accompanying reference. In my opinion, presenting lists of properties/examples in such a context with a bullet list makes it more readable, not less. It allows to scan down the list and quickly find what one is interested in. Compare with Mgkrupa's change above where most of the properties were lumped into a single paragraph, where one now needs to parse a whole paragraph in detail to find something. I am also not saying that we should use bullet lists everywhere. If some properties/examples are more involved and necessitate more explanation, having a separate paragraph for each is perfectly fine. Would appreciate reading other people's opinion. PatrickR2 (talk) 02:26, 12 January 2023 (UTC)

Wikipedia is a large and heterogeneous enough place that you aren't going to find agreement about a subject like this. Personally I think bullet lists should be avoided in this kind of situation. In my view bullet lists are best as either (a) directly encoding something that is obviously a collection of (small) homogeneous items where there is little chance any of the specific items needs additional commentary or expansion, or (b) a temporary lazy placeholder on the way to a proper write-up in prose, to be abandoned at the earliest convenience.

I strongly dislike lists of properties (and similar situations) because once started they are almost impossible to displace as a means of organization and difficult to extend or reorganize without doing a complete rewrite. Very often the elements of a seemingly disparate list of trivia turn out to have some kind of internal interrelationships, groups with shared context, variation in size/complexity, and so on, but these either don't get added because they don't fit in the list format, or they get encoded awkwardly e.g. by adding extra bullets that don't actually belong on equal footing with the rest, adding additional levels of hierarchy, including material in only one bullet that properly belongs in multiple, or redundantly duplicating the same material across multiple bullets. From a technical perspective I dislike mediawiki markup lists (from asterisks) because adding block quotations, block formulas, images, etc. doesn't really work very well with them, requiring various obscure and finicky workarounds.

By comparison, sections, paragraphs and sentences are extremely malleable and can fit whatever narrative structure is appropriate for the content.

On the flip side, one advantage that grab-bag bullet lists do have is that they make it very easy for people to throw extra items into the end of the list without thinking very hard. But this is a mixed blessing, as it can lead to a bloated disorganized mess. –jacobolus (t) 03:21, 12 January 2023 (UTC)

I am well aware of your points, and am personally very careful to avoid the lists of pitfalls you mention when I edit an article that I care about, listing the items in a logically reasonable progression as much as possible, avoiding redundancies, etc, etc. And yes, as you mentioned, not everybody is so careful and it is easy to misuse. But I stand by my point in the particular instances I have listed, that it makes it a lot easier to find information in those contexts. You can also find a disorganized mess, full of redundancies, trivia added in a haphazard way, etc when using paragraphs if people are not careful (I have seen it and could point to examples if necessary). For example, are you really advocating to get rid of the bullets in the Baire space article and replace them with a separate paragraph for each bullet? I am not convinced that would be an improvement. PatrickR2 (talk) 06:54, 12 January 2023 (UTC)

The Baire space article dramatically overuses bullet lists (more or less consists entirely of bullet lists), but since it’s not that far removed from a stub (the "start" class assessment seems fair), I would consider the lists to be more or less placeholders until someone comes along who wants to expand it into a more fully fleshed article with a more reader-friendly narrative structure.

The article currently doesn’t provide much motivation, history, or context, and is so technical that it is almost completely inaccessible to someone who isn’t already a mathematical expert. The individual bullet list items are bare-bones factual statements without explaining why anyone thought those were interesting things to investigate or why anyone should care. They aren’t organized or structured in any way, even though there are surely natural groupings and relationships between them.

The current list-heavy format in my opinion makes it hard to expand or reorganize those sections without doing a complete rewrite, but if someone knows a lot and cares about Baire spaces they should still give it a shot. Personally I am not very knowledgeable about or interested in this subject, so I’ll stay out of it.

YMMV. –jacobolus (t) 07:48, 12 January 2023 (UTC)

To me, a bulleted list like the one currently in dense-in-itself is an outline for how an article should be structured, but is not in itself something that should be considered part of a finished article. Bulleted lists can be used in more-complete articles, but only sparingly; it is not a good idea to have a section that consists only of a bulleted list, and bulleted lists work better when the bullets themselves are more fleshed out rather than bare factoids. MOS:USEPROSE is good advice. As for Baire space, the numbered list in the "definitions" section looks ok to me, but would be better as a bulleted list because the numbers are meaningless: it gives a list of alternatives to be compared to each other that would be too cumbersome to fit into a single sentence. However, the organization of "properties" and "examples" as long undigested lists of bullets is just bad. Find some way of grouping these into related subsets of properties and examples and make a prose paragraph for each subset.

To put it more briefly: Bulleted lists are a good way of formatting multiple things that are explicitly supposed to be parallel to each other, like the multiple equivalent definitions in Baire space. They are not a good way of organizing a non-parallel sequence of disconnected ideas, like the instance in dense-in-itself and the definitions and examples sections of Baire space. —David Eppstein (talk) 08:31, 12 January 2023 (UTC)

FYI, don't confuse Baire space, which is a more specialized topic of less interest to a general public, with the article Baire category theorem, which contains more motivation and applications to other fields of mathematics. For those who care about these things, the Baire space article has a lot of information specifically about that, all backed up with references, which anyone interested can use to dig further. And if they don't care about the topic, that's does not hurt anyone. PatrickR2 (talk) 08:43, 12 January 2023 (UTC)

Quoting PatrickR2:

"when I edit an article that I care about, listing the items in a logically reasonable progression as much as possible"

In at least some (but not all) instances, PatrickR2 and I fundamentally disagree on whether or not a list is appropriate. Consider the article "Separated sets" for instance. On 12 January 2023, PatrickR2 started the following discussion in its talk page Talk:Separated sets:

"Why did you change the staggered formatting of the various properties in the Definitions section? It was really nice to visually indicate that each property was a strengthening of the previous ones."

The staggered format that PatrickR2 was referring is the can be found in the 6 February 2022 version of that article. I've reproduced below a truncated version of the relevant part:

There are various ways in which two subsets of a topological space X can be considered to be separated.

• A and B are disjoint if their [...]
  • A and B are separated in X if each is [...]
  • A and B are separated by neighbourhoods if there are [...]
    • A and B are separated by closed neighbourhoods if there is a [...]
      • A and B are separated by a function if there exists [...]
        • A and B are precisely separated by a function if there exists [...]

/endquote Now, the list above is indeed ordered "in a logically reasonable progression" but I consider that "staggered" format inappropriate for any Wikipedia article and so I "flattened it" to this (I think that the bullet points need to be gotten rid of entirely and turned into paragraphs but that'll have to wait for a future edit). In that discussion, I stated that bullet lists are "not encyclopedic and goes against Wikipedia's manual of style" (I also said this in Talk:Dense-in-itself) Patrick disagreed, stating that

"If it was a regular bullet list, I would agree with you. But the previous layout was more than a simple list. It was also intuitively conveying in a visual manner the relationship between the properties."

I fundamentally disagree (side note: this was not always the case though since for a long time, I would frequently make lists; I stopped after being told to/why and I'm glad that I did because I've since found that avoiding lists has forced an improvement in the quality of my contributions). This disagreement has spread to several articles so far (Nowhere dense set, Dense-in-itself, and Separated sets). I don't want it have this conversation over and over again so I too would like to know where the community stands on this issue. Mgkrupa 21:02, 12 January 2023 (UTC)

Perhaps the logical relationships between the different ways sets can be separated might be indicated with a diagram instead of a hierarchical bullet list. –jacobolus (t) 18:01, 13 January 2023 (UTC)

I agree strongly with Mgkrupa in the particular instance of Separated sets. I just took 5 minutes to convert the first bullet point into prose (it was not terribly difficult). I also agree with jacobolus that these containment relations are well suited to being represented by a diagram. --JBL (talk) 19:25, 13 January 2023 (UTC)

Now I've done half of them (also adding one citation, and tweaking for MOS:MATH#TONE). Someone with more than one topology textbook on their shelf (i.e., not me) should be able to finish easily, I would think. --JBL (talk) 20:12, 13 January 2023 (UTC)

I have removed the remaining bullets. Also added a sentence at the top saying that various properties are presented in increasing order, each stronger than the previous one, so there should be no need for an extra diagram. (In addition, the point that each property is stronger than the previous one was already reiterated in every paragraph anyway.) PatrickR2 (talk) 19:44, 14 January 2023 (UTC)

Thank you! --JBL (talk) 00:51, 16 January 2023 (UTC)

Already much better! Mgkrupa 00:19, 18 January 2023 (UTC)

Thanks for the feedback. I'll make some changes to the Baire space article. PatrickR2 (talk) 20:42, 12 January 2023 (UTC)

Dispute resolution: Monty Hall problem proof

There's a dispute at the Monty Hall problem article about how best to present a proof solving the problem using Bayesian statistics. We're hoping interested editors can help us decide between two options. Thank you. GabeTucker (talk) 18:29, 19 January 2023 (UTC)

Hello

Hello, I am an Iranian. I am fluent in languages ​​such as English-Arabic. I can improve many articles. I want to contribute to this project. How is the working environment of this project? Mohammad.Hosein.J.Shia (talk) 10:06, 20 January 2023 (UTC)

The answer is in User talk:Mohammad.Hosein.J.Shia#Welcome. D.Lazard (talk) 14:19, 20 January 2023 (UTC)

Welcome. Take a peek at WP:MOS, start making small changes and progress to larger changes as you get more comfortable with the tools and customs. Don't be afraid to ask for help should you feel the need. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:03, 20 January 2023 (UTC)

Unreviewed Featured articles year-end summary

Restoring older Featured articles to standard:

year-end 2022 summary

Unreviewed featured articles/2020 (URFA/2020) is a systematic approach to reviewing older Featured articles (FAs) to ensure they still meet the FA standards. A January 2022 Signpost article called "Forgotten Featured" explored the effort.

Progress is recorded at the monthly stats page. Through 2022, with 4,526 very old (from the 2004–2009 period) and old (2010–2015) FAs initially needing review:

• 357 FAs were delisted at Featured article review (FAR).
• 222 FAs were kept at FAR or deemed "satisfactory" by three URFA reviewers, with hundreds more being marked as "satisfactory", but awaiting three reviews.
• FAs needing review were reduced from 77% of total FAs at the end of 2020 to 64% at the end of 2022.

Of the FAs kept, deemed satisfactory by three reviewers, or delisted, about 60% had prior review between 2004 and 2007; another 20% dated to the period from 2008–2009; and another 20% to 2010–2015. Roughly two-thirds of the old FAs reviewed have retained FA status or been marked "satisfactory", while two-thirds of the very old FAs have been defeatured.

Entering its third year, URFA is working to help maintain FA standards; FAs are being restored not only via FAR, but also via improvements initiated after articles are reviewed and talk pages are noticed. Since the Featured Article Save Award (FASA) was added to the FAR process a year ago, 38 FAs were restored to FA status by editors other than the original FAC nominator. Ten FAs restored to status have been listed at WP:MILLION, recognizing articles with annual readership over a million pageviews, and many have been rerun as Today's featured article, helping increase mainpage diversity.

Examples of 2022 "FAR saves" of very old featured articles

Solar System 2007 FA J. K. Rowling 2007 FA June 26, 2022 TFA Antarctica 2006 FA Joan of Arc 2006 FA Speed of light 2010 FA

All received a Million Award

But there remain almost 4,000 old and very old FAs to be reviewed. Some topic areas and WikiProjects have been more proactive than others in restoring or maintaining their old FAs. As seen in the chart below, the following have very high ratios of FAs kept to those delisted (ordered from highest ratio):

• Biology
• Physics and astronomy
• Warfare
• Video gaming

and others have a good ratio of kept to delisted FAs:

• Literature and theatre
• Engineering and technology
• Religion, mysticism and mythology
• Media
• Geology and geophysics

... so kudos to those editors who pitched in to help maintain older FAs !

FAs reviewed at URFA/2020 through 2022 by content area

FAs reviewed at URFA/2020 from November 21, 2020 to December 31, 2022 (VO, O) Topic area Delisted Kept Total Reviewed Ratio Kept to Delisted (overall 0.62) Remaining to review for 2004–7 promotions Art, architecture and archaeology 10 6 16 0.60 19 Biology 13 41 54 3.15 67 Business, economics and finance 6 1 7 0.17 2 Chemistry and mineralogy 2 1 3 0.50 7 Computing 4 1 5 0.25 0 Culture and society 9 1 10 0.11 8 Education 22 1 23 0.05 3 Engineering and technology 3 3 6 1.00 5 Food and drink 2 0 2 0.00 3 Geography and places 40 6 46 0.15 22 Geology and geophysics 3 2 5 0.67 1 Health and medicine 8 3 11 0.38 5 Heraldry, honors, and vexillology 11 1 12 0.09 6 History 27 14 41 0.52 38 Language and linguistics 3 0 3 0.00 3 Law 11 1 12 0.09 3 Literature and theatre 13 14 27 1.08 24 Mathematics 1 2 3 2.00 3 Media 14 10 24 0.71 40 Meteorology 15 6 21 0.40 31 Music 27 8 35 0.30 55 Philosophy and psychology 0 1 1 – 2 Physics and astronomy 3 7 10 2.33 24 Politics and government 19 4 23 0.21 9 Religion, mysticism and mythology 14 14 28 1.00 8 Royalty and nobility 10 6 16 0.60 44 Sport and recreation 32 12 44 0.38 39 Transport 8 2 10 0.25 11 Video gaming 3 5 8 1.67 23 Warfare 26 49 75 1.88 31 Total 359 Note A 222 Note B 581 0.62 536 Noting some minor differences in tallies: A URFA/2020 archives show 357, which does not include those delisted which were featured after 2015; FAR archives show 358, so tally is off by at least one, not worth looking for. B FAR archives show 63 kept at FAR since URFA started at end of Nov 2020. URFA/2020 shows 61 Kept at FAR, meaning two kept were outside of scope of URFA/2020. Total URFA/2020 Keeps (Kept at FAR plus those with three Satisfactory marks) is 150 + 72 = 222.

But looking only at the oldest FAs (from the 2004–2007 period), there are 12 content areas with more than 20 FAs still needing review: Biology, Music, Royalty and nobility, Media, Sport and recreation, History, Warfare, Meteorology, Physics and astronomy, Literature and theatre, Video gaming, and Geography and places. In the coming weeks, URFA/2020 editors will be posting lists to individual WikiProjects with the goal of getting these oldest-of-the-old FAs reviewed during 2023.

Ideas for how you can help are listed below and at the Signpost article.

• Review a 2004 to 2007 FA. With three "Satisfactory" marks, article can be moved to the FAR not needed section.
• Review "your" articles: Did you nominate a featured article between 2004 and 2015 that you have continuously maintained? Check these articles, update as needed, and mark them as 'Satisfactory' at URFA/2020. A continuously maintained FA is a good predictor that standards are still met, and with two more "Satisfactory" marks, "your" articles can be listed as "FAR not needed". If they no longer meet the FA standards, please begin the FAR process by posting your concerns on the article's talk page.
• Review articles that already have one "Satisfactory" mark: more FAs can be indicated as "FAR not needed" if other reviewers will have a look at those already indicated as maintained by the original nominator. If you find issues, you can enter them at the talk page.
• Fix an existing featured article: Choose an article at URFA/2020 or FAR and bring it back to FA standards. Enlist the help of the original nominator, frequent FA reviewers, WikiProjects listed on the talk page, or editors that have written similar topics. When the article returns to FA standards, please mark it as 'Satisfactory' at URFA/2020 or note your progress in the article's FAR.
• Review and nominate an article to FAR that has been 'noticed' of a FAR needed but issues raised on talk have not been addressed. Sometimes nominating at FAR draws additional editors to help improve the article that would otherwise not look at it.

More regular URFA and FAR reviewers will help assure that FAs continue to represent examples of Wikipedia's best work. If you have any questions or feedback, please visit Wikipedia talk:Unreviewed featured articles/2020/4Q2022.

FAs last reviewed from 2004 to 2007 of interest to this WikiProject

If you review an article on this list, please add commentary at the article talk page, with a section heading == [[URFA/2020]] review== and also add either Notes or Noticed to WP:URFA/2020A, per the instructions at WP:URFA/2020. Comments added here may be swept up in archives and lost, and more editors will see comments on article talk. SandyGeorgia (Talk) 21:29, 20 January 2023 (UTC)

1. 1 − 2 + 3 − 4 + ⋯
2. Archimedes
3. Georg Cantor

"Consider" is a command; Is this appropriate for an encyclopedia?

There are probably too many mathematical topics to fix this, but language such as this seems to violate WP:HOWTO.— Vchimpanzee • talk • contributions • 22:39, 2 January 2023 (UTC)

Can you point to an example? PatrickR2 (talk) 22:42, 2 January 2023 (UTC)

I was afraid you'd ask that. It's not in my history for some reason. Now I don't remember.— Vchimpanzee • talk • contributions • 22:53, 2 January 2023 (UTC)

There is a similar situation on Abel–Plana formula. "Let" is used at the beginning of a section. Is this acceptable?— Vchimpanzee • talk • contributions • 23:05, 2 January 2023 (UTC)

The section of the article titled Abel–Plana formula that begins with "Let" in fact begins with this:

Let $f$ be holomorphic on $\Re (z)\geq 0$, such that $f(0)=0$, $f(z)=O(|z|^{k})$ and for $\operatorname {arg} (z)\in (-\beta ,\beta )$, $f(z)=O(|z|^{-1-\delta })$.

That is obviously not anything at all like a "How to". To think that it is is to construe a standard and universally known figure of speech literally. The purpose of the word "let" is to specify the notational conventions used in the succeeding text and some of the hypotheses of the theorem whose conclusion will follow. Michael Hardy (talk) 01:03, 8 January 2023 (UTC)

MOS:MATH#TONE is the relevant style guideline, FWIW. --JBL (talk) 23:08, 2 January 2023 (UTC)

That seems to support a change, but there are probably a lot of places where this is wrong.— Vchimpanzee • talk • contributions • 23:17, 2 January 2023 (UTC)

Note that 'Let' and Consider that' are two of its examples, so obviously it is easy to see that they should be changed where seen and not if and only if each case has been debated! ;-) NadVolum (talk) 23:52, 2 January 2023 (UTC)

The examples given in MOS:MATH#TONE may describe an appropriate method for avoiding sentences like "Define X to be ..." in cases where the subsequent usage of X is simple enough that the definition can be crammed into the next sentence. But the effect of this replacement is to make sentences longer and more complicated, unnecessarily making them worse with regard to WP:TECHNICAL. This is worse when both the definition of X and the usage of it are themselves more complicated than the examples given. I think the cure is worse than the disease. To be concrete, here's an example from Malfatti circles, a Good Article.

• Current text: Given a triangle ABC and its three Malfatti circles, let D, E, and F be the points where two of the circles touch each other, opposite vertices A, B, and C respectively. Then the three lines AD, BE, and CF meet in a single triangle center known as the first Ajima–Malfatti point. (This is actually simplified from the actual text of the article, in which the second sentence is even longer.)
• Changed to match the examples in MOS:MATH#TONE: Given a triangle ABC and its three Malfatti circles, if D, E, and F are the points where two of the circles touch each other, opposite vertices A, B, and C respectively, then the three lines AD, BE, and CF meet in a single triangle center known as the first Ajima–Malfatti point.

That changed sentence is far too long and convoluted, and its overall structure is much harder to follow. Removing the imperative is not an improvement. Using a larger number of shorter sentences is usually better than avoiding imperative. There is nothing wrong with imperative sentences, and much wrong with blanket prohibitions against them. Additionally, this point of grammar has nothing to do with WP:NOTHOWTO, which is bad advice about never having content that describes algorithms rather than bad advice about never using imperative grammar. —David Eppstein (talk) 00:40, 3 January 2023 (UTC)

I 100% agree here with David Eppstein: the cure is far worse than the disease here, and the guidelines are misapplied or simply wrong. - CRGreathouse (t | c) 06:33, 3 January 2023 (UTC)

Can we get some kind of RFC started to amend MOS:MATH#TONE? Insisting on replacing language like "π is a mathematical constant" with language like "The letter π denotes a mathematical constant" seems like a recipe for boring, borderline unreadable prose. If anything, we should aim to do replacements in the opposite direction wherever possible. –jacobolus (t) 07:32, 3 January 2023 (UTC)

That example is intended to illustrate the principle that sentences should not begin with mathematical notation. That is a fine principle, that is observed in most math writing. It is almost totally independent of the "let"/"consider" issue that we are currently discussing. Mgnbar (talk) 08:33, 3 January 2023 (UTC)

Yeah I think the examples there are poor. For example, Let H be the corresponding subgroup of G. H is then finite. can be equally well fixed by rewriting it as Let H be the corresponding subgroup of G. Then H is finite. -- the problem has nothing to do with "let", and this is confused by the text. The others are similar. --JBL (talk) 19:59, 3 January 2023 (UTC)

No, this has nothing to do with WP:NOTHOWTO. This kind of construction is ubiquitous in mathematical writing, and is not at all the same as a recipe or instruction manual. –jacobolus (t) 07:26, 3 January 2023 (UTC)

I agree with this. --JBL (talk) 20:08, 3 January 2023 (UTC)

I agree entirely with you, and also with David Eppstein above. PatrickR2 (talk) 02:14, 4 January 2023 (UTC)

No, imperatives of the form "Let $N$ be an integer..." do not violate WP:NOTHOWTO. The imperative "Consider that..." is only poor form in so far as it can be superfluous syllables, like the often-eliminable "Note that...". XOR'easter (talk) 15:23, 3 January 2023 (UTC)

I'm glad I got the discussion started. I may have pointed to the wrong policy, but it seemed like these articles were violating something. Now that I see what others think, it may not be a problem.— Vchimpanzee • talk • contributions • 22:58, 3 January 2023 (UTC)

Mathematical writing necessarily involves introducing many new labels, definitions, notations, and structures, often as a hypothetical. There aren’t really any ways to do this that don’t end up sounding sort of forced/formal, and a bit awkward/unfamiliar to people who don’t commonly read mathematical writing. These imperative “Let ...” constructions come straight out of Euclid, and are if anything a way of removing a recipe-like action. Instead of saying “Draw an arbitrary triangle on your paper and label the vertices A, B, and C”, we invoke an abstract triangle out of thin air: “Let ABC be a triangle ...”. –jacobolus (t) 04:34, 4 January 2023 (UTC)

Currently, "Let" is a disambiguation page, but is there a page on wikipedia that explains "Let (mathematical topics)" ? --SilverMatsu (talk) 17:54, 22 January 2023 (UTC)

Let expression also discusses the mathematical grammatical use of "let". --{{u|Mark viking}} {Talk} 18:35, 22 January 2023 (UTC)

MOS:MATH

Pulling out something not related to this discussion: I think this old version of the relevant section was superior in many ways to the current version. (The major edits to that section were in this batch of edits by Magyar25, followed by the mid-section addition of a see-also template by Matthiaspaul.) I propose to revert the section on Writing style in mathematics to the earlier version. (I have not looked at the changes to other sections of MOS:MATH in the same batch of edits; hopefully they are better?) --JBL (talk) 20:06, 3 January 2023 (UTC)

That version may be better but they're both pretty bad IMO. A major rewrite is in order, if someone has the energy for it. - CRGreathouse (t | c) 14:45, 9 January 2023 (UTC)

"top priority" assessment in this wikiproject

This Wikiproject's priority/importance assessment seems to be somewhat variable/arbitrary. Has there been any effort by anyone to look through the lists of Top, High, and possibly Mid importance categories and figure out if they match anyone's gut feeling about relative importance of topics? As an example, here is the list of current "Top" importance mathematicians: Archimedes, Michael Atiyah, Georg Cantor, Shiing-Shen Chern, Paul Erdős, Euclid, Leonhard Euler, Kurt Gödel, Alexander Grothendieck, Jacques Hadamard, Felix Hausdorff, David Hilbert, Donald Knuth, Henri Lebesgue, Benoit Mandelbrot, James Clerk Maxwell, Isaac Newton, Henri Poincaré, Pythagoras, Srinivasa Ramanujan, Bernhard Riemann, Bertrand Russell, Jean-Pierre Serre, Alan Turing, Karl Weierstrass, André Weil. This seems to be a somewhat idiosyncratic list, missing many of the most famous and influential mathematicians in history and including some who seem to me to be less important.

I just added Carl Friedrich Gauss, René Descartes, Apollonius of Perga, Brahmagupta, John von Neumann, Aryabhata, Joseph-Louis Lagrange, Joseph Fourier, Gottfried Wilhelm Leibniz, Muhammad ibn Musa al-Khwarizmi, Emmy Noether, John Napier, Pierre de Fermat, Augustin-Louis Cauchy, Ptolemy, William Rowan Hamilton, Blaise Pascal, Andrey Kolmogorov, but I am sure there are many more who belong in this list that I am not thinking of off the top of my head. –jacobolus (t) 02:15, 22 January 2023 (UTC)

Perhaps the priority assessment for mathematicians should happen on a different scale to the assessment for mathematics pages? Of those mathematicians listed, how many of them could we really say are of an equal priority for presentation on the wikipedia as, say, Calculus or Manifold or Algebra? Not many: probably Euler, Euclid, Newton, Leibniz, and maybe a few others. I think compared to some of the top priority mathematical pages on the project, most of the mathematicians in top should really be ranked high, and some even mid.

I don't have much skin in the game really, but maybe a good heuristic is if the mathematician appears in the lead of a top priority mathematical article, we should consider them a top priority mathematician article? Tazerenix (talk) 02:57, 22 January 2023 (UTC)

I am demoting Knuth, Hadamard, and Atiyah to 'high' priority. –jacobolus (t) 05:00, 22 January 2023 (UTC)

I definitely think we have too many mathematicians at top priority. I would prefer to demote the vast majority to high. Maybe Gauss, Euclid, Euler, Brahmagupta, al-Khwarizmi as top and the rest to high. A few others, perhaps (Cauchy? Hilbert? Weierstrass?), but not many. - CRGreathouse (t | c) 07:02, 22 January 2023 (UTC)

There are thousands of articles about mathematicians on Wikipedia. It seems entirely fine to me if a few dozen of them are "top" priority. –jacobolus (t) 08:47, 22 January 2023 (UTC)

What about those who should be considered top priority in some other field but not in Mathematics, e.g., Donald Knuth? --Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:40, 22 January 2023 (UTC)

In practice, the "importance" ratings are not important. Hardly anyone is more likely to write about Fourier or less likely to write about Hadamard because their importance ratings have changed. —Kusma (talk) 13:38, 22 January 2023 (UTC)

My understanding is that they have accomplished a bit more at some other Wikiprojects, where there was a concerted effort to bring articles among the top couple levels of the importance scale up to “B” level or the like. There are many extremely influential mathematicians and many fundamental mathematical topics which currently have mediocre articles. Someone can click through to e.g. Top-importance C-class or High-importance Start-class articles to get some ideas for articles that are especially in need of care and attention. –jacobolus (t) 18:44, 22 January 2023 (UTC)

Invitation

Hello all, I would like to invite you to attend in Articles for deletion/Similarity-based-TOPSIS and submit your opinion. I know that this article is in the field of operations research but there is no project related to operations research. Thank you in advance. Scholartop (talk) 06:28, 23 January 2023 (UTC)

Harish Chandra Rajpoot links

The IP accounts Special:Contributions/103.21.125.84 and Special:Contributions/103.21.127.79 keep adding links to academia.edu and arXiv articles by Harish Chandra Rajpoot to the external links sections, e.g. to Trapezohedron, Great-circle distance, Solid angle, Descartes' theorem, Circle packing. My speculation is that these IPs are being used by Mr. Rajpoot himself (apparently a graduate student at IIT Bombay) to promote his papers here. I removed several of these links because, while relevant, the content raises some other red flags: Rajpoot's papers don't cite any prior sources and name known results after himself. I left a comment on his talk page suggesting he may want to try publishing his work in a peer-reviewed journal; in response he put back a new link, this time to the paper "HCR’S THEORY OF POLYGON 'Solid Angle Subtended By Any Polygonal Plane at Any Point in the Space'" "published" in the journal International Journal of Mathematics and Physical Sciences Research by "Research Publish Journals", which does not seem to be peer reviewed. Does someone else want to try to talk to this IP user and try to get them to engage in conversation? –jacobolus (t) 16:52, 26 January 2023 (UTC)

Including maths rating

I would gladly include {{maths rating}} in some other articles that almost contain mathematical topics. However, is it still allowed to include this template in articles that contain fewer mathematical subjects? I was considering that it could be possible to add it in Quasicrystal since it has fewer mathematical subjects, but most of this describes chemistry. I am not sure whether it would be appropriate for this project. Dedhert.Jr (talk) 12:45, 25 January 2023 (UTC)

I went ahead and added it to Quasicrystal. In general there doesn't seem to be any problem with putting partially mathematical topics into the math wikiproject. –jacobolus (t) 16:59, 26 January 2023 (UTC)

I see. Thank you. Dedhert.Jr (talk) 02:25, 27 January 2023 (UTC)

Discussion at Wikipedia:Village pump (idea lab) § Standardizing Mathematical Notation

 You are invited to join the discussion at Wikipedia:Village pump (idea lab) § Standardizing Mathematical Notation. CactiStaccingCrane 13:40, 29 January 2023 (UTC)

Feb 2023

BIT predicate

Over on BIT predicate, we have an IP editor who seems intent on cramming as much off-topic notation-heavy WP:TECHNICAL detail as possible into the history section. More eyes on this would be helpful. —David Eppstein (talk) 21:50, 28 January 2023 (UTC)

@David Eppstein: The Ackermann coding is already discussed in the history section. It is clearly not off-topic. Where else would such content go?

That aside, your combative behavior over this constructive edit (calling it an "attack" and talking about "hurting my feelings") has been disturbing. One expects more maturity from a professor. See WP:AGF and WP:PA. 2601:547:501:8F90:6D91:586F:CC4B:73D2 (talk) 21:59, 28 January 2023 (UTC)

Your edit has been reverted by multiple people now. If you think there are good reasons for it, please open a discussion on the talk page of BIT predicate first so a consensus can be reached on whether this belongs in the history section, or in another section, or should not be in the article at all. PatrickR2 (talk) 16:13, 29 January 2023 (UTC)

@PatrickR2: What do you mean by "multiple people"? Also, see WP:OWNERSHIP. 2601:547:501:8F90:75EF:C82F:5D9:1C9 (talk) 23:20, 29 January 2023 (UTC)

Multiple, as in more than one: David Eppstein and Russ Woodroofe have both reverted you. 128.164.177.55 (talk) 16:12, 30 January 2023 (UTC)

WP:OWNERSHIP doesn't mean that editors who care about specific pages can't make arguments for their preferred versions or ask other editors to go to the talk page and establish some consensus before making significant changes. To quote that page, "Even though editors can never 'own' an article, it is important to respect the work and ideas of your fellow contributors. Therefore, be cautious when removing or rewriting large amounts of content, particularly if this content was written by one editor; it is more effective to try to work with the editor than against them—even if you think they are acting as if they "own" the article. [...] In many cases, a core group of editors will have worked to build the article up to its present state and will revert edits that they find detrimental in order, they believe, to preserve the quality of the encyclopedia. Such reversion does not indicate an "ownership" problem [...] Where disagreement persists after such a reversion, the editor proposing the change should first take the matter to the talk page, without personal comments or accusations of ownership. In this way, the specifics of any change can be discussed with the editors who are familiar with the article, who are likewise expected to discuss the content civilly." –jacobolus (t) 02:26, 1 February 2023 (UTC)

about Delta invariant

I suggest moving this article to the drafts space. I think the subject of this article meets WP:GNG, but I don't think this article meets the criteria for a stub. I thought about moving this article to the draft space, but WP:DRAFTIFY said articles older than 90 days should not be draftified without prior consensus at AfD, so it seems necessary to discuss it first. If someone extends this article, I will withdraw this suggestion. thanks ! SilverMatsu (talk) 11:22, 31 January 2023 (UTC)

No need to draftify. The content of this article is essentially reduced to an implicit link to the definition given in another article. So, I'll redirect this article to the anchor that I have already added in that article. D.Lazard (talk) 12:06, 31 January 2023 (UTC)

 Done D.Lazard (talk) 12:34, 31 January 2023 (UTC)

I agree. Thank you ! --SilverMatsu (talk) 13:30, 31 January 2023 (UTC)

Just popping in to say that there is another notion of delta invariant in K-stability of Fano varieties (see K-stability_of_Fano_varieties#Delta_invariant) which is probably mildly more esoteric than the notion for curves. I'm not suggesting anyone do anything with this information but if the article Delta invariant was to return it could even be a disambiguation page. Tazerenix (talk) 01:37, 1 February 2023 (UTC)

Thank you for letting me know. I added Template:Redirect to the top of the section. If someone adds an explanation about another notion of delta invariant to wikipedia, I think that they will create separate articles for each notion, or add explanations to existing separate articles for each notion, so create a Dab page at that time I agree that there is a need.--SilverMatsu (talk) 03:42, 1 February 2023 (UTC)

Root of unity modulo n

I am not sure that this article is not ready to have its own. It has lack context and many things. Most of the texts, as I glanced at, especially in this part, use many second-person pronouns; however, MOS:YOU mentions that one should avoid such words. Because of these problems, would it be possible to merge it into Roots of unity? Dedhert.Jr (talk) 15:14, 3 February 2023 (UTC)

I have cleaned the lead up to understand the real content of the article. IMO, Root of unity modulo n, Primitive root modulo n and Carmichael function must be merged in a single article, which could be called Root of unity modulo n. D.Lazard (talk) 17:10, 3 February 2023 (UTC)

would it be possible to merge it into Roots of unity? No. --JBL (talk) 22:29, 3 February 2023 (UTC)

Discussion at Help talk:Citation Style 1§ Proposal: Add parameter |eudml=

 You are invited to join the discussion at Help talk:Citation Style 1§ Proposal: Add parameter |eudml=. Need advice on whether the European Digital Mathematics Library (Parameter |eudml=) meets WP:GNG. thanks ! SilverMatsu (talk) 07:06, 4 February 2023 (UTC)

what is a cantellated great icosahedron?

Ya got yer

• great icosahedron (regular)
• truncated great icosahedron
• great icosidodecahedron (rectified)
• truncated great stellated dodecahedron (degenerate)
• great stellated dodecahedron (regular)

But where are the cantellate (great rhombicosidodecahedron is something else) and the omnitruncate? Are they also degenerate? It would be good to note that somewhere. —Tamfang (talk) 05:39, 5 February 2023 (UTC)

This type of thread is better reserved for Wikipedia:Reference desk/Mathematics. Partofthemachine (talk) 05:42, 5 February 2023 (UTC)

I put it here because on Refdesk (with which I am better acquainted than with Projects) my last sentence is likely to provoke "that belongs on the relevant Talk page(s)." Because you ask nicely I'll try it there, omitting that sentence. —Tamfang (talk) 06:28, 5 February 2023 (UTC)

Project-independent quality assessments

See Wikipedia:Village pump (proposals)#Project-independent quality assessments. This proposes support for quality assessment at the article level, recorded in {{WikiProject banner shell}}, and inherited by the wikiproject banners. However, wikiprojects that prefer to use custom approaches to quality assessment can continue to do so. Aymatth2 (talk) 20:23, 6 February 2023 (UTC)

RfD requiring input

Input is requested at the RfD concerning the target of the redirect page Free term. 66.44.62.177 (talk) 01:13, 8 February 2023 (UTC)

Lead Sentence to Integral

I randomly came across this village pump that points at the lead sentence is... not hitting the mark. Its too complex for a novice, not useful to an expert, and generally not helpful. I would generally agree. Now I know I should be be bold and change it, but I am not sure how things have changed in the decade since I lasted edited math articles regularly. Here are my thoughts about the sentence, I thought I would see if there was any agreement before I tried changing anything. For reference the sentence currently is:

In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data

Here are my issues

• Assigning numbers to functions is both trying to be too technical and failing to be technically accurate. Its tip-toeing around integral as an operator, and what do you say to someone who said "Wait, you said a number and infinity is not a number, my calc prof said so but integrals can be infinite." or "You talk about displacement, isn't displacement a vector and not a number."
• in a way that describes I legitimately do know this means. Is way a reference way to linearity?
• displacement, area, volume, and other concepts feels like we are cramming too many applications in for a first sentence, we will get to all of these in a bit.
• combining if we are jumping to the hole infinitesimal thing, is there a reason not to at least say its a sum?
• infinitesimal is a term one typically only encounters in calculus or mathematical contexts that assume calculus. So most readers who understood this term would already know what an integral was.
• data the word is so generic its distracting, it makes me thing 'Am I working with functions and numbers or more general data?'

Does anyone else on the math project feel it needs a rewrite, or are we generally fine with it as it is? I bring this up here instead of the talk page of the article, because I came across it in the village pump, so I see it as a good community discussion.Thenub314 (talk) 21:55, 9 February 2023 (UTC)

What a terrible first sentence. Surely it is not hard to come up with something much better. Just as an example:

"In mathematics, an integral is a way of computing the area under a function, or more generally the volume under the graphs of functions of more than one variable. The region under the graph of a function may have an irregular shape (so that the familiar formula of area = base x height for regular shapes does not apply), and so integration uses the techniques of calculus and infinitesimals to compute areas and volumes."

Now that you have alerted WP:MATH to this, the discussion can be moved to the talk page. Tazerenix (talk) 21:56, 9 February 2023 (UTC)

This is not constructive, but: I notice that Integral was introduced as an example in that discussion as follows: For example, look at Mensural notation, a very technical and complex subject in music. ... Now look at Integral, which is a very basic concept in maths. I can't imagine trying to discuss this subject with someone who suffers from this degree of misunderstanding about technicality, complexity, and simplicity.

Separately, "the area under a function" is a no-go for many reasons. --JBL (talk) 23:37, 9 February 2023 (UTC)

I think that thinking "the area under a function" is a no-go is exactly what leads to an unreadable lead sentence. It captures 90% of the use case of integrals, and what they were originally invented for, and can easily be expanded upon in the next sentence or two. Tazerenix (talk) 00:51, 10 February 2023 (UTC)

"the area under a function" is a meaningless phrase. But also it is false that this is what they were originally invented for -- no one is or ever has been interested in computing areas under graphs of functions, that's a totally artificial framework that happens (miraculously!) to extend to allow one to compute interesting things. --JBL (talk) 18:09, 10 February 2023 (UTC)

An integral should be described off the bat as a continuous analog of a sum. –jacobolus (t) 02:36, 10 February 2023 (UTC)

"In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and other ways of measuring shapes." XOR'easter (talk) 12:37, 10 February 2023 (UTC)

It looks much better after your changes. Thanks for dealing with infinitesimal properly. I'd make the first sentence more general, e.g., In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, their generalizations, momenta and other physical quantities. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 17:08, 10 February 2023 (UTC)

This addition is much too physics-specific for my taste. It makes it look like integrals are only used for physical quantities. Many integrals are unphysical. Areas and volumes can be but are not always physical. —David Eppstein (talk) 17:44, 10 February 2023 (UTC)

For a concrete example, a cumulative distribution function in probability is not about summing a physical quantity over a geometrical shape. It might be better to say that an integral is used to sum up the continuous values of a function in some part of its domain. We could still offer physical examples such as position displacement as the integral of velocity for some duration or total mass as the integral of mass density in some region. –jacobolus (t) 19:15, 10 February 2023 (UTC)

I'm going to continue to not be constructive (sorry to all): "continuous" and "domain" are both jargon, and "sum up he continuous values of a function" does not sound to me like it could be deciphered by someone who didn't already know what it meant. An integral of velocity is a displacement (also jargon, sadly), not a position. --JBL (talk) 20:30, 10 February 2023 (UTC)

I agree with you that in articles with topics as fundamental as integral it is best to err in the direction of too chatty and novice-friendly than the other way. Ideally a non-technical reader should be able to read the first 2–3 sections and have at least a vague idea what concept is being defined and what its context is.

I think it's potentially fine to wiki-link terms like velocity, displacement (geometry), domain of a function (though that article's lead is too technical) or 'continuous' which many readers will have heard of before (though Wikipedia in general needs a much better basic explanation of what 'continuous' / 'continuum' means than provided at continuous function, linear continuum, list of continuity-related mathematical topics which redirects from Continuity (mathematics), etc.).

What kind of definition of integral would you propose that can be understood by a layperson such as a middle school student or a politician without being too imprecise for someone like a math undergraduate?

It’s also sometimes possible to take a couple of swings at definitions within the same article lead, aimed at different audiences. –jacobolus (t) 21:47, 10 February 2023 (UTC)

Silvanus Thompson says:

The great secret has already been revealed that this mysterious symbol ${\textstyle \int }$, which is after all only a long S, merely means “the sum of,” or “the sum of all such quantities as.” It therefore resembles that other symbol ${\textstyle \sum }$ (the Greek Sigma), which is also a sign of summation. There is this difference, however, in the practice of mathematical men as to the use of these signs, that while ${\textstyle \sum }$ is generally used to indicate the sum of a number of finite quantities, the integral sign ${\textstyle \int }$ is generally used to indicate the summing up of a vast number of small quantities of indefinitely minute magnitude, mere elements in fact, that go to make up the total required. Thus ${\textstyle \int dy=y}$, and ${\textstyle \int dx=x}$.

Any one can understand how the whole of anything can be conceived of as made up of a lot of little bits; and the smaller the bits the more of them there will be. Thus, a line one inch long may be conceived as made up of $10$ pieces, each ${\textstyle {\tfrac {1}{10}}}$ of an inch long; or of $100$ parts, each part being ${\textstyle {\tfrac {1}{100}}}$ of an inch long; or of ${\textstyle 1{,}000{,}000}$ parts, each of which is ${\textstyle {\tfrac {1}{1{,}000{,}000}}}$ of an inch long; or, pushing the thought to the limits of conceivability, it may be regarded as made up of an infinite number of elements each of which is infinitesimally small.

Yes, you will say, but what is the use of thinking of anything that way? Why not think of it straight off, as a whole? The simple reason is that there are a vast number of cases in which one cannot calculate the bigness of the thing as a whole without reckoning up the sum of a lot of small parts. The process of “integrating” is to enable us to calculate totals that otherwise we should be unable to estimate directly.

[...]

–jacobolus (t) 21:59, 10 February 2023 (UTC)

What kind of definition of integral would you propose that can be understood by a layperson such as a middle school student or a politician without being too imprecise for someone like a math undergraduate? I think this is an extremely difficult question; hence the labeling of my comments as non-constructive, the small font, and the apologies. --JBL (talk) 22:52, 11 February 2023 (UTC)

Clearly the answer is that the integral computes the area under the graph of a function? Tazerenix (talk) 23:17, 11 February 2023 (UTC)

What part of a circle is under its perimeter? XOR'easter (talk) 14:39, 12 February 2023 (UTC)

The whole disk is under the graph of the function f(x,y)=1 restricted to the disk.

Anyway, I didn't say the integral *only* computes the area under graphs of functions. But if our standard is what would a layperson or politican understand, you are all assuming way too much mathematical knowledge to think they can parse the sentence "The integral is the continuous analog of the sum" or "The integral sums up an infinite number of infinitesimal quantities" Tazerenix (talk) 20:33, 12 February 2023 (UTC)

If that meaning of "under the graph of the function" already makes sense, you're not learning what an integral is from Wikipedia. XOR'easter (talk) 14:36, 13 February 2023 (UTC)

That is a special case and wont cast much light on, e.g., ${\textstyle \iiint _{D}\mathbf {r} \times \mathbf {p} \,dx\,dy\,dz.}$ The first sentence should be general. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 22:02, 12 February 2023 (UTC)

Touché -- the difficult question is not a definition, but a first sentence of an encyclopedia article with the requested properties. --JBL (talk) 19:40, 13 February 2023 (UTC)

I suggests the following for the firat paragraph:

In mathematics, an integral is, roughly speaking, the sum of infinitely many quantities that are each infinitely small. For example, a surface in a plane can be divided into narrow strips whose areas are approximated by the product of their widths by their lengths; when the widths of the strips tend to zero, their areas tend each to zero, and their number tend to the infinity; the infinite sum of these infinitesimal areas form an integral equal to the area of the surface. Also, the distance traveled by a vehicle, is the product of the speed by the time of the travel; when the speed varies, one divides the time in smaller and smaller intervals. At the limit, the traveled distance is an integral that is the sum of the products of infinitively small time intervals by the instantaneous speed during each interval.

Integration is the process of computing an integral. It is, with differentiation, a fundamental operation of calculus, and is widely used in all mathematics, as well as in physics, and most sciences and technologies that use mathematics.

I have removed the notes and citations, which should be kept is this is accepted. Also, some more linkd should be added; however this must be done with care, as an informal explantion must not be overlinked.

Feel free to improve this draft.

IMO, such informal examples is the best way for explaining what is integration and why it is used almos everywhere. Clearly, if this is accepted, some more work is needed for the remainder of the lead and of the article. D.Lazard (talk) 16:02, 12 February 2023 (UTC)

I have painful memories of trying as a teenager to make sense of such language in "Calculus for the Practical Man", and I only started to understand Calculus when I read a copy of Thomas's Calculus and Analytic Geometry, loaned by a Jr. High teacher for me to read in class, which used Epsilontics. What about In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, their generalizations, momenta, other physical quantities, and more abstract physical or mathematical entities. It can be thought of non-rigorously the sum of infinitely many quantities that are each infinitely small. ...?? --Shmuel (Seymour J.) Metz Username:Chatul (talk) 22:02, 12 February 2023 (UTC)

Collapsed proofs: WP:ACCESSIBILITY concerns

Hello, a common method of organising mathematical proofs seems to be to place them inside {{collapse top}} and {{collapse bottom}}. This is specified in Wikipedia:WikiProject Mathematics/Proofs. However, this conflicts with two broader guidances Wikipedia:Manual of Style#Scrolling lists and collapsible content and Wikipedia:Accessibility. If there is some reason why the local consensus should override the sitewide consensus, I'd like to know. Otherwise, if this is an oversight, then does anyone have any alternatives that would be suitable? Pinging users who participated in the proceeding discussion on my talkpage: @DMacks and D.Lazard: Mako001 (C)  (T)  🇺🇦 04:54, 9 February 2023 (UTC)

I want to say: I don't like collapsed proofs either. For example, I noticed some people prefer to print out Wikipedia articles and then the print-out wouldn't contain collapsed materials. If it is desirable to hide proofs, for a better flow, for example, then a better solution is to put the proofs in the footnotes. -- Taku (talk) 07:49, 9 February 2023 (UTC)

It should be technically possible to implement this in such a way that a print stylesheet expands them automatically, though many readers may prefer to have proofs collapsed even when printing.

Putting long proofs in footnotes is not a good solution in practice. They are then detached from the content and hard to read. –jacobolus (t) 02:25, 10 February 2023 (UTC)

But putting them in {{collapse top}} and {{collapse bottom}} makes them impossible to read for many (if not most) readers (i.e. anyone using a mobile device). Setting all proofs to auto expand would "solve" the accessibility problem, but would make (for want of a better term) "a bit of a mess". Mako001 (C)  (T)  🇺🇦 11:34, 10 February 2023 (UTC)

I don't ever read Wikipedia on a mobile device, but I just navigated to Homomorphism#Epimorphism on my phone and the proof at the bottom of that section (intended to be collapsable and collapsed by default) shows up inline in the content not possible to collapse.

This seems like a problem; that content should be collapsed and only show when a reader tries to expand, and I would assume it would be the same on either desktop or mobile. Why can't the CSS/javascript be set up so that mobile devices can properly expand/collapse these sections? –jacobolus (t) 18:54, 10 February 2023 (UTC)

@Jacobolus: Hmm, I'm seeing the same thing. You would have to ask the WMF why the Minerva skin (mobile view) doesn't work with collapsible content properly. In any case, we need to focus on what we are able to do something about. Mako001 (C)  (T)  🇺🇦 01:50, 11 February 2023 (UTC)

Well, collapsing the proof usually makes the article more readable (unless the article itself is about the proof of something), especially if there are multiple proofs and each one is long. PatrickR2 (talk) 21:57, 9 February 2023 (UTC)

Proofs are in many cases irrelevant and distracting to most readers while still being helpful (or even indispensible) for readers who care about the details for one reason or another. Figuring out how to elide tedious or distracting details is a persistent problem that all mathematical writing must deal with. There are no perfect answers. Some possibilities, none of which will satisfy all authors or all readers: (1) skip proofs altogether but link to a source which includes them, (2) put proof sketches but leave out the details, (3) put proofs in a collapsing section, (4) put proofs in a footnote, (5) put proofs in a floating box to the margin of the main content, (6) put full proofs inline in the text. I think local per-page consensus is probably better to aim for than a blanket site-wide policy. One more thing to notice: Wikipedia mobile rendering by default collapses article sections, and readers must tap to expand them; so collapsing elements are clearly not entirely anathema to Wikipedia. –jacobolus (t) 02:30, 10 February 2023 (UTC)

Sure, there is no perfect solution. In fact, solutions probably would depend on articles. I would however say: if the proofs are irrelevant, those proofs should not be in the article in the first place. Unlike research papers or monographs, in Wikipedia, we don’t need to justify the results with proofs; references to the reliable sources would do. If the proofs are relevant, they don’t need to be hidden. It’s actually the matter of why we put proofs in the first place. The reason is that proofs are integral parts of mathematics. It’s sometimes important to know how some facts are true not just if they are true. —- Taku (talk) 05:53, 10 February 2023 (UTC)

There is no absolute standard by which we can decide what is "irrelevant". Wikipedia needs to serve a very wide range of audiences, ranging from members of the general public who have a curiosity about some topic's basic definition and context, through students who are trying to learn about something for the first time and don't yet understand the details, through practitioners in related fields who want a quick reference of concrete results they can use, through historians who want to know the evolution of an idea with numerous citations and experts who want to read generalizations and relations to more advanced topics.

The problem with proofs (though other kinds of technical content have similar issues, such as large tables of statistical data, detailed timelines, code samples for complicated algorithms, details of chemistry experiments, or full phylogenetic trees) is that they are both necessary to make convincing mathematical arguments, while also being difficult to skim (especially for non experts) and taking significant effort to fully comprehend. If non-specialists hit a wall of formulas or a detailed proof they are likely to be intimidated, discouraged, or bored, and at worst bounce away even if they might be interested in other parts of the page; by contrast, if specialists can’t see a proof they will be unable to fully validate the claims made, and if students can’t see proofs they may develop a false conception about whether/why something is true and what is needed to demonstrate that.

The point of collapsing the proofs is that it is effectively the same as removing them for that part of the audience who wants to skim past or ignore them, except they can still be seen for that part of the audience who is interested.

Not every mathematical claim needs to be proven in an encyclopedia article (probably most don’t), but personally I think there are many pages that would benefit from including a few more (collapsed) proofs of statements that are currently just stated. YMMV. –jacobolus (t) 06:27, 10 February 2023 (UTC)

So, suggestion: When using {{refn}}, you can give a footnote a name, like "Proof", which displays in the article like this . This would make it clear where the proof is, leave it acessible to all readers, but still move it out of the way. Would this work? Mako001 (C)  (T)  🇺🇦 11:27, 10 February 2023 (UTC)

There are different reasons for including or not a proof in Wikipedia. Proofs deserve to be included when they provide insights on a result and the involved concept; in this case, they must be given is plain text and not collapsed. On the other hand, a long techncal proof may have no encyclopedic value if a reference for it is provided.

I see several reasons for providing proofs that are not included in the flow of the text, which are related to WP:Verifiability and WP:LEAST. In many articles, properties or formulas are presented as bulleted lists (for example, List of integrals#Integrals of simple functions and Heronian triangle#Properties of side lengths). In this case, per WP:Verifiability, as source is normally provided for each item. This is rarely done, and when it is done, it is boring for the reader to get access to many sources. So, providing a proof allows readers to verify the assertions without searching in the literature. Also, in some cases, some of the listed properties may appear as "magic", and some readers may want to understand why they are true without accessing the provided source. In both cases, putting the proof in an explanatory footnote seems the best solution. An example of this is Heronian triangle#Properties of side lengths, where I have added such footnotes because I was too lazy for searching the sources.

In my opinion, the cases where collapsed proof are the best solution are rare. The main case is for a rather long proof that is too technical for the article that contain it, and for which a single and not too technical source is hardly to find. I have encountered this in Homomorphism#Monomorphism and Homomorphism#Epimorphism. In particular, in the latter section, the sentence the two definitions of epimorphism are equivalent for sets, vector spaces, abelian groups, modules (see below for a proof), and groups requires verifiability, and I do not know any source that does not requires a good knowledge of category theory. This the reason for which I have added a proof in a collapsed box (at the end of the section, for not breaking the flow).

In summary, for a guideline, I recommend something like For a proof that, otherwise, would break the flow of reading, use a footnote, and reserves collapsed boxes at the end of the section for exceptional cases. — Preceding unsigned comment added by D.Lazard (talk • contribs)

It is my understanding that collapsible proofs do not actually break accessibility. The relevant guideline is MOS:PRECOLLAPSE, and it is simply that in the absence of JavaScript and/or CSS, the content is not hidden. The templates collapse top/bottom have been implemented in accordance with this guideline and fallback gracefully to show the content in the absence of JS. I saw some other comments too that screenreaders work fine with collapsed sections (didn't save the link though). So there no accessibility problem with collapsing proofs. It is only MOS:COLLAPSE which states "Collapsible templates should not conceal article content by default upon page loading." which explicitly contradicts the usage of collapsed proofs. And arguably, if the proofs were expanded by default on page load, it would be following the guideline.

Now as far as actual style, the Wikipedia:WikiProject_Mathematics/Proofs sort of hints that long proofs are not suitable for WP. For example, considering the Homomorphism page, I think it would be better to cite the proofs that require a good knowledge of category theory, than to do WP:OR and construct an elementary proof out of whole cloth. The elementary proofs can be added to other sites such as Wikibooks, ProofWiki, etc. Mathnerd314159 (talk) 18:07, 10 February 2023 (UTC)

D.Lazard has already said what I wanted to say but better. But to add his and to respond to jacobolus: I think it's essentially the matter of what proofs we should include and what we shouldn't. To echo D.Lazard, we shouldn't include proofs that merely serve to justify some facts; references to reliable sources are preferrable ways, like any other facts in Wikipedia. However, some proofs do serve to help understand the concepts or the facts discussed in the article. Here is an example: the article Bounded operator includes a (short) proof of the fact that an operator is bounded if and only if it is continuous. This fact can be easily referenced by reliable sources but giving the proof is helpful, since a reader can see how the continuity is used and can also see how the proof actually proves stronger continuity (Lipschitz continuity). Hiding it is not only unnecessary, but would make the article less helpful. There does arise an occasion where we feel a need to give a proof or some short justification to defend ourselves against experts who find the statement suspicious (e.g., some algebraic fact is stated without the Noetherian assumption.) In such a case, the use of footnote is a better solution, since most readers wouldn't care about such technical issues. -- Taku (talk) 09:12, 11 February 2023 (UTC)

Very well said. I agree with this. PatrickR2 (talk) 21:26, 13 February 2023 (UTC)

There is actually one more case: de Rham theorem currently redirects to de Rham cohomology; the theorem is discussed there but without a full proof. We could add a collapsed full proof but a better solution is to stop the redirecting and then put a non-hidden full proof to the de Rham theorem article. (By the way, which I think we should do.) —- Taku (talk) 09:29, 13 February 2023 (UTC)

I've seen texts with proofs in an appendix. How about putting proof for foo in foo/proofs and linking to them? — Preceding unsigned comment added by Chatul (talk • contribs) 06:08, 13 February 2023 (UTC)

That has been determined to go against WP:SP which states that "using subpages for permanent content that is meant to be part of the encyclopedia" is disallowed. Mathnerd314159 (talk) 00:48, 14 February 2023 (UTC)

If the proof itself is notable, a self-contained topic, and would overload the main page on the theorem, then WP:SPLITting it into a separate page is widely endorsed. What's forbidden is the slash to indicate a subpage, and the general idea of each article needing to be its own topic. We already do that: for Fermat's Last Theorem, we have splitoff articles Proof of Fermat's Last Theorem for specific exponents and Wiles's proof of Fermat's Last Theorem. This approach also helps provide a criterion for whether to include the proof: whether external sources actually comment on it beyond merely stating the proof itself. DMacks (talk) 04:50, 14 February 2023 (UTC)

References

should we have an article for a 'geometric figure'?

Geometry is often defined or described as the study of the properties/relationships of "geometric figures", but we don't really have a good basic definition/explanation for what that means. The existing article shape seems focused on description of a "single" object of some sort (e.g. a polygon, closed curve, or whatever), and especially with classifying shapes up to similarity (i.e. separating "shape" from "size"), whereas the article configuration (geometry) seems primarily concerned with incidence relations between finitely many / discrete collections of points and lines, rather than e.g. metrical relationships like distance or angle, pencils of lines, arbitrary curves, etc. Should we try to add a new such article, and what would be a good accessible definition? Geometric figure currently redirects to Shape § In geometry which doesn’t seem like it really covers the topic.

Related, geometric object currently redirects to Geometry § Objects which has no basic definition, just a (short, nowhere near exhaustive) list of specific types: {Lines, Planes, Angles, Curves, Surfaces, Manifolds}. Nowhere in that page are such basic concepts (related to geometric objects) defined/discussed as 'locus', 'envelope', 'pencil', 'join', 'meet', 'intersection', etc. Perhaps we could also make a page about that one. Anyone have a suggestion of a good definition, or an idea which sources to look to for one? (And while we're here, mathematical object could use a lot of help.) –jacobolus (t) 01:08, 14 February 2023 (UTC)

I don't understand the distinction you are trying to make between single objects and multiple objects. It seems to be a distinction of grammar and convention rather than anything intrinsic. A finite set of points is both a single set and multiple points. A polygon, which you describe as a single object, could be a finite set of vertices and edges, an infinite set of boundary points, or a different infinite set of boundary and interior points. Even a point, which you might think of as unavoidably singular, could be considered as equivalent to a line in the projective dual plane, and therefore equivalent to an infinite set of points on that dual line. —David Eppstein (talk) 01:20, 14 February 2023 (UTC)

You are missing my point; I assume I wasn't clear enough. I am not trying to make any claim about what what the limits of a "geometric object" could be, which types of objects should be considered primitives (in one or another context), whether an object should be defined in terms of set theory, or any other such thing. (Though those are all worthy questions which should probably be discussed somewhere on Wikipedia.)

My claim is that the article shape as it currently exists does not describe any arbitrary collections of geometric primitives, but only certain ones which it considers to be "shapes", which is a small subset of what I would consider to be the universe of "geometric figures". We don't really anywhere a good basic explanation or definition about these topics.

If I want to wiki-link from any arbitrary article to "geometric object" or "geometric figure" (or whatever similar term you might prefer, perhaps "configuration" or "arrangement" or ...?) there is currently no good endpoint for that wiki-link to point. –jacobolus (t) 01:48, 14 February 2023 (UTC)

So this discussion is a bit more concrete, here are definitions from Kisilev (Geometry):

1. Geometric figures. [...] A set of points, lines, surfaces, or solids positioned in a certain way in space is generally called a geometric figure. Geometric figures can move through space without change. Two geometric figures are called congruent, if by moving one of the figures it is possible to superimpose it onto the other so that the two figures befome identified with each other in all their parts.

2. Geometry. A theory studying properties of geometric figures is called geometry, which translates from Greek as "land-measuring". This name was given to the theory because the main purpose of geometry in antiquity was to measure distances and areas on the Earth's surface.

First concepts of geometry as well as their basic properties, are introduced as idealizations of the corresponding common notions and everyday experiences. [...]

And Hadamard (Lessons in Geometry):

1. A region of space which is bounded in all directions is called a volume. [...]

Any collection of points, lines, surfaces, and volumes is called a figure. [...]

2. Geometry is the study of the properties of figures and of the relations between them. [...]

–jacobolus (t) 03:35, 14 February 2023 (UTC)

As an example of the kind of wiki-link I am thinking of, in angle we have:

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

This definition of angle originated with Sidorov (Encyclopedia of Mathematics) which more explicitly uses the term geometric figure. But the word figure in the angle article is not defined or wiki-linked, and it may not be immediately obvious to all readers what it means. Similarly, in congruence (geometry) we have:

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

In this case there is neither definition nor link for what 'figure' means, though the term is used throughout the article. Then we have geometry itself:

Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land', and μέτρον (métron) 'a measure') is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures.

Again, no explanation anywhere of what figure means. In polygon we have:

In geometry, a polygon (/ˈpɒlɪɡɒn/) is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

But in this case figure is wiki-linked to shape, which defines:

A shape or figure is a graphical representation of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type.

From there, graphical representation links to graphics, which defines:

Graphics (from Ancient Greek γραφικός (graphikós) 'pertaining to drawing, painting, writing, etc.') are visual images or designs on some surface, such as a wall, canvas, screen, paper, or stone, to inform, illustrate, or entertain.

This does not seem like a correct/adequate definition for this purpose. In my understanding the word figure in geometry refers to the collection of geometric objects and their specified (or derived) relationships, rather than a physical picture drawn on a piece of paper. I think it would be useful to have a better definition of geometric figure somewhere, because in my opinion no current Wikipedia article adequately handles this. –jacobolus (t) 04:24, 14 February 2023 (UTC)

If I understand right, it does seem weird to speak of a figure consisting of one circle and one triangle as a single shape, linguistically speaking. Maybe the shape article should be renamed as a figure? A figure seems a bit more general. —- Taku (talk) 18:35, 14 February 2023 (UTC)

Basic Question

OK, I have a super basic question because I am rusty. How does the archiving of talk pages work? I thought it was done by bots, but visiting some pages I edited a decade ago, they have these enormous talk pages going back a decade. Is this done manually? Thenub314 (talk) 15:58, 15 February 2023 (UTC)

@Thenub314 It's only automatic if the page has been set up for auto archiving. If you think there are talk pages that need archiving manually please see Help:Archiving a talk page for suggested methods. Nthep (talk) 16:35, 15 February 2023 (UTC)

great books about calculus

Hello, I want to expand and update the contents such as integral, differential, Fourier series, limits of continuity of functions by using two very rich and important books in the book of calculus.

references:

aetemad.iut.ac.ir https://aetemad.iut.ac.ir › filesPDF Essential calculus with applications / by Richard A. Silverman.

stewartcalculus.com https://www.stewartcalculus.com Stewart Calculus Textbooks and Online Course Materials

Mohammad.Hosein.J.Shia (talk) 09:33, 15 February 2023 (UTC)

It's been more than half a century since I looked at them, but I was impressed at the time by

• Apostol, Tom M. (1960). Mathematical Analysis: A Modern Approach to Advanced Calculus. Addison-Wesley Publishing Company.
• Thomas, George Brinton Jr. Calculus and Analytic Geometry (6th ed.). Addison-Wesley Publishing Company. ISBN 978-0201162905.

Both of these are available in more recent editions. Also,Apostol has written a two volume Calculus book that I would certainly want to check if I were teaching a course. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 11:25, 15 February 2023 (UTC) -- Revised 15:52, 15 February 2023 (UTC)

You make a good point. By using these four books and other old and new books, we can expand the topics of mathematics. Mohammad.Hosein.J.Shia (talk) 13:36, 15 February 2023 (UTC)

Don't forget Spivak Thenub314 (talk) 16:00, 15 February 2023 (UTC)

ok

Mohammad.Hosein.J.Shia (talk) 16:31, 15 February 2023 (UTC)

Try Goursat (1904) https://archive.org/details/courseinmathemat01gouruoft/

Courant (1937) https://archive.org/details/ost-math-courant-differentialintegralcalculusvoli/

Apostol (1967) https://archive.org/details/calculus0000apos/

Piskunov (1969) https://archive.org/details/n.-piskunov-differential-and-integral-calculus-mir-1969/

–jacobolus (t) 15:12, 15 February 2023 (UTC)

According to the sources mentioned by Mr. Jacobolus, the best sources are ebooks. Mohammad.Hosein.J.Shia (talk) 16:31, 15 February 2023 (UTC)

These are all scans of physical books. –jacobolus (t) 17:06, 15 February 2023 (UTC)

We can search in this,book address[1]Mohammad.Hosein.J.Shia (talk) 07:40, 16 February 2023 (UTC)

Good article reassessment for Albert Einstein

Albert Einstein has been nominated for a good article reassessment. If you are interested in the discussion, please participate by adding your comments to the reassessment page. If concerns are not addressed during the review period, the good article status may be removed from the article. Onegreatjoke (talk) 18:06, 17 February 2023 (UTC)

Move discussions about Prime and e (mathematical constant)

In Talk:Prime (disambiguation), it is discussed whether Prime should remain a redirect to Prime number or should be moved to Prime (disambiguation).

In Talk:e (mathematical constant)#Requested move 14 February 2023, it is discussed whether e (mathematical constant) should moved to e (number). D.Lazard (talk) 12:24, 18 February 2023 (UTC)

Proposal: move Gregory's series to arctangent series

I’m not sure if a discussion here is sufficient or if I should try a more formal process, but it seems like it might be an improvement to move Gregory's series to arctangent series, since this was discovered independently by Kerala school mathematicians in the 14th–15th century, Gregory in 1671, Leibniz in 1673, and perhaps various others. That article can then be expanded to fill in some of the historical/mathematical details of the separate derivations, as well as subsequent developments, connections to other areas of mathematics, etc.

We already have an article Madhava series which covers various other series as well as this one, but calling this Gregory's series seems to be somewhat pushing a POV, as all of the names "Gregory series", "Leibniz series", "Madhava series", "Nilakantha series", "Gregory–Leibniz series", "Madhava–Gregory series", "Madhava–Leibniz series", "Gregory–Nilakantha series", "Leibniz–Gregory–Nilakantha series", "Madhava–Nilakantha series", etc. can be found in the literature, with no clear preference. The name "arctangent series" also gets regularly used in practice (along with similar names like "arctan series", "inverse tangent series", "Taylor series for arctan", etc.), and it seems to me that a neutral descriptive title would best match Wikipedia:Article titles. Thoughts? –jacobolus (t) 06:55, 17 February 2023 (UTC)

I can agree with what he said Mohammad.Hosein.J.Shia (talk) 09:45, 17 February 2023 (UTC)

I did a Google search of "arctangent series" and "Gregory's series" and Gregory's series got six times as many hits. People can find arctangent anyway so I don't see how this proposal helps readers. It is not our duty to right great wrongs. As to the various other names there already is a Madhava series article. NadVolum (talk) 11:44, 17 February 2023 (UTC)

If I do a Google scholar search of papers since 1980, of the form: ("Gregory's series" OR "Gregory series") -"Madhava-Gregory" -"Leibniz-Gregory" -"Nilakantha-gregory" and likewise for other names, I get:

• Leibniz: 401 results (some sources mean specifically the series for arctan(1))
• Gregory: 349
• Madhava: 43 (many for the sine series)
• Nilakantha: 12
• Gregory–Leibniz: 159 (also counting Leibniz–Gregory)
• Madhava–Leibniz: 49
• Madhava–Gregory: 40
• Nilakantha–Leibniz: 2
• Nilakantha-Gregory: 4
• Madhava–Nilakantha: 6
• Madhava–Gregory–Leibniz: 19 (including other orders)
• Nilakantha–Gregory–Leibniz: 3

Then we also have (combining e.g. "arctan series", "series for arctant", and "series for the arctan"):

• arctangent: 205
• arctan: 224
• inverse tangent: 135
• inverse tan: 4

(The numbers for all of the above names are not entirely reliable, as these terms are also sometimes used for something else.)

But my basic point is that there’s not currently any strong consensus in the literature about what the name should be. –jacobolus (t) 18:18, 17 February 2023 (UTC)

While we are at it, "Gregory series" seems somewhat more popular than "Gregory's series". –jacobolus (t) 19:11, 17 February 2023 (UTC)

What is the point in doing a Google scholar search for this? It is secondary or high school mathematics. NadVolum (talk) 23:51, 17 February 2023 (UTC)

The point is to figure out what name is used in recent literature. A google scholar search is generally a much better way to count than a web search, as fewer of the results are complete garbage (e.g. SEO spam, blog posts, plagiarized copies of Wikipedia, etc.). Plenty of high school / undergraduate level topics are discussed in journals, books, etc. included in citation indices such as Google scholar. –jacobolus (t) 01:05, 18 February 2023 (UTC)

I suppose with ChatGPT it won't be long before mathematicians are scammed uysing messages mentioning Gregory series ;-) NadVolum (talk) 20:33, 19 February 2023 (UTC)

This discussion shows a redirect from Arctangent series to Gregory's series is needed.  Done. D.Lazard (talk) 12:42, 18 February 2023 (UTC)

Sounds like nobody else thinks there is any issue, so I’ll leave the title at Gregory's series. Hopefully we can still expand this over time, add some more figures, etc. Can anyone find a clear source where one of Madhava of Sangamagrama's followers directly credited him for the Maclaurin series for arctangent? The sources I saw seem to suggest that current scholarly consensus leans more toward this being worked out by one of Madhava's followers in the 15th century, instead of Madhava himself. Madhava series § Madhava's arctangent series quotes "Madhava's own words" but from what I can tell these are not Madhava's words, but those of a later follower. –jacobolus (t) 23:48, 19 February 2023 (UTC)

Khayyam-Newton expansion in math Ittihad

Hello, according to a discussion, I have read a method in books called Khayyam-Newton expansion in the unification of mathematics. I want to include this article in the Etihad (mathematics) article so that they can get acquainted with the common method of two scientists, one of whom is Iranian and the other is European.

I proceed according to the example This method is obtained in the form of Khayyam's triangle and Newton's union. ${\textstyle (a+b)^{5}=a^{5}+5a^{4}b+10a^{3}b^{2}+10a^{2}b^{3}+5ab^{4}+b^{5}}$Mohammad.Hosein.J.Shia (talk) 09:57, 17 February 2023 (UTC)

In English, the formula for expanding powers of a sum of two terms is called the binomial theorem. When the power is not a positive integer, there are infinitely many terms in the expansion and it is called the binomial series. And of course there is lots of related content in the articles on binomial coefficients and Pascal's triangle. --JBL (talk) 17:38, 17 February 2023 (UTC)

I can write an article about this topic Just wants a references Mohammad.Hosein.J.Shia (talk) 18:55, 17 February 2023 (UTC)

Of course, Pascal's triangle is also a complement to Khayyam's triangle. I mean, according to the Persian, German, English, and Arabic books, this theorem of Khayyam and Pascal's triangle can be generalized for coefficients. Mohammad.Hosein.J.Shia (talk) 10:01, 19 February 2023 (UTC)

By its generalization, you mean maybe the article we already have at multinomial theorem? —David Eppstein (talk) 20:44, 19 February 2023 (UTC)

Yes Mohammad.Hosein.J.Shia (talk) 11:12, 20 February 2023 (UTC)

Merge discussions about algebraic manifold

 You are invited to join the discussion at Talk:Algebraic variety#Merger proposal. --SilverMatsu (talk) 23:00, 20 February 2023 (UTC)

References in the article Point (geometry)

I have updated some references in the article Point (geometry). However, I could not find sources for corresponding the footnotes Bracewell 1986 and Schwartz 1950. I have found three sources that correspond to the footnotes. Any assistance would be appreciated. Dedhert.Jr (talk) 12:44, 23 February 2023 (UTC)

Just guessing but it seems plausible that they are

• Bracewell, Ronald N. The Fourier transform and its applications. Third edition. McGraw-Hill Series in Electrical Engineering. Circuits and Systems. McGraw-Hill Book Co., New York, 1986. xx+474 pp. ISBN: 0-07-007015-6
• Schwartz, L. Théorie des distributions. Tome I. (French) Publ. Inst. Math. Univ. Strasbourg, 9. Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1091 Hermann & Cie, Paris, 1950. 148 pp.

--JBL (talk) 18:12, 23 February 2023 (UTC)

Thank you. I knew that the footnote Bracewell must be connected to The Fourier transforms..., but I cannot find the accurate one. I'll go add it later. Dedhert.Jr (talk) 02:24, 24 February 2023 (UTC)

Just one more thing before I'll add some references. This article has already used CS1 in the lead, but I didn't notice and accidentally add the sources with CS2 in the references section. Along with inline citations, should I change all of them to inline citations with {{sfnp}} in notes and convert them to CS2 in references, or change all of them with no inline citations? My apologies for asking this, because I honestly was perplexed with WP:CITEVAR, and seek consensus first before changing them. Any explanation would be appreciated. Dedhert.Jr (talk) 16:56, 24 February 2023 (UTC)

Before you started, the article was already using an inconsistent mix of (full ref in footnote, formatted in CS1) and (harvnb in footnote, manually and inconsistently formatted full ref later). I don't think there is any single consistent style that you can fall back to. So it should be ok to just pick a single consistent style and reformat everything to be in that style. —David Eppstein (talk) 17:33, 24 February 2023 (UTC)

If that's the case, I'll change it to CS1. For the time being, I will keep using short citations, but some changes to {{sfn}} or {{sfnp}} (or {{harvtxt}} for multiple short citations in one <ref>). Please revert it if I did a mistake there. Will discuss later if someone wants to change them. Dedhert.Jr (talk) 09:44, 25 February 2023 (UTC)

I'd just go for CS1 style as it seems more popular and more or less the same idea as CS2, and the names 'cite journal', 'cite book', etc. are helpful for understanding at a glance what type of source is being cited. But I honestly don't understand why there are two whole separate sets of templates. YMMV. –jacobolus (t) 21:53, 24 February 2023 (UTC)

My personal preference is for CS2 because. All. The periods. Annoy. Me. and because I'd rather just have one template than have to figure out which of 10 different cite templates is the best fit for each citation. But the differences are small. As for why: it grew up that way and now it's difficult to change. —David Eppstein (talk) 21:59, 24 February 2023 (UTC)

As an aside: One thing people might not know about (I didn't until recently) but can be very useful when these templates inevitably break in complicated cases is using {{wikicite|ref={{harvid|Name|Year}} |reference=...}}, which can be wrapped around plain-text citations (or other cite templates with ref=none set on them) and then highlight/pop up everything inside when used with {{harvp}}, {{sfn}}, and the like. This is handy when a paper has been reprinted several times in different books, or when a book was translated from another language edition, or when a paper was split into several parts and published serially across multiple issues of a journal, etc. Downside: it's harder for machines to figure out the citation metadata if you use plain text. Upside: Citation Bot won't come and try to add 50 different useless identifiers from random citation indices. –jacobolus (t) 22:32, 24 February 2023 (UTC)

"Improper point" listed at Redirects for discussion

The redirect Improper point has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2023 February 26 § Improper point until a consensus is reached. —Mx. Granger (talk · contribs) 21:54, 26 February 2023 (UTC)

Mar 2023

"Mode-k flattening" listed at Redirects for discussion

The redirect Mode-k flattening has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2023 March 8 § Mode-k flattening until a consensus is reached. -- 65.92.244.151 (talk) 23:25, 9 March 2023 (UTC)

Merger proposal input requested

Formal request has been received to merge: Hermitian variety into Unital (geometry); dated: February 2023. Proposer's Rationale: If I was more confident in my knowledge of this field and Wikipedia-editing skills, I would just do this myself. Edrudathec. Discuss >>>here<<<. GenQuest ^"scribble" 20:10, 13 March 2023 (UTC)

Convergence Solved Leibniz formula for pi

I believe to have solved the convergence issue of the Leibniz formula for pi. [2]https://archive.org/details/improving-the-convergence-of-madhava-gregory-series-and-a-rudimentary-calculation-for. I have updated a couple of pages - Gregory's Series and Leibniz formula for pi. Please can some-one verify this against the published material and find out how to do edits across other places where they say convergence is an issue. Brian (talk) 07:10, 15 March 2023 (UTC)

Wikipedia is not the place to publish or publicize your original research. Nor is it the place to ask editors to find your mistakes. Nor is putting something on archive.org the same thing as publishing it in a peer-reviewed publication. —David Eppstein (talk) 07:13, 15 March 2023 (UTC)

I didn’t try to read your paper, but you should try asking for help on some other forum (reddit? stack exchange?). The only vaguely appropriate venue here is Wikipedia:Reference desk/Mathematics. But you might want to start by researching the large, large amount of past work that has been done on this problem. If you have a good idea about a practical way to compute π, it is pretty likely that other people have had very similar ideas already. –jacobolus (t) 15:12, 15 March 2023 (UTC)

Okay I read your paper. Your idea is essentially the same as Archimedes's Measurement of a Circle from about 250 BC (except you switch over to using Gregory's series at some point instead of continuing with polygon division). (Also see Pi § Polygon approximation era and Viète's formula.) I can guarantee you someone has tried this before somewhere and written about it, and I imagine you could find a reference if you hunted for it. –jacobolus (t) 17:33, 15 March 2023 (UTC)

Thanks! - I know the issue is the word 'Discovery'. When you look at the solution it is quite obvious this is not new.

May be you meant - Liu Hui's method or Viète's formula, not about Archimedes is it?

There was an anomaly I came across in trigonometry - deep in the derivations - surprised it was there in basic math. Looking for an answer, I came across this page - and I couldn't beleive what I was reading. A little effort and you can see the solution right in front of you - you don't need extensive derivations and experimentation, to get to this formula - a 13year old can come up with it.

And yet all over wikipedia is plastred a notion that this series is not useful.

In my document and talks I have mentioned this frustration.

People (not well read mathematicians) looking for ideas end up on this platform. There is a good reason why I put this there - we'll know in time.

A little inkling that solutions exist could be in those sentences.

Hope you know how many places people vouch by this link of Leibniz and Gregory's formula.

Currently my only beef is with the sentence that the series does not converge quickly. That sentence (and many others pages) sitting in wikipedia haave misled so many I believe. May be I wrote it on the page a bit too strongly.

Mathematicians are not in error but the ones the maintain the record because it looks like information is withheld.

Nevertheless - I respect the way you guard these pages. And I will take your point and leave it at that.

Thanks for taking the effort to read the paper - I see you are better than others on this forum that interact personally. Brian (talk) 19:10, 15 March 2023 (UTC)

Archimedes repeatedly applied the identity

$\cot {\tfrac {1}{2}}\theta =\cot \theta +{\sqrt {\cot ^{2}\theta +1}},\qquad 0<\theta <\pi$

except expressed as a geometric construction, in the style of his time and context. (Desmos plot)–jacobolus (t) 20:37, 15 March 2023 (UTC)

You can read about this in Miel, George (1983). "Of calculations past and present: the Archimedean algorithm" (PDF). American Mathematical Monthly. 90 (1): 17–35. –jacobolus (t) 20:55, 15 March 2023 (UTC)

You are right - all of them in history have been repeatedly been dividing angles. It is not uncommon - each method is a discovery - even if it is related. Isn't it? That's what wikipedia shows again and again - isn't it? But the real proof of all these is the limit identity of tan isn't it?

But the problem the paper address is not the limit identity isn't it? It merely says its an extra and attributes it to the limit identity doesn't it?

However the paper addresses the ignorance of the convergence doesn't it? Brian (talk) 21:25, 15 March 2023 (UTC)

Here is one example of a paper adopting more or less the same approach you suggest, but with a lot more work put into the explanation and experiments. I am sure the idea is older than this though. Fernández Guasti, M. (2005). "Blending two major techniques in order to compute π". International Journal of Mathematical Education in Science and Technology. 36 (1): 85–92. doi:10.1080/002073904123313.. –jacobolus (t) 18:31, 15 March 2023 (UTC)

Thanks, I am not a mathematician. I believe you are. If so even you, will come up with it in just a few minutes. I mean no details, experiments required. In one of my videos I say just this. Brian (talk) 19:16, 15 March 2023 (UTC)

For Wikipedia's purpose what matters is whether you can find reliable sources which make particular claims. It would e.g. be conceivably possible to mention this M. Fernández Guasti paper because it was published in a peer-reviewed journal, even if the journal is sort of obscure and low-impact. Though I would recommend against including more than a sentence or two at most, since it is not an especially novel, effective, or historically important method of improving the convergence calculations of π. On the other hand, adding a section based on e.g. a YouTube video or a PDF self-published to the internet archive by an amateur does not meet Wikipedia guidelines. –jacobolus (t) 21:24, 15 March 2023 (UTC)

Yes this is right. I shouldn't be adding items that aren't peer reviewed. At least history of this document will be a testament that I tried to tell wikipedians that a sentence in there was incorrect and misleading to many. Brian (talk) 21:28, 15 March 2023 (UTC)

And Jacob, your arguments are quite fine. But you are missing the point - I feel burried in formation in the papers is not wikipedia spirit. TLDR is! so then people can look the burried stuff Brian (talk) 21:31, 15 March 2023 (UTC)

Oh and this is a very very good example..your answers mentions so may papers but they don't mention the tan limit identity though which is the root... because that is not connected in wikipedia! Brian (talk) 21:42, 15 March 2023 (UTC)

Your "tan limit identity" is not in any fundamental way different from the method of Archimedes (also Liu Hui, Aryabhata, Jamshīd al-Kāshī, François Viète, Adriaan van Roomen, Ludolph van Ceulen, and Willebrord Snellius), except for being a self-published paper from 2023 instead of a historically famous work from centuries ago. (I'm not trying to sound harsh or dismissive here: this is a true and meaningful insight which is why it has come up and been used repeatedly by mathematicians and amateurs over the past 2+ millennia. There's nothing wrong with rediscovering previously known ideas for oneself.) –jacobolus (t) 22:01, 15 March 2023 (UTC)

it is not fundamentally different - it is fundamental Brian (talk) 05:23, 16 March 2023 (UTC)

Dave, I believe you haven't checked math.stackexchange either? :), Its ok - I see no point in any discussion here. Brian (talk) 19:20, 15 March 2023 (UTC)

You might have gotten our replies mixed up. I mentioned you could start a conversation at e.g. reddit or stack exchange if you want feedback on your paper. David only said that Wikipedia is not a good venue for original research. –jacobolus (t) 21:39, 15 March 2023 (UTC)

Yes, that is what I meant when I made that sarcastic comment. I had already suggested it on stackexchange - [3]. That's where I was pursuing it. Wikipedia was a sideline attempt to get attention so I could correct a mistake in laymans view of pi calculation. Brian (talk) 21:47, 15 March 2023 (UTC)

Can you explain what the "mistake" is?

That this series converges incredibly slowly for $x=1$ is a straight-forward factual statement. It takes about 5 billion terms to get 10 digits! Note that this is an entirely different claim from anything about the convergence near $x=\tan \left(2^{-n}\arctan 1\right).$ –jacobolus (t) 21:49, 15 March 2023 (UTC)

Thanks- Just correct this part.

"Finding ways to get around this slow convergence has been a subject of great mathematical interest." - you can change it to something like "Quite a lot of methods are available for improving this convergnce" (you may make a better sentence) ... then add a few references to the paper you mentioned to me and any other peer reviewed information will be better. Also many places in wikipedia this type of line exists.. that undermines the Leibniz formula... I don't believe I am the right person for this kind of job because I am not an accomplished mathematician. But there are people who can correct this misleading so, when people like me show up we know to dig further. Thanks for getting to the point. Brian (talk) 21:59, 15 March 2023 (UTC)

I will indeed add material there, but it is a nontrivial undertaking which requires actually doing the research and writing. –jacobolus (t) 22:03, 15 March 2023 (UTC)

Yes now you understand, where I am coming from. I wish, I wish... wikipedia had pointed to the tan limit identity with respect to this convergence - because they are closely related - I was a pain for me to figure it out - something so simple and already known - just not connected. We need a right person for this job. Brian (talk) 22:12, 15 March 2023 (UTC)

Here's what the "Gregory's series" article looked like a month ago. In the future I intend to add some more figures showing how convergence is much (much!) faster closer to 0, discussing Madhava's correction term, evaluation for $x=1/{\sqrt {3}}$, Machin-like formulas, Euler transform (originally due to Newton), and so on. –jacobolus (t) 22:32, 15 March 2023 (UTC)

Thanks! Brian (talk) 22:34, 15 March 2023 (UTC)

Oh and there appears to be a serious anomaly inside trigonometry related to this formula. Hope you can find references to that as well,or a soution to that then all will be perfect. Thanks again. Brian (talk) 23:10, 15 March 2023 (UTC)

I don't understand what you mean. –jacobolus (t) 23:19, 15 March 2023 (UTC)

Ok don't bother about it for now. I'll show it to you when I get it all verified. Then we can find the references. Brian (talk) 23:21, 15 March 2023 (UTC)

Requested move at Talk:Transcendence degree#Requested move 18 March 2023

There is a requested move discussion at Talk:Transcendence degree#Requested move 18 March 2023 that may be of interest to members of this WikiProject. Favonian (talk) 09:11, 25 March 2023 (UTC)

In the News

FYI, there's some nominations for In the News of interest to this project:

• Abel prize
• Einstein problem
• Turing award

Andrew🐉(talk) 15:57, 25 March 2023 (UTC)

Filter (set theory)

This article was created in May 2022 using content from Filter (mathematics) and Filters in topology, as explained at Talk:Filter_(mathematics)#Proposal:_Move_this_article_to_Filter_(order_theory). Unfortunately, this new article is now extremely long (about 141 KB) and it seems that it will need to be condensed. –LaundryPizza03 (dc̄) 05:26, 26 March 2023 (UTC)

Somehow related point: I am not quite convinced if it makes sense to have separate articles for a filter in general and a filter for sets. On the other hand, it does seem to make sense to isolate the usage in topology. I am not a set-theorist so maybe there is a reason. -- Taku (talk) 08:17, 26 March 2023 (UTC)

So, maybe one option is to merge Filter (set theory) into Filter (mathematics)? In the process, maybe we can drastically cut down the length. -- Taku (talk) 08:19, 26 March 2023 (UTC)

I was questioning the need for this article as well; the topic is too similar and the split was poorly explained. –LaundryPizza03 (dc̄) 00:18, 27 March 2023 (UTC)

"Mode-k flattening"

FYI Mode-k flattening (edit | talk | history | protect | delete | links | watch | logs | views) has been nominated for renaming to some title to be determined. Some of the suggestions are "mode-m flattening", "mode-n flattening", "mode flattening", "flattening", etc. For the discussion, see the talk page. -- 65.92.244.151 (talk) 21:32, 21 March 2023 (UTC)

Moved to talk:mode-k flattening

65.92.244.151 (talk) 21:32, 21 March 2023 (UTC)

This discussion at talk:Mode-k flattening got closed without too much participation. I proposed merging into tensor reshaping instead. Does that seem reasonable to folks here? –jacobolus (t) 15:58, 28 March 2023 (UTC)

Mathematical

Grade 9 2023 197.184.163.18 (talk) 01:31, 8 September 2023 (UTC)

Apr 2023

Dirichlet's theorem on arithmetic progressions

Looks like the beginnings of an edit war at Dirichlet's theorem on arithmetic progressions.—Myasuda (talk) 14:42, 1 April 2023 (UTC)

The excitement seems to be over: the editor on one side of the issue thought it would be a persuasive tactic to start insulting and hounding other editors, and creating sockpuppets to push their view. They got indef-blocked for their efforts. —David Eppstein (talk) 21:32, 1 April 2023 (UTC)

Mathematics Genealogy Project

I have asked whether Mathematics Genealogy Project can be considered a reliable source Wikipedia:Reliable_sources/Noticeboard#Mathematics_Genealogy_Project. Any comments from member of this project? 76.14.122.5 (talk) 19:55, 2 April 2023 (UTC)

Coxeter-Dynkin representations of polytopes

About families of polytopes, I keep seeing the phrase "represented by permutations of rings of the Coxeter-Dynkin diagram." The word permutations looks wrong to me: the number of rings is not constant, and two rings are not distinguishable. Why not combinations? Looking for the sense of the community on this. —Tamfang (talk) 03:24, 5 April 2023 (UTC)

The right question to ask about our polytope cruft is usually: is any of this covered by reliable sources? If so what terminology do they use? If not it should just be removed. It certainly needs disambiguation concerning whether "rings" here means some kind of algebraic structure, the ringed nodes of a Coxeter-Dynkin diagram, or something else. —David Eppstein (talk) 05:54, 5 April 2023 (UTC)

GCD matrix

I have fixed the references in the article GCD matrix, and I have changed some headings as well. The only problem is that the lead section because it was too short and did not entirely summarize the whole article; maybe someone can help to rewrite it. Regards, Dedhert.Jr (talk) 12:57, 5 April 2023 (UTC)

Requested move at Talk:Ex Falso (tag editor)#Requested move 7 April 2023

There is a requested move discussion at Talk:Ex Falso (tag editor)#Requested move 7 April 2023 that may be of interest to members of this WikiProject. ASUKITE 19:48, 7 April 2023 (UTC)

Project-independent quality assessments

Quality assessments by Wikipedia editors rate articles in terms of completeness, organization, prose quality, sourcing, etc. Most wikiprojects follow the general guidelines at Wikipedia:Content assessment, but some have specialized assessment guidelines. A recent Village pump proposal was approved and has been implemented to add a |class= parameter to {{WikiProject banner shell}}, which can display a general quality assessment for an article, and to let project banner templates "inherit" this assessment.

No action is required if your wikiproject follows the standard assessment approach. Over time, quality assessments will be migrated up to {{WikiProject banner shell}}, and your project banner will automatically "inherit" any changes to the general assessments for the purpose of assigning categories.

However, if your project has decided to "opt out" and follow a non-standard quality assessment approach, all you have to do is modify your wikiproject banner template to pass {{WPBannerMeta}} a new |QUALITY_CRITERIA=custom parameter. If this is done, changes to the general quality assessment will be ignored, and your project-level assessment will be displayed and used to create categories, as at present. Aymatth2 (talk) 14:19, 12 April 2023 (UTC)

Good article reassessment for Albert Einstein

Albert Einstein has been nominated for a good article reassessment. If you are interested in the discussion, please participate by adding your comments to the reassessment page. If concerns are not addressed during the review period, the good article status may be removed from the article. ~~ AirshipJungleman29 (talk) 23:03, 17 April 2023 (UTC)

Wikipedia:Articles for deletion/Connes connection

Hello everyone,

There is an AfD that can use some inputs from the members of the project: Wikipedia:Articles for deletion/Connes connection. The article which the afd is about was started by me. There are suggestions in the AfD that the topic may be too niche for there to be a standalone article on it. Perhaps. But I can't find good merger targets; for example, the article noncommutative geometry seems to be a poor choice since having some technical materials damages the tone and the balance of the article (i.e., it should be general in tone and not too technical). -- Taku (talk) 16:32, 18 April 2023 (UTC)

Request for comment on draft

I'm reviewing Draft:Divisibility for all divisors relative prime to 10 at AfC, and wanted to ask those more familiar with the subject matter whether this looks like a typical (or even viable) maths article? The first thing that caught my attention, apart from the copious 'maths script', is the referencing, which is few and far between, suggesting there could be some OR included among it. But again, if that's how these things are routinely done on en.wiki, then who am I to criticise? Any comments appreciated – thanks! -- DoubleGrazing (talk) 09:33, 7 April 2023 (UTC)

The draft is implicitly alleged as WP:OR, since it presents a method without providing the name of its author or a citation that describes the method. The presentation is very confusing, and this makes difficult to see whether the method was previously known. The citations that are not general texts on number theory are either unpublished or published in journals for college students. So, no reliable sources. In short, definitively not suitable for Wikipedia. D.Lazard (talk) 15:35, 7 April 2023 (UTC)

Thank you @D.Lazard, much appreciated! -- DoubleGrazing (talk) 15:40, 7 April 2023 (UTC)

It now has some citations, but still fails as to OR: it reads like an extended homework essay of "everything I've learned about divisors". It would be acceptable as an essay for school credit, but it is not how one organizes knowledge in an encyclopedia. 67.198.37.16 (talk) 21:36, 21 April 2023 (UTC)

Order of operations

A minor skirmish at Order of operations has been reported at ANI. Perhaps people here could contribute to the article to provide other views. Johnuniq (talk) 04:53, 22 April 2023 (UTC)

The most recent change to the article was made by an editor who signed himself 2601:18f:107f:e2a0:7142:367:472:ca68 and who restored Mr. Swordfish's version of the article. Rick Norwood (talk) 09:37, 22 April 2023 (UTC)

Ergodicity

This page has been edited recently by an editor who insists on restoring an overly vague and broad introductory sub-section on ergodicity in geometry (https://en.wikipedia.org/wiki/Ergodicity#In_classical_mechanics_and_geometry). I strongly believe these edits are, at best, misled. They started taunting about 3RR so i'm bringing this to a larger audience here. More generally i think this page could use the help of more mathematically competent editors (not necessarily on this issue alone).

To be more precise: some time ago the section about "Ergodicity in physics and geometry" was added (among others), with the noble purpose of making the article less dry and more palatable to people with no mathematical background. Reading the geometry section i found it extremely badly (though very enthusiastically) written, mentioning in a too precise (for an introductory section) the geodesic flow (with far too much emphasis put on the symplectic aspects which are not germane to the article, at least not in an introductory section with no mention of their relevance), and mentions on some topics in ergodic theory which, again, should not appear in the introductory section (if i'm generous the last paragraph seems to refer, without ever mentioning it explicitely, to the link between the geodesic flow and symbolic dynamics, and the measure classification of shifts---once again, not a topic directly related to the subject of the article).

I edited this section down to the geodesic flow on flat tori, the simplest example for the theory of flows in Riemannian geometry, with an additional mention of negatively curved surfaces and Riemannian manifolds without giving details (note that these topics are referred to again in the more technical body of the article, with links to more detailed specific articles about them). You can see this version here : https://en.wikipedia.org/w/index.php?title=Ergodicity&oldid=1150858382#In_geometry.

To sum up: i replaced an overly broad and confused/confusing introductory paragraph (in my view as a mathematician) with a more to-the-point and precise paragraph, somebody's taken issue with it and seems to enjoy taunting an unproductive edit war about it.

Finally, if there are interested people i'd suggest them to take a look at the parts on physics to see if a similar mess of the topic is not made in them (i lack the expertise, inclination and time to do this myself). Cheers,jraimbau (talk) 07:40, 21 April 2023 (UTC)

The person that jraimbau is complaining about is me. Many of you might know who I am, as I've been posting here at WP:M for 18+ years. You probably also know that I prefer to remain anonymous, precisely because I'm easily exhausted by character attacks, such as the above.

I posted the following reply to him, on Talk:Ergodicity, which I copy here:

We live in the age of search engines. College professors post class notes on ergodicity on-line. There are dozens of PDF's out there. Download them. Read them. Educate yourself. Once you find some evidence that I'm wrong about something, and are able to articulate what it is, then sure ... there's plenty of subtlety and fine points that are hard to capture in such a short article.

As to encyclopedic content, well ... there's a way to understand that, too. Go out and talk, face-to-face, with actual people who are actually trying to learn mathematics from Wikipedia. I have. The consistent complaint that I hear is that they are frustrated with the wall of formulas, lacking in any sort of explanation or intuitive insight into what is "actually happening" with those formulas. What I am trying to do here, as with all the other edits I've made, is to explain complex mathematical topics to non-experts, using plain and simple sentences, plain and simple verbal explanations. Now, of course, if someone wants the actual precise and exact definition of something, then yes, they'd have to stare at the formulas and ponder what they actually mean. But for those who only want a general survey, an overview, then a more informal introduction is exactly what is needed. This is what we should strive for: an encyclopedia that non-experts find informative, and experts find useful. 67.198.37.16 (talk) 20:35, 21 April 2023 (UTC)

The issue i have with your edits is not informality, and you do not address the problems with the "geometry" paragraph that i mention above. Why should there be a long discussion of the relation of geodesic flow with symplectic geometry in an introductory paragraph in this article? This is not justified anywhere, not in your version of the article nor in you talk page comments. I'm inferring that you are enthusiastic about the subject but have no real grasp on the topic as you learned it haphazardly from "PDF's out there" (which you don't cite in the article), and the result is a mess that would do nothing but confuse a serious beginner. If you construe these observations as a "character attack" so be it, but as far as i can see i've been less insulting, if more direct, in this conversation than you have.

In any case, and whatever our very divergent opinions, it would be helpful if you could provide actual, pointed criticisms instead of the general issues you allude to in your reply above. To corner an issue, exactly do you think is wrong with this : https://en.wikipedia.org/w/index.php?title=Ergodicity&oldid=1150858382#In_geometry as compared to the current version, as an informal short introduction to the ergodicity (not ergodic theory) of geodesic flows on Riemannian manifolds? This version is certainly not a "wall of formulas". jraimbau (talk) 06:10, 22 April 2023 (UTC)

Earlier versions of the article said, "the case of classical mechanics is handled in the subsection titled 'geometry', below." Two or three issues became apparent. One editor noted that "below" no longer makes sense with the new cell-phone navigation system. Another was that your edit removed all references to classical mechanics (flat tori are not classical mechanics, and also, they're trivial.) Third, there was some squirrely statement about how one cannot know how to move in a straight lines on a curved surface, or something equally weird. Looking at the edit history, I saw that it was you who added that remark. I concluded that you did not know Riemannian geometry, and so I used the word "geodesic" more than once, hoping it would set off a light-bulb. I also got the impression that you were unaware that classical mechanics is "just" symplectic geometry. So I tried to emphasize that, too. The motion of mechanical systems, as studied in classical mechanics, is given by solutions to the Hamilton-Jacobi equations. This is standard undergraduate college physics. So, here's the kicker: geodesics on Riemannian manifolds are given by solutions to the Hamilton-Jacobi equations on the tangent bundle. In this sense, motion on Reimannian manifolds is a special case of classical mechanics. This is because the tangent bundle is always a symplectic manifold.

Proving ergodicity is hard, so one always looks for simpler cases. The first case where ergodicity was proved in the non-trivial case is the Bolza surface, I think in the 1930's, which kind of launched the whole project of ergodicity in geometry. The next interesting results on "flat space" were Yakov Sinai's work in the 1960's(??) on a model, intended to approximate the atoms of a physical gas with hard elastic spheres. (Gasses are one of the classical topics in physics, and are used to illustrate all the basic thermodynamic relationships. Thus, being able to rigorously prove that a gas actually is ergodic is a big deal.) Sinai's system is now known as "Sinai's billiards" or (rarely?) the "hard-sphere gas". Many(?) other gases have been studied. If I recall correctly, the hexagon gas is exactly solvable (where the things bouncing around are hexagons. Something like that. (The hexagon gas might be a special case of a translation surface??) One can get the various thermodynamic parameters for it.) To summarize: geometry is a special case of classical mechanics. But you've cut all that out. 67.198.37.16 (talk) 15:06, 22 April 2023 (UTC)

Less important, but still worth reviewing, is that there are different types of ergodicity. Perhaps this should go in a section called "types of ergodicity". There are classification theorems that show that most "commonplace" ergodic systems are isomorphic to one of the Bernoulli schemes. There are countably many Bernoulli schemes. There are other classification theorems that show that, for certain kinds of systems, there are uncountably many different kinds of ergodicity. These are popularly called "anti-classification" theorems. "Anti-classification" is some attempt at humor: the systems are still classifiable; there are just uncountably many distinct classifications. (The ergodicity class would be "enumerated" by the infinitely long sequence of digits that specify a specific point on the Cantor set.) 67.198.37.16 (talk) 15:59, 22 April 2023 (UTC)

Reply at https://en.wikipedia.org/wiki/Talk:Ergodicity#Recent_edits jraimbau for those who wish to read it. (talk) 16:59, 22 April 2023 (UTC)

Change Quality of Akima spline from Stub to Start

Akima spline
It has enough words to be considered so.
Supyovalk (talk) 18:33, 26 April 2023 (UTC)

@Supyovalk: I have done this but you could simply have done it yourself. --JBL (talk) 20:05, 26 April 2023 (UTC)

May 2023

Parity of zero

There is a discussion at Talk:Parity_of_zero#Deleted_pieces that could benefit from a third perspective. MartinPoulter (talk) 21:00, 1 May 2023 (UTC)

@MartinPoulter: I have restored the status quo ante and encouraged the other editor to engage on the talk-page; I would also like to encourage you to engage constructively on the talk-page (e.g., by discussing substantive points raised by LdV rather than proceduralism). To everyone else, it is still probably the case that a few more eyes on the page would be helpful. --JBL (talk) 22:02, 1 May 2023 (UTC)

Expanding the engineering mathematics page

Hi, I am wondering if I could expand the engineering mathematics. I'm hoping to hear from people here as to the recommended structure. I was thinking a section for each major topic, a brief history of each, a short summary of the concept, and a list of the applications and other wikipedia pages that go deeper.

Thanks :) TattersallOriginal Duke Of Earl (talk) 01:19, 1 May 2023 (UTC)

I guess that you are talking of the page Engineering mathematics. This page is rather short, and certainly deserves to be expanded. However, this is a very difficult task, and I am not sure that there are sufficiently reliable sources for the modern evolution of the concept. In fact, before computers, the mathematics used by engineers were well defined, and there was many textbooks of "mathematics for engineers". However, since the rise of computers, the mathematics used by engineers depend dramatically on their speciality, and cover together virtually all mathematics. For example, discrete mathematics are fundamental for engineers in computing, and were not considered before as engineering mathematics. In other words, with the multiplication of the engineering fields, I am not sure that "engineering mathematics" remains a relevant encyclopedic concept. D.Lazard (talk) 09:38, 1 May 2023 (UTC)

@D.Lazard I agree with your point that engineering mathematics is nearing a redundancy. But I imagine the page to instead reflect the topics that undergraduates should expect to cover. Whilst graduate engineers, maybe the majority, use the range of mathematical concepts far less than they once did because the computer allows for much of the maths to be forgotten; perhaps in the scope of university studies, the page could be expanded? TattersallOriginal Duke Of Earl (talk) 09:48, 1 May 2023 (UTC)

Umm, you can go to seminars on AI, where speakers will happily go on and on about how homology (mathematics) on graphs can be used to obtain XYZ for some problem PQR. Looking around, I thought I saw undergrads in the room. Is AI a part of engineering, or not? I don't think homology can be "forgotten", since anything ChatGPT would say about it would almost surely be wrong. 67.198.37.16 (talk) 20:59, 1 May 2023 (UTC)

I don’t quite understand? I meant that an arguable majority of engineers go into the industry where they don’t use signal analysis since uni for their flow meter instrumentation job for example. In that way much of the maths is “forgotten” because it isn’t utilised for their career. But a page that expands on the mathematics engineers should expect to cover before they graduate may be really helpful. :) 14.202.62.220 (talk) 23:05, 1 May 2023 (UTC)

Probably the majority of students won't care as their university program will tell them what they are supposed to study. The question is why such a curriculum needs to be a topic in this encyclopedia. PatrickR2 (talk) 00:05, 2 May 2023 (UTC)

@PatrickR2 I personally believe that knowledge or insight should be available to people prior to them undertaking a degree. Perhaps children in school will avoid or may even choose to pursue a career in engineering because of the resources they find online. Isn't that the purpose of Wikipedia? Hope that helps understanding of my perspective :) TattersallOriginal Duke Of Earl (talk) 00:08, 2 May 2023 (UTC)

I think that, rather than getting drawn into philosophical arguments, you should be bold and make improvements to the article (in keeping with our usual policies like WP:NOR and WP:NOT). JBL (talk) 00:31, 2 May 2023 (UTC)

@JBLI should've prefaced this much sooner which is completely on me. This is my first week on wikipedia, I've only done copy edits and fixing grammar so I was worried if I just went for it I would be screwing it up for someone else :) but I'll go for it ! TattersallOriginal Duke Of Earl (talk) 00:33, 2 May 2023 (UTC)

It can't hurt to find textbooks called things like Mathematics for Engineers, see what topics they tend to cover, and write summaries of that. XOR'easter (talk) 20:50, 3 May 2023 (UTC)

It would probably be reasonable to look at what mathematical coursework engineering students do as undergraduates and then what kind of mathematical coursework is common to popular engineering disciplines (e.g. electrical, mechanical, civil, geotechnical, chemical, aerospace, ... engineering). Niche tools applied occasionally by expert specialists would be out of scope for any reasonable article. –jacobolus (t) 04:17, 2 May 2023 (UTC)

@Jacobolus Definitely, I am currently an undergraduate of engineering in my final year so I am going to use that for inspiration and look into other universities to gauge a general focus. 14.202.62.220 (talk) 04:47, 2 May 2023 (UTC)

Are you (14.202.62.220) the same person as (TattersallOriginal Duke Of Earl)? PatrickR2 (talk) 21:48, 3 May 2023 (UTC)

@PatrickR2 Hi, yes I am, not sure what's going on with my username not showing in my last reply, must've been logged out :) TattersallOriginal Duke Of Earl (talk) 22:37, 3 May 2023 (UTC)

General references

Please see Wikipedia:Village pump (idea lab)#Deprecate future use of general references? I remember seeing this approach to sourcing being more common in math-related articles in the past, so if you have developed any advice or best practices, please join the discussion. WhatamIdoing (talk) 00:20, 13 May 2023 (UTC)

Almgren (1962). "The homotopy groups of the integral cycle groups".

I was trying on improving the reference list in the Almgren isomorphism theorem and I noticed that Almgren (1962) have two versions, that is ver. Topology (Elsevier) and ver. PhD thesis. I added ver. Topology (Elsevier), but I couldn't read ver. PhD thesis, so what should I do with the latter ? SilverMatsu (talk) 00:58, 18 May 2023 (UTC)

Does the journal version suffice to support the statements made in the article? If so, I would replace the reference to the thesis with the reference to Topology, as this has been peer-reviewed and will be more accessible to most readers. Felix QW (talk) 09:43, 18 May 2023 (UTC)

This overview of his work in the AMS notices seems to suggest that the PhD thesis was essentially the same as the version published in the journal, so I suspect that anything from his thesis supporting the Wikipedia article could indeed be found there too. Felix QW (talk) 09:47, 18 May 2023 (UTC)

Thank you for your advice and reference. Since there seems to be more references likes you gave me, so it seemed better to change Almgren (1962) from harv to harvtxt and and insert it in the body of the article, then add more references. --SilverMatsu (talk) 01:52, 21 May 2023 (UTC)

Article stuck in AfC - - Hurwitz spaces

Hi! My article about Hurwitz spaces Draft:Hurwitz space has been stuck in AfC for one month. It makes me sad because I spend quite some time on it. Could someone review it please? Thanks a lot! :) Beranger Seguin (talk) 10:45, 23 May 2023 (UTC)

If you look at the banner created by {{AfC submission}}, you will see Review waiting, please be patient. and This may take 4 months or more,; it's only been one month. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:24, 23 May 2023 (UTC)

Rewriting “Goppa code”

Hello everyone,

First, my name is Foobanana, and I'm a mathematician with expertise in algebraic geometry codes. I want to rewrite the page on algebraic geometry codes, titled "Goppa code" — it's definitely not reader-friendly, and has the added bonus of having a misleading title.

I would like to rewrite this page, and wanted to ask whether or not the rewriting of that page has been taken, since I’m new to editing wiki pages. I'd hate to make a lot of edits if someone else is currently working on a rewrite, even though I know that's unlikely :)

Hopefully I’m posting this in the right forum, but if I’m not then definitely let me know. Foobanana (talk) 01:51, 9 May 2023 (UTC)

Hi, Foobanana. Welcome to Wikipedia.

No page is "taken". You can be bold and edit whatever you want. But here are two caveats. First, you might want to skim the page's edit history, and the page's talk page, to see whether there has been much recent editing and/or argument. Second, despite your asking here, someone may rewrite your version anyway (in a month, year, or decade). Sometimes experts find that aspect of Wikipedia annoying. In my experience, the best way to "defend" against it is to construct the article around the Wikipedia:Reliable sources --- rather your own expertise, which we can't verify anyway --- from the start. Regards, Mgnbar (talk) 11:53, 9 May 2023 (UTC)

Thank you Mgnbar, I appreciate the response and the links you provided — especially the reliable sources page since I’m new :) Foobanana (talk) 01:17, 24 May 2023 (UTC)

Numberphile up for deletion

Numberphile, the most prominent Mathematics YouTube channel, is listed at Wikipedia:Articles for deletion/Numberphile. You may want to a add to the discussion. Salix alba (talk): 17:32, 10 May 2023 (UTC)

I have no opinion on the deletion. But I do think that new followers of Numberphile should be wary. In his video, Powell’s Pi Paradox: the genius 14th century Indian solution, he illustrates the video with a picture of himself made-up to look like the Indian mathematician (whose actual appearance is presumably unknown at this time) and he uses modern mathematical notation (aka Latex) to describe numbers which by his own admission (at the very end of the video) were originally merely given in poetry (verses in sanskrit). JRSpriggs (talk) 19:24, 21 May 2023 (UTC)

That's a different YouTube channel. eviolite (talk) 22:18, 21 May 2023 (UTC)

Yes, thanks for pointing that out. What I should have said is that one of the guest-hosts of Numberphile is Matt Parker the host of Stand-up Maths including Calculating π by hand. And Matt Parker as the host of Mathologer is the one who impersonated the Indian mathematician Madhava. For more on Madhava, see The man who invented calculus: the life and work of Madhava (Lecture 1) by P P Divakaran. — Preceding unsigned comment added by JRSpriggs (talk • contribs)

Matt Parker is not the host of Mathologer. The host of Mathologer is Burkard Polster. —David Eppstein (talk) 17:44, 23 May 2023 (UTC)

OK, then my apologies to Numberphile and Matt Parker. JRSpriggs (talk) 18:03, 23 May 2023 (UTC)

According to Mathologer's YouTube channel's "About": "In real life the Mathologer is a math(s) professor at Monash University in Melbourne, Australia and goes by the name of Burkard Polster.".

What is the point you are trying to make here? This was a thread about an AfD, which closed some time ago. Pop-science youtube channels are not great sources in any situation, even ones with generally good reputations (like Numberphile and Mathologer). --JBL (talk) 19:13, 23 May 2023 (UTC)

I can find no indication from Monash University itself that Burkard Polster has any connection to it. JRSpriggs (talk) 19:19, 23 May 2023 (UTC)

https://research.monash.edu/en/persons/burkard-polster XOR'easter (talk) 19:39, 23 May 2023 (UTC)

And I'm pretty sure that his picture of Madhava came from Wikimedia Commons. XOR'easter (talk) 19:42, 23 May 2023 (UTC)

And where did the Commons get the picture? Surely, they did not use a time machine and go back and take a photograph of him. Is it a photo of a painting done historically? By whom? JRSpriggs (talk) 00:19, 24 May 2023 (UTC)

You know you can look at the commons index page to find the answers to questions like this, right? They got it from a Feb. 2016 Wordpress post, https://agarwaltv.wordpress.com/2016/02/06/madhava-of-sangamagrama-contribution-to-calculus-was-much-before-europeans/ I am skeptical that it passes WP:PORTRAIT, but that should at least make it obvious that the origin of the image is unrelated to a YouTube channel that is unrelated to the one that was proposed for deletion. —David Eppstein (talk) 18:52, 24 May 2023 (UTC)

Thanks to XOR'easter for proposing the deletion of the image because of inadequate sourcing. I would like to point out that there appear to be the faint signs of eyeglasses on the person in the picture which would be an anachronism for Madhava. Commons getting the image from Wordpress does not exclude the possibility that Wordpress got it directly or indirectly from the Mathologer video. Someone dishonest enough to impersonate Madhava might also be dishonest enough to change his own name to Burkard Polster. JRSpriggs (talk) 20:54, 24 May 2023 (UTC)

The Mathologer video was made in 2023. Get off this stupid hobbyhorse about how wrong they are for using their time machine to cause someone else to make a possibly-unfree image seven years earlier that sort of maybe resembles their host if you squint hard enough and don't pay any attention to the dates. —David Eppstein (talk) 21:20, 24 May 2023 (UTC)

+1. --JBL (talk) 23:13, 24 May 2023 (UTC)

Can you please stop? Burkard Polster is a fine mathematician who has done more than nearly anyone else alive to popularize mathematics, first through accessible books and now through an excellent, accessible, long-running YouTube show. His video is not confusing anyone other than you about Madhava from what I can tell. –jacobolus (t) 23:47, 24 May 2023 (UTC)

If you have a problem with this image, the oldest source TinEye finds is from The Telegraph, a Calcutta newspaper, with the caption "A digital image of Madhava drawn up by the Madhava Ganitha Kendram, a voluntary association working to revive his works, with inputs provided by descendants of the mathematician-astronomer". The copyright status of the image is not clear, so it should perhaps be deleted on that basis, but it is clearly not intended to be an impersonation, anachronism, or cultural insult. Here is another 2014 article about the painting, which was commissioned by the Kerala State Science and Technology Museum (KSSTM) in Thiruvananthapuram. My guess is that both the museum and the voluntary association would be happy to have their painting used widely to represent Madhava as an alternative to leaving him "faceless", but it would be worth trying to find their contact info and ask them directly for a copyright release. –jacobolus (t) 23:53, 24 May 2023 (UTC)

You got me on the dates. I was wrong. I apologize to Mathologer (Burkard Polster) for falsely accusing him. And I apologize to you-all for wasting your time with my fevered imagining. JRSpriggs (talk) 04:46, 25 May 2023 (UTC)

Robertson–Seymour theorem

The article titled Robertson–Seymour theorem begins like this:

In graph theory, the Robertson–Seymour theorem (also called the graph minor theorem) states that the undirected graphs, partially ordered by the graph minor relationship, form a well-quasi-ordering.

I wonder about that. My understanding has been that this theorem states that the set of forbidden minors – the minimal elements – is in every instance finite. Is the statement above to be understood as implying finiteness? Michael Hardy (talk) 21:48, 27 May 2023 (UTC) Michael Hardy (talk) 21:48, 27 May 2023 (UTC)

References

Yes. Up to graph isomorphism. It's the "up to isomorphism" part that the "quasi" in wqo entails. —David Eppstein (talk) 22:36, 27 May 2023 (UTC)

Functional decomposition

Hi! Can somebody please have a look at the article Functional decomposition? It collects useful information about several applications of the concept (which does exist e.g. in software and systems engineering), and presents (in section 1) a mathematical theory seemingly intended to cover all applications. My impression is that this theory is pretty nonsensical from a mathematical point of view; I used my favorite tags {{clarify [span]}} to flag some issues. Since there are almost no inline references, I can't judge whether the theory is just poorly presented, or is WP:OR; I guess, the latter applies. - Jochen Burghardt (talk) 17:05, 23 May 2023 (UTC)

IMO, this is pure WP:OR. I have tagged the article inside {{multiple issues}}. I have also PRODed it. As the talk page is empty, it seems that nobody is really interested in this poorly and vaguely written article. If the article is dePRODed, one can nominate it to AfD. Another solution would be to redirect it to Polynomial decomposition, which is the only nontrivial theory on the subject (One of the sources of the latter article is called "functional decomposition", but, as far as I remember, it is only about polynomial functions). D.Lazard (talk) 18:21, 23 May 2023 (UTC)

It's not an article on mathematics, its an article about engineering. The right way to do it is very often bitterly argued on mailing lists and staff meetings. Getting it right means a pay-raise, getting it wrong risks getting fired. The article might feel like OR, but I'm pretty sure the topic will be explicitly discussed in undergrad engineering textbooks. I won't de-PROD it, but I think it would be fair to notify the owning projects (WP:M is not one of them, the WP:M banner does not appear on the talk page.) It would also be fair to remove the lead sentence "In mathematics...". I'll do these two things now. 67.198.37.16 (talk) 00:27, 27 May 2023 (UTC)

The article is now at AfD. See Wikipedia:Articles for deletion/Functional decomposition. D.Lazard (talk) 17:22, 28 May 2023 (UTC)

Ptolemy RM

There is currently an on-going requested move discussion pertaining to Ptolemy at Talk:Ptolemy#Requested move 25 May 2023 that might be of interest to this WikiProject. Walrasiad (talk) 17:11, 29 May 2023 (UTC)

Cone

Cone

Cone
A right circular cone with the radius of its base r, its height h, its slant height c and its angle θ.
Type	Solid figure
Faces	1 circular face and 1 conic surface
Euler char.	2
Symmetry group	O(2) × SO(1)
Surface area	πr2 + πrℓ
Volume	(πr2h)/3

This infobox tells us what the quantities r, h, c, and θ are, but not ℓ. Then it refers to ℓ in a formula. We are told c is the slant height. But the formula makes sense only if ℓ is the slant height. Then in the body of the article, the letter ℓ is used for the slant height and c for the circumference.

(And the callous indifference of many mathematicians to the typographical difference between things like O(2)×SO(1) and O(2) × SO(1) is appalling. What appears above is after I corrected it, changing the former to the latter. Why are mathematicians unaware of the fact that this kind of thing was central to the way Donald Knuth designed TeX, and for good reasons, and that its intended effect does not depend on its being noticed by the reader?) Michael Hardy (talk) 18:32, 29 May 2023 (UTC)

Errors in LaTeX

An error LaTeX

Just a technical problem. I was looking at the article Locally linear graph, but I found one of the sections, and in this section, there is an error LaTeX in the first paragraph that mentions the construction of Kneser graph algebraically. I've looked at the edit source, trying to add space between K and G in $KG_{a,b}$. When I tried to preview my edit, there is no error appeared. I don't understand how did this happen. Dedhert.Jr (talk) 10:03, 18 May 2023 (UTC)

This is probably due to a communication error between servers ("cannot connect to Restbase"). When such an error appear, the first thing to do is to reload the page, or, when editing, to hit again the preview button. In some cases, a wp:dummy edit could be useful for forcing a new compilation of the page ("compilation" is probably not theright technical term). This is probaly the reason of success of your edit tentative. D.Lazard (talk) 10:27, 18 May 2023 (UTC)

This should not be called "LaTeX", lest those who master it think they have learned LaTeX. Genuine LaTeX involves immensely more than the software used here. Michael Hardy (talk) 15:34, 30 May 2023 (UTC)

Jun 2023

Talk:Pascal's triangle#Addition of a section on the base of the natural log (e)

I would appreciate it if someone else could add their feedback here. --JBL (talk) 17:07, 1 June 2023 (UTC)

Requested move at Talk:Ultrafilter (set theory)#Requested move 1 June 2023

There is a requested move discussion at Talk:Ultrafilter (set theory)#Requested move 1 June 2023 that may be of interest to members of this WikiProject. PatrickR2 (talk) 05:08, 2 June 2023 (UTC)

Creation of a 'Women in mathematics' page

Hi all, would there be any appetite for creating a page for Women in mathematics (which is currently a redirect to timeline of women in mathematics)? This would be a pretty large project, requiring lots of research to be done, and which would hopefully parallel pages like women in engineering, women in computing or women in science. Things that might live on this page include history of women in mathematics, modern statistics for number of women studying mathematics at university (undergraduate, postgraduate) and women holding academic positions, factors discouraging women from pursuing mathematics and achievements of women in mathematics.

I personally identify as male, and so I couldn't do the topic justice myself. It would be really nice to have female-identifying contributors! For context I am a PhD candidate in mathematics, so I'm also not qualified on the history side. Zephyr the west wind (talk) 22:40, 1 June 2023 (UTC)

There are many books on this topic, so it should be easy to justify it as notable. Just avoid Osen's Women in Mathematics (for reasons that should be apparent if you read the linked article). See Category:Women in mathematics for related topics. —David Eppstein (talk) 23:26, 1 June 2023 (UTC)

The fact that it cites Lise Meitner as a mathematician rather than as a female chemist and physicist who did the work for which Otto Hahn got the Nobel prize is enough to raise my eyebrows. However, I find the author's focus on its subjects' victimization by society to be reasonable, given the history of misogyny. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:51, 2 June 2023 (UTC)

The focus is not the reason to avoid it. The reason to avoid it is that its biography of Hypatia is based entirely on a piece of children's historical fiction replete with faked quotes justifying early-20th-century-American moral values, and that it cannot even spell the names of three of its other subjects correctly. The issue with Meitner is another piece in the same puzzle. Nothing it says can be relied on. —David Eppstein (talk) 18:04, 2 June 2023 (UTC)

I also lack the history qualifications, but I would love to see someone with a suitable background doing such an article. Feel free to use this protest against misogynist prejudice.

It may be hard to prevent the article from being dominated by a single figure, given the importance of Emmy Noether's work, but there have certinly been quite a few major female mathematicians in recent centuries. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:51, 2 June 2023 (UTC)

I am strongly opposed to the "great woman" theory of women in mathematics, where we hear only about one or two superstars such as Noether and a few up-and-coming "science communicators". It would be as if we had an article ostensibly about mathematics that only told readers about Archimedes and the soldier on the beach, Galois's duel, and Euler going blind. There are some 1800 notable women mathematicians listed in List of women in mathematics. Most are accomplished professors and researchers but not superstars. Rather than focusing on a few personalities any such article should focus on broad trends, what barriers existed and still exist for women in the field, what resources are available, etc. —David Eppstein (talk) 18:09, 2 June 2023 (UTC)

It is certainly necessary to cover the many solid female mathematicians, but to ignore the superstars would create a false picture, just as ignoring Gauss would create a false picture of male mathematicians. That said, all of the issues that Zephyr the west wind mentioned are important. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 21:19, 2 June 2023 (UTC)

With that title it might also cover women in mathematics now, the gradual acceptance of women in maths aroud the world so now for instance in Sudi Arabia one can have news like this Saudi women making their mark in science where women graduates outnumber men in mathematics. NadVolum (talk) 18:54, 2 June 2023 (UTC)

Thank you for the responses. I've started a draft here Draft:Women_in_mathematics which as of me writing this comment is very bare-bones and which you are all welcome to work on! I will myself focus on finding concrete statistics for the time being. Zephyr the west wind (talk) 22:19, 2 June 2023 (UTC)

One possible resource for a particular era: [4]. —JBL (talk) 22:53, 2 June 2023 (UTC)

I think the history section should be split up into a collection of "key time periods" where the major advances/problems can be discussed. It seems difficult to avoid the "great women" story entirely, since early on so few women had any opportunities that they stand out like lighthouses. Perhaps a good narrative is to slowly transition the history section from "Great women" to "Democratization of academics" to reflect the progress in the form of the article itself.

It seems the key time periods are probably something like:

• Female mathematicians in antiquity (most famously Hypatia, although I'm sure a historial survey which didn't focus on "great women" would turn up many interesting things to discuss about how the average woman in antiquity knew/used a lot more mathematics than we suspect. Don't know any good sources for that though).
• "Pre-Noether"/Renaissance to Mid 1800s : Female mathematics during the period where academics was strictly the cultural domain of men. Main story beat here is Sophie Germain corresponding with Legendre and Gauss under a male pseudonym (later revealing herself to Gauss' surprise). Note that at this time academics was in most cases still dominated by wealth, and Germain for example was the daughter of a wealthy merchant. Other discussions: Nightingale's development of statistics and communication in mathematics outside traditional (male) educated circles;
• Noether/Late 1800s/Early 1900s: This is when it started to become more legally accepted that women could participate in academic circles, if not yet culturally. Main story beats are Sofya Kovalevskaya becoming the first full professor in Europe, Noether and her obstructions to formal academic position + her significant achievements. Other key figures being Ada Lovelace.
• Post-Noether/Contemporary: 20th century, when the real democratization of academics happened (due to massive expansion in access to education among all classes). Slow march towards equality of opportunity and outcome.

Could either include a discussion of the contemporary state of women in mathematics here, or in the following section of the article. Tazerenix (talk) 01:43, 3 June 2023 (UTC)

how the average woman in antiquity knew/used a lot more mathematics than we suspect: I am not sure that makes much sense. The "average woman" knew practically nothing about mathematics. That has not changed today, but neither did and does the "average man". The average person in the street is completely ignorant of mathematics. PatrickR2 (talk) 01:52, 3 June 2023 (UTC)

I don't necessarily mean median person. I was referring to the fact that many people used mathematics in ancient times for, for example, bookkeeping and transactions, and I highly doubt such behaviour was restricted only to men (although I of course don't have any sources to back this claim up). It seems like the sort of thing which should be investigated when writing the page to do due diligence to the history of women in mathematics. Tazerenix (talk) 02:06, 3 June 2023 (UTC)

Well, (not even taking about women here) bookkeeping and counting are not exactly mathematics. (and furthermore, in ancient times people engaged in such activities were part of an educated elite). But ok. PatrickR2 (talk) 03:11, 3 June 2023 (UTC)

On the use of Mathematics StackExchange and MathOverflow as references

I recently made some modifications to the Compactly generated space article that included the use of references to Math StackExchange for justification of certain results. Another editor then came along and removed all references to Math SE, based on the fact that WP:RSP lists the whole StackExchange network (to which both Math SE and MathOverflow belong) as "generally unreliable". For background, by their own admission: "I'm not a mathematician, I've just seen some previous discussions around stackexchange.". This brings up the question: Is is appropriate to use Math StackExchange (Math SE) or MathOverflow (MO) as references in Wikipedia mathematics article?

Here is the way I see it. Claims made in Wikipedia must be verifiable WP:V in reliable sources. But for mathematics the notion of "verifiable" could be viewed a little differently than in other fields. In mathematics, a verifiable source may mean a reference to a textbook or a peer reviewed journal (where we take it on faith that the result has passed scrutiny from some experts and is therefore reliable.) That's the usual and preferable case. Or if the first type of reference is not readily available, it could be a reference to a post on Math SE or MO that gives explanation and a detailed proof of a result. This type of post often gives very clear and in-depth justifications, with answers often written by experts in the field, with peer feedback visible to all. Most importantly, it is "verifiable" in the sense that anyone with the proper background can sit down with pen and paper and read a Math SE or MO post to verify it themselves instead of taking it on faith. And sometimes I find it beneficial to combine both types of references; for example, a textbook exercise stated without justification, together with a detailed explanation in Math SE/MO if available.

At the same time, I agree that the average post on the various stackexchange sites is not "reliable" for general Wikipedia usage. And even on the two math related sites, there is wide variation in the quality of the posts. The difficulty is to choose posts of sufficient quality, and it is a judgement call that would be hard to make by a WikiGnome with no expertise in the field. But if we make a blanket prohibition to use Math SE/MO references just because it's easy to enforce automatically, that would cause a loss of valuable information in support of claims in Wikipedia.

Finally, strictly speaking it may not be entirely prohibited, as WP:RSP also mentions: Context matters tremendously when determining the reliability of sources, and their appropriate use on Wikipedia. Sources which are generally unreliable may still be useful in some situations. And in WP:What "Ignore all rules" means: Don't follow written instructions mindlessly, but rather, consider how the encyclopedia is improved or damaged by each edit.

So, what is this community's opinion about this topic? PatrickR2 (talk) 02:46, 4 June 2023 (UTC)

Just to dismiss some of the rather arrogant comments, no I'm do not work as a mathematician but that doesn't mean I don't understand the nature of mathematical proves. Saying I'm a wikignome with no expertise in the field is a foolish supposition based on no evidence. It's true I am a wikignome, something I do as mindless distraction from whatever it is I do in the real world (which I have no interest in discussing). The issue in question is covered by WP:UGC and the previous discussions on WP:RSN 1, 2, 3. As I pointed out to PatrickR2 previously per WP:LOCALCON any discussion about this needs to happen on WP:RSN. -- LCU ActivelyDisinterested ∆transmissions∆ °co-ords° 14:26, 4 June 2023 (UTC)

At this point, I am just trying to gauge the opinion of the mathematics community (this Project in particular) regarding this issue. This is best discussed in this forum first, and not in WP:RSN. (Not it could also be discussed over there afterwards.) PatrickR2 (talk) 19:18, 4 June 2023 (UTC)

To clarify, when I said "no expertise in the field", I meant no expertise in the field being discussed. In this particular example, the topic was about general topology. I am competent enough to understand and discuss results in that field, but for example would not feel competent to understand some posts about algebraic geometry or analytic number theory. Similarly, someone is not well versed in general topology would not be equipped to judge the validity of MO/MSE posts in that particular field. PatrickR2 (talk) 22:06, 4 June 2023 (UTC)

Without taking a position on SE, I note that arXiv is also not considered a RS. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 15:50, 4 June 2023 (UTC)

Wikipedia:CALC is also relevant. In practice it gives wide latitude in math articles. But my understanding is that MathOverflow et al. are not Wikipedia:Reliable sources.

Now, if your goal here is to discuss changing that policy, then there are lot of details to work out. As I understand it, literally any garbage can be posted to MathOverflow. The site maintains quality through up-voting and down-voting by peers. So do you propose that we accept posts that meet a certain up-voting threshold, or what? Regards, Mgnbar (talk) 16:21, 4 June 2023 (UTC)

I don't dispute that anybody can post anything to MathOverflow or Math SE or any of the other stackexchange sites. We also cannot rely on a certain up-voting threshold, as that is not a necessary reliable indicator of quality (although there is some correlation). What I am saying is that there are some posts on Math SE or MO that are of high quality and provide valuable information in support of results stated in Wikipedia or valuable extra commentary on those. And it would be sad if we could not refer to them.

And I am also saying that there is no automatic way to decide what is good and what is not so good. It is a judgement call that is made on a case by case basis by people with the required background to judge the contents of these posts. But that is not that much different from classical types of references, namely an editor with the required background checks a paper in the literature or a textbook and refers to it. And in the rare cases that a later editor happens to double check it and sees that the referred paper said something a different, or that the textbook was not a correct source for the claim, it is then corrected. All I am advocating for is to be less legalistic, follow the spirit of the law. (I fully understand why these laws are there: nobody wants a bunch of random editors starting to put a bunch of random crap in there). PatrickR2 (talk) 19:35, 4 June 2023 (UTC)

I would suggest links to MathOverflow or Math might be better suited to the external links section. -- LCU ActivelyDisinterested ∆transmissions∆ °co-ords° 19:39, 4 June 2023 (UTC)

Could you expand on what that would look like? I am not quite sure I follow. PatrickR2 (talk) 19:50, 4 June 2023 (UTC)

Do you mean inline citation would instead refer to a note at the bottom, and the note at the bottom would say "See external links", and the external links section would have a list of relevant links to MO/MSE posts? PatrickR2 (talk) 19:53, 4 June 2023 (UTC)

No I still mean it shouldn't be used for referencing, but that it should be included separately in the external links section so as to direct readers to other sources that be helpful with the subject matter. -- LCU ActivelyDisinterested ∆transmissions∆ °co-ords° 19:59, 4 June 2023 (UTC)

Usually not in the external links section either, WP:ELNO point #10 is usually read as excluding such links. MrOllie (talk) 20:01, 4 June 2023 (UTC)

Eeurgh I'd missed that. -- LCU ActivelyDisinterested ∆transmissions∆ °co-ords° 20:02, 4 June 2023 (UTC)

Again, the lawyers here are speaking. In WP:ELNO it says one should generally avoid ... (notice the word "generally"). All your legalese is making Wikipedia a poorer source of information in my opinion. PatrickR2 (talk) 20:15, 4 June 2023 (UTC)

As I said below your reading of "generally" is the legalese reading. It's there for other exceptions, not so it can be ignored. But I think you're right in your other comment, I don't see that Math SE/MP should be treated as a social networking site (I may be wrong in that, but it doesn't seem to fit my understanding of a SN site). -- LCU ActivelyDisinterested ∆transmissions∆ °co-ords° 20:20, 4 June 2023 (UTC)

(aaaand David Eppstein showed I was wrong under in under three minutes) -- LCU ActivelyDisinterested ∆transmissions∆ °co-ords° 20:27, 4 June 2023 (UTC)

This isn't a enforcing a technicality - the spirit of the guideline is to prevent exactly this kind of thing. MrOllie (talk) 20:23, 4 June 2023 (UTC)

Also note that Math SE/MP are not "social networking sites". If anything, they are the antithesis of such sites. PatrickR2 (talk) 20:17, 4 June 2023 (UTC)

They are certainly social networking sites (as is Quora, for example). --JBL (talk) 21:46, 4 June 2023 (UTC)

See the quote at MathOverflow#Reception: Math Overflow is almost an anti-social network, focused solely on productively addressing the problems posed by its users. PatrickR2 (talk) 22:20, 4 June 2023 (UTC)

Or easier: no inline citation. Just add to the external links section a few MO/MSE links useful to the topic at hand. That would work out, in the sense that there is no direct claim of use as reliable source, and at the same time the information is readily available. PatrickR2 (talk) 20:11, 4 June 2023 (UTC)

No. WP:ELNO. It may not be a social networking site but it's a discussion forum, prohibited by #10. —David Eppstein (talk) 20:23, 4 June 2023 (UTC)

May I ask your opinion about WP:ELMAYBE: Sites that fail to meet criteria for reliable sources yet still contain information about the subject of the article from knowledgeable sources PatrickR2 (talk) 20:47, 4 June 2023 (UTC)

Not an exception to ELNO. —David Eppstein (talk) 21:39, 4 June 2023 (UTC)

Hmm, maybe. Maybe debatable, as MO seems more a question and answer site than a discussion forum. But thanks for your opinion. PatrickR2 (talk) 21:42, 4 June 2023 (UTC)

People make posts, comment on them, comment on the comments, upvote and downvote items, have user profiles that accumulate "badges" and "reputation"... it's not meaningfully different in operation from anything that WP:ELNO explicitly excludes. I've seen the occasional subreddit where the commenters are decently well-informed and maybe even subject-matter experts, but that doesn't make Reddit an exception to WP:UGC either. XOR'easter (talk) 23:00, 4 June 2023 (UTC)

On rare occasion when a stack exchange answer is written by someone considered a recognized expert in that specific topic, we can use that escape clause from WP:SPS. But most of the time they fail WP:USERGENERATED and do not count as reliable sources. The same thing is generally true for arXiv preprints that are not yet published, although more of those probably can be justified as being by recognized experts (especially in the cases of heavily-cited but unpublished arXiv preprints). —David Eppstein (talk) 19:43, 4 June 2023 (UTC)

I think this summarizes the situation pretty well. XOR'easter (talk) 22:53, 4 June 2023 (UTC)

Also, regarding WP:UGC, is says Content from websites whose content is largely user-generated is generally unacceptable. Notice the word "generally". It does not have an explicit prohibition to all UCG contents. Even WP:RSP says that such contents can be useful in some situations. PatrickR2 (talk) 19:44, 4 June 2023 (UTC)

That's not the get out you think it is, as with WP:IAR it's only meant for edge-cases (as with David Eppstein comment about WP:SPS above). -- LCU ActivelyDisinterested ∆transmissions∆ °co-ords° 19:49, 4 June 2023 (UTC)

We have that ambiguity in the guideline because we have carved out exceptions elsewhere. 'I would really like to use this cite' is not one of those exceptions. MrOllie (talk) 20:02, 4 June 2023 (UTC)

To be clear, WP:CALC is also not one of those exceptions. For basic arithmetic or simple algebraic manipulation, WP:CALC might justify the omission of any sources, but it does not justify using an otherwise-unreliable source. For more complicated mathematics, such as detailed proofs, WP:CALC does not apply. —David Eppstein (talk) 20:21, 4 June 2023 (UTC)

I think there is quite enough maths around for Wikipedia without needing ArXiv etc! However if they are cited in a reliable source or discussed in the news then that can well make them okay as WP:PRIMARY sources. If a recognized expert wrote something in ArXiv I'd still want a mention elsewhere but I think I could then extend to recognizing it as a reliable source without caveats. NadVolum (talk) 20:05, 4 June 2023 (UTC)

I agree with the revert at Compactly generated space. In particular, it looks to me like PatrickR2 took a bunch of cn tags from the article, posted them as questions on Stackexchange, and then used the solutions that resulted as references. This is not appreciably different than if I took a cn tag, wrote a blog-post about it, and then cited my blog -- an obvious violation of our policies. A more plausible use-case for Stackexchange with Wikipedia would be to make reference requests -- but then the books or articles that get dug up that way would be the references, not the SE post. --JBL (talk) 21:53, 4 June 2023 (UTC)

Perhaps WP:CALC should be modified slightly to include not just "routine calculations" but also "routine proofs"? It is clearly written with the intention of allowing expert editors to make straightforward justifications for claims in the text of an article without needing to find an explicit literature reference for every single detail. In that sense the only difference between "routine calculations" and "routine proofs"/"routine justification for a not especially complicated mathematical idea" is the level of the mathematics itself, and the Math wikiproject is already given plenty of leeway when it comes to that. From the perspective of mathematics, a routine proof or routine justification for an idea is often just as mechanical as a routine calculation.

At the very least, maybe WP:CALC could be clarified to explicitly describe what sorts of "routine" things are and are not acceptable? If the consensus is despite the mild benefit, we simply shouldn't cite Mathoverflow/SE, then thats a shame but lets write it down somewhere? Tazerenix (talk) 01:14, 5 June 2023 (UTC)

We have far too many detailed and unsourced workings-out of uninformative and routine proofs of the sort that undergraduates would often see in their undergraduate classes, probably added to Wikipedia by those same undergraduates. When a proof is particularly elegant, and including it would be helpful to reader understanding of the topic, it should also be easily sourceable. When a proof is just routine grinding through the details of an induction, it is not particularly helpful, and I would not want to encourage the addition of more such content. —David Eppstein (talk) 02:07, 5 June 2023 (UTC)

Totally in agreement with you on this. PatrickR2 (talk) 02:35, 5 June 2023 (UTC)

I meant, totally in agreement that we have too many detailed working outs of uninformative and routine proofs. On the other hand, it is often the case that mentioning some key ideas in the derivation of something, in addition to a sourced reference, can be useful in clarifying a concept. But cluttering Wikipedia with the full details of a routine proof does not seem optimal. If we cannot find a good source for a "routine proof", but one is available on MO/MSE, it would be a shame not to be able to use it. But like Tazerenix said, if that's what the community decides, it should be mentioned somewhere. PatrickR2 (talk) 02:47, 5 June 2023 (UTC)

We simultaneously have too many detailed derivations while also often missing crucial conceptual explanations, intuition, pictures, connections, historical discussion, ...

I chalk it up to: good writing is hard even for a focused professional writer or team with deep subject expertise, a well-defined audience, and a clear vision. Here we have a heterogeneous group of hobbyist volunteers writing for an unknown assortment of readers, piling bits on a hodgepodge of material accreted over years or decades, and trying to coordinate despite substantially varying goals and preferences.

Reading articles about basic technical topics here typically leaves me simultaneously frustrated thinking about how extraordinarily much better they could be if someone serious would be willing to devote a few dozen hours of sustained effort to each article, especially considering Wikipedia is often people's first destination to learn about something, but also amazed that it works as well as it does. –jacobolus (t) 05:15, 5 June 2023 (UTC)

I agree with this as well. I think proofs should generally be avoided, unless on a page for a specific theorem and it is possible to describe the proof (and even then not necessarily to give the proof) in a reasonably short span. (An extreme example of the bad way this can go, which also contains many routine parts, is at Monotone convergence theorem.) Gumshoe2 (talk) 05:54, 5 June 2023 (UTC)

Thank you all for the discussion. I will respect the consensus here: except for very rare cases mentioned by David Eppstein, we should not be using MO/Math SE as references in Wikipedia mathematics articles. PatrickR2 (talk) 17:37, 5 June 2023 (UTC)

Incidentally, while we were having this discussion, events have been taking place on StackOverflow, including MathOverflow: the management has decreed that most AI-generated content must be allowed, and in exchange the moderators have gone on strike. If the inability to block AI content continues, the site will be even less usable than before as a source. See [5]. —David Eppstein (talk) 06:46, 5 June 2023 (UTC)

@David Eppstein: I don't think you should ever hope to see any shred of honesty from Stackexchange, Inc. Michael Hardy (talk) 00:22, 6 June 2023 (UTC)

My first RfD

I have sent MathematicsAndStatistics and Mathematics and Statistics to RfD. Since this is a complicated case, I would really appreciate your input. (Currently it seems as if we might either keep them as redirects to Mathematics or setindexify them, but there isn't consensus yet.) Duckmather (talk) 18:26, 8 June 2023 (UTC)

Discussion is taking place here. Felix QW (talk) 18:39, 8 June 2023 (UTC)

What is the reason for suggesting that they be deleted? They are both getting hits, presumably from search engine results. Perhaps they should redirect to Mathematical statistics instead, if that's what people meany by searching for this pair of terms. Tayste (edits) 18:43, 8 June 2023 (UTC)

"Cumulative density function"

Currently Cumulative density function is a disambiguation page explaining that it's a misnomer resulting from confusion between Cumulative distribution function and Probability density function. Its deletion is proposed at Wikipedia:Articles for deletion/Cumulative density function. You can comment there. In fact, Google Scholar shows 53100 hits for that exact phrase, showing that even authors of scholarly papers are often so confused that they use that phrase. Thus it appears to me to be very useful as a means of correcting an appallingly widespread error. Michael Hardy (talk) 14:54, 14 June 2023 (UTC)

About an hour and a half after this message, the AfD was closed as "keep". --JBL (talk) 17:31, 14 June 2023 (UTC)

I have some concerns about the outcome here, which I've expressed at talk:cumulative density function#Disambiguation pages and common errors. --Trovatore (talk) 18:09, 14 June 2023 (UTC)

Should "Mathematics Subject Classification" (2020) be in "Authority Control"?

Current Wikidata has d:P3285 for the 2010 Mathematics Subject Classification classification. When this is updated for 2020 or a new property is introduced, the Template:Authority Control could populate MSC2020 ID from WikiData. While Authority Control seems to be mainly for Authors/Artists, it does include subjects from some National Libraries. The 2020 CSV file has 6603 entries, with 63 2-character prefixes and 597 3-characters ones. Partial Differential Equations (prefix 35) has the most descendants at 317, over Number Theory at 302. Based on What Links Here, Wikidata has less than 500 uses of P3285 currently. Comments? RDBrown (talk) 07:12, 15 June 2023 (UTC)

Why can't mathematicians spell?

I found this in the article titled Bessel function:

Plot of the Hankel function of the first kind H⁽¹⁾
_n(x) with n=-0.5 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D

I changed it to this:

Plot of the Hankel function of the first kind H⁽¹⁾
_n(x) with n = −0.5 in the complex plane from −2 − 2i to 2 + 2i with colors created with Mathematica 13.1 function ComplexPlot3D

Note:

n=-0.5 versus

n = −0.5

so both the horizontal spacing and the minus sign are different.

-2-2i versus

−2 − 2i

so horizontal spacing and the two minus signs and italicization are different.

I have been forced to learn that some otherwise conscious people don't notice that there is less space between the minus sign and the first 2 then between the second minus sign and the second 2, for a reason.

Not only in non-TeX mathematical notation in Wikipedia articles, and not only in Wikipedia's TeX-like software, but also in daily use of LaTeX on the job, mathematicians are incredibly callous about things like this, although when Donald Knuth created TeX he said it was for the purpose of making attention to things like this possible that he did that. And he succeeded brilliantly, and most mathematicians appear not to want to know that.

The reason why one font looks good and another looks horrible is a lot of tiny details that go unnoticed by people who nevertheless think the aesthetic differences are conspicuous. Yet one mathematician I know of, when his attention was called to one of those differences in detail, said he doesn't think anyone will even notice. You can't miss the point more completely: the effects of such details happen whether their cause is noticed or not.

Here I think a sort of literacy campaign for mathematicians may be in order. Michael Hardy (talk) 18:50, 14 June 2023 (UTC)

It's not a matter of literacy, it's a matter of style. And for 99% of people 2+2i and 2 + 2i is exactly the same thing. So 99% of people just don't care because they got the message across, even if not up to the stylistic standards of professional publishing. Headbomb {t · c · p · b} 19:10, 14 June 2023 (UTC)

@Headbomb: You are mistaken and you are naive. Notice that I said the many tiny differences of this kind are the cause of one font looking good and another looking bad. And there is probably no instance of this sort of thing that will not make the difference between understanding and failing to understand in at least some contexts. Michael Hardy (talk) 19:27, 14 June 2023 (UTC)

I've taught math and physics for well over 10 years now, included entire classes on how to style equations, variables, etc. My opinion is informed, no matter how much you dislike it. Headbomb {t · c · p · b} 19:30, 14 June 2023 (UTC)

I am certainly not convinced that everyone who has taught classes on this for a long time is well informed about at least some of the matters that I raised. Michael Hardy (talk) 19:40, 14 June 2023 (UTC)

Illustrating with one of your examples, I see that you now improved the result by tweaking for example the formula {{math|-2-2i}} by manually adding "&nbsp" around the minus sign to make some space around it and manually adding double quotes around the "i" to make it italic. The result looks ok, but it seems way too complicated for editors to do routinely. We should encourage people to take advantage of the automatic formatting provided by Tex and use <math>-2-2i</math>. The result will be both easier to maintain and perfectly formatted. PatrickR2 (talk) 19:23, 14 June 2023 (UTC)

@PatrickR2: . . . . . or maybe <math display=inline>-2-2i</math> Perhaps this is no longer as problematic as it used to be. In the past you could get some hideous font mismatches by doing that in an inline setting. Michael Hardy (talk) 19:29, 14 June 2023 (UTC)

I could be missing something, but I have never seen it to be a problem without "display=inline". PatrickR2 (talk) 05:33, 15 June 2023 (UTC)

The addition of display=inline is only needed when you want to force inline style per se, for instance if you have a sum like ${\textstyle \sum _{n=0}^{\infty }n.}$ If you just have a one-off fraction you can alternately use \tfrac, e.g. $\tan {\tfrac {1}{2}}\theta .$ Whenever the formula is already all on a line, display=inline doesn't make much practical difference, e.g. $e=mc^{2}$ vs. ${\textstyle e=mc^{2}}$ render the same. One place that the inline style is unexpectedly helpful is in making square roots take less vertical space, e.g. ${\sqrt {x^{2}+y^{2}}}$ vs. ${\textstyle {\sqrt {x^{2}+y^{2}}}.}$ –jacobolus (t) 15:30, 15 June 2023 (UTC)

Good to know. Thanks for the explanation. PatrickR2 (talk) 20:36, 15 June 2023 (UTC)

@PatrickR2: And just using TeX doesn't fully solve the literacy problem. If you write <math> X/\sim rather than <math> X/{\sim}</math> (referring to a quotient space of a space "X" by an equivalence "~", then you get an incorrect result: you see ${\textstyle X/\sim }$ where you should see ${\textstyle X/{\sim }.}$ The reason why that is software functioning just as it ought to function, for good reason, is something that too many users fail to understand. And many many other things like that. Michael Hardy (talk) 19:33, 14 June 2023 (UTC)

Seems to me like a pretty bizarre use of the words "spell" and "literacy"! Could you clarify to what extent you are speaking about something objective? From your comments so far, it seems like you just have some very strong personal preferences.

I think the much more serious problem is the inconsistent vertical/font alignment of latex. Is there a reason it's never been fixed? Gumshoe2 (talk) 22:57, 14 June 2023 (UTC)

Because the Wikimedia developers are at best indifferent to and at worst hostile to LaTeX-based mathematics markup. It has always been a badly-working patch while they wait for decades for MathML to take over. For a few years we had workarounds to let us run MathJax in place of their bad formatting but they killed them off. —David Eppstein (talk) 03:35, 15 June 2023 (UTC)

If they really want MathML then they need to do something about the repurposing of <math>...</math> for LaTeX. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 11:25, 15 June 2023 (UTC)

The section title is appalling: it begs the question and totally misleads the reader. Style may be important, but it is very different from spelling; the text presents no evidence that the literacy and spelling skills of mathematicians are in any way deficient, and, in any case, improving those skills would in no way address the stylistic issues that Michael Hardy is concerned with.

As a side note, mathematicians are used to dealing with journals that have house styles. Tweaking the markup in that context is pointless because the editors will change it after submission. Even articles submitted to arXiv are often intended for publication elsewhere. It's likely that habits relevant to journals carry over to text intended for wiki. -- Shmuel (Seymour J.) Metz Username:Chatul (talk)

Well at least the math tag defaults to using SVG now instead of generating png imge files. That is making the math template redundant at least, perhaps something can be done about that. I don't believe MathML has enough support in browsers to be the default - anybody got any ideas what on earth has happened with that effort? As to typing − versus -, I really don't feel like saying that all the mathematicians who came before Knuth or utf-8 can't spell! In terms of the literati of the future I give that a 👎. NadVolum (talk) 14:15, 15 June 2023 (UTC)

If the text is in the body of the article, the top example should be replaced by:

Plot of the Hankel function of the first kind $H_{n}^{(1)}(x)$ with $n=-0.5$ in the complex plane from $-2-2i$ to $2+2i$ with colors created with Mathematica 13.1 function ComplexPlot3D

Unfortunately LaTeX in captions breaks mediawiki (when a user clicks the image to see it rendered larger, the LaTeX does not render in the image viewer mode) so in this case Michael Hardy's version using math templates is the appropriate alternative. But the original version is also fine enough considering it was added by some untrained volunteer. The trivial spacing differences are not a big deal. Fix such formatting when you come across it and and then move on with your day. –jacobolus (t) 15:38, 15 June 2023 (UTC)

Also Michael Hardy's version contains four "& nbsp;" that are here only for making more difficult to read the source code, since Michael Hardy certainly knows that lines cannot be brocken inside {{math}}. D.Lazard (talk) 16:04, 15 June 2023 (UTC)

I'm pretty indifferent to extraneous explicit  s in the markup, but fair enough, you are right that ideally they should be left out. Either way, this doesn't seem like a reason to start a conversation here. Fix such problems case by case and move on with your day. –jacobolus (t) 19:08, 15 June 2023 (UTC)

So SVG doesn't work well if used in the caption of an image and one clicks on the image? That sounds like a solvable problem surely? NadVolum (talk) 17:21, 15 June 2023 (UTC)

Both the original code and your alternative are buggy. ComplexPlot3D is a function in the Wolfram language so should be typeset as code like other such language constructs: {{code|ComplexPlot3D}} typesets as ComplexPlot3D. --{{u|Mark viking}} {Talk} 17:46, 15 June 2023 (UTC)

Some people have objected to the word "spell." Since orthography consists of more than what is usually called spelling, just changing "spelling" to "orthography" ought to make it fully unobjectionable.

There do exist orthographic standards in mathematical notation. And mathematicians are usually callously indifferent to them and don't realize that they exist and have difficulty understanding why they ought to exist. But they make a practical difference. Donald Knuth, when he invented TeX, was absolutely clear that those have virtually the highest priority in his work on TeX. Failure to adhere to them does strike some people the same way bad spelling does. Maybe I will come back and try to explain why this is not all just subjective taste at some point. Some of the comments here seem like people belligerently insisting on a right to be ignorant. Michael Hardy (talk) 21:22, 16 June 2023 (UTC)

Does anyone know precisely what causes phantom scrollbars in <math display=block>?

Here are some recent examples that on my browser generate them (I'm not trying to pick on you user:sbb; your recent changes applying display=block to existing formulas were just already close at hand, so I didn't have to hunt around as much for examples):

$$J^{-1}={\begin{pmatrix}{\dfrac {x}{r}}&{\dfrac {y}{r}}&{\dfrac {z}{r}}\\\\{\dfrac {xz}{r^{2}{\sqrt {x^{2}+y^{2}}}}}&{\dfrac {yz}{r^{2}{\sqrt {x^{2}+y^{2}}}}}&{\dfrac {-(x^{2}+y^{2})}{r^{2}{\sqrt {x^{2}+y^{2}}}}}\\\\{\dfrac {-y}{x^{2}+y^{2}}}&{\dfrac {x}{x^{2}+y^{2}}}&0\end{pmatrix}}.$$

$${\begin{aligned}{\frac {d}{dx}}[\sin(x)+C]&={\frac {d}{dx}}\sin(x)+{\frac {d}{dx}}C\\&=\cos(x)+0\\&=\cos(x)\end{aligned}}$$

$${\begin{aligned}\langle -\Delta f,f\rangle _{L^{2}}&=-\int _{-\infty }^{\infty }f''(x){\overline {f(x)}}\,dx\\[5pt]&=-\left[f'(x){\overline {f(x)}}\right]_{-\infty }^{\infty }+\int _{-\infty }^{\infty }f'(x){\overline {f'(x)}}\,dx\\[5pt]&=\int _{-\infty }^{\infty }\vert f'(x)\vert ^{2}\,dx\geq 0.\end{aligned}}$$

$${\begin{aligned}\ln(z)&={\frac {(z-1)^{1}}{1}}-{\frac {(z-1)^{2}}{2}}+{\frac {(z-1)^{3}}{3}}-{\frac {(z-1)^{4}}{4}}+\cdots \\&=\sum _{k=1}^{\infty }(-1)^{k+1}{\frac {(z-1)^{k}}{k}}\end{aligned}}$$

$${\begin{aligned}t'&=\gamma \left(t-{\frac {vx}{c^{2}}}\right),\\[2pt]x'&=\gamma \left(x-vt\right).\end{aligned}}$$

$$n!_{(\alpha )}={\begin{cases}n\cdot (n-\alpha )!_{(\alpha )}&{\text{ if }}n>\alpha \,;\\n&{\text{ if }}1\leq n\leq \alpha \,;{\text{and}}\\(n+\alpha )!_{(\alpha )}/(n+\alpha )&{\text{ if }}n\leq 0{\text{ and is not a negative multiple of }}\alpha \,;\end{cases}}$$

$${\begin{aligned}\int _{0}^{\infty }{\frac {\sin t}{t}}\,dt&=\lim _{s\to 0}\int _{0}^{\infty }e^{-st}{\frac {\sin t}{t}}\,dt=\lim _{s\to 0}{\mathcal {L}}\left[{\frac {\sin t}{t}}\right]\\[6pt]&=\lim _{s\to 0}\int _{s}^{\infty }{\frac {du}{u^{2}+1}}=\lim _{s\to 0}\arctan u{\Biggr |}_{s}^{\infty }\\[6pt]&=\lim _{s\to 0}\left[{\frac {\pi }{2}}-\arctan(s)\right]={\frac {\pi }{2}}.\end{aligned}}$$

$${\begin{aligned}\int {\sqrt {a^{2}+x^{2}}}\,dx&={\frac {a^{2}}{2}}(\sec \theta \tan \theta +\ln |\sec \theta +\tan \theta |)+C\\[6pt]&={\frac {a^{2}}{2}}\left({\sqrt {1+{\frac {x^{2}}{a^{2}}}}}\cdot {\frac {x}{a}}+\ln \left|{\sqrt {1+{\frac {x^{2}}{a^{2}}}}}+{\frac {x}{a}}\right|\right)+C\\[6pt]&={\frac {1}{2}}\left(x{\sqrt {a^{2}+x^{2}}}+a^{2}\ln \left|{\frac {x+{\sqrt {a^{2}+x^{2}}}}{a}}\right|\right)+C.\end{aligned}}$$

In my browser, they not only cause an eyesore, but also hijack my mouse scrollwheel/touchpad scoll gesture so that it only scrolls the math container box rather than the whole page. It's incredibly frustrating.

They often show up with multi-line "align" formulas, big matrices, "cases", and other similar formulas, but not always and I can't figure out quite what distinguishes the formulas where they appear from the formulas where they do not.

Does anyone have any reliable workaround(s) to make them go away? –jacobolus (t) 01:45, 17 June 2023 (UTC)

Kindly (no picking received, understood), I have been been playing with such maths, trying to understand the scrollbars issues. I haven't nailed it down precisely, but I've noticed that adding [2pt]] after the \\ on lines the precede fractions has seemed to reduce or eliminate the scrollbars. Will test and get back...  — sbb (talk) 01:57, 17 June 2023 (UTC)

I see the phantom scrollbars as well, on Firefox 114.0.1 on Windows 10. -- King of ♥ ♦ ♣ ♠ 06:48, 17 June 2023 (UTC)

I see them on Microsoft Edge and Firefox on my laptop, but not on Safari on an iPad. It is definitely suboptimal. 100.36.106.199 (talk) 14:13, 17 June 2023 (UTC)

They also exist in iPad Safari, but scroll bars there auto-hide when not actively being scrolled. The content of the math boxes will still sometimes (not always) hijack your scroll gesture if you try to touch them and swipe your finger to scroll. –jacobolus (t) 14:22, 17 June 2023 (UTC)

For what it's worth, I use Chromium on Ubuntu 20.04 and there the behaviour is as jacobolus describes for Safari on iPad. Felix QW (talk) 15:35, 17 June 2023 (UTC)

Also exists on MacBook Safari. Similar to what Jacobolus describes, it's hidden until you deliberately attempt to scroll the content, then the scroll bar appears and sections of content move slightly as result. DB1729^talk 15:35, 17 June 2023 (UTC)

History of the separation axioms

This page, history of the separation axioms, is kind of strange. From what I can find, the given references don't say anything about the history of the separation axioms, other than these four sentences in Willard's book:

"The T2 axiom is included in the original list of axioms for a topology given by Hausdorff. The T0 axiom is usually credited to Kolmogoroff and the T1 axiom to Frechet or Riesz. Tietze was the first to use the term "separation axiom," in 1923. The T0 identification is due to M. H. Stone."

However, none of the above quoted content has made it into the wikipage. The content of the wikipage seems to be more like an essay contrasting the definitions made by different textbooks, and speculatively interpolating/suggesting a historical interpretation. At the end of the day I think it only beleaguers the simple point that different authors use different conventions ... which doesn't warrant a whole wikipage.

Unless someone would like to improve the article I will probably nominate it for deletion soon. Gumshoe2 (talk) 19:41, 16 June 2023 (UTC)

Please don't nominate it for deletion. The article, originally written in 2005, clearly explains the different and conflicting conventions that have evolved over time in the definitions of separation axioms (especially the inclusion of T_1 or not in the higher axioms). It mentions as landmarks for both categories Steen & Seebach (1970) and Kelley (1955), and refers to Willard as the more commonly used convention nowadays. So it is a very useful article in that sense. It is true that it is not an article about the history of each separation axiom (such a history is best kept together with each separation axiom article). But it is an article about how the separation axiom conventions have evolved over time, clearly explaining that there were (and still are) some of these differences and why and which is the more common convention nowadays. Very valuable to have this overview in one place. Maybe you would prefer a different article title to better reflect the contents? PatrickR2 (talk) 21:39, 16 June 2023 (UTC)

Also note that there is no dispute about the T0, T1, T2 axioms. All authors treated those in the same way, which is why no details are given about those in the article. The differences start with T3. PatrickR2 (talk) 22:20, 16 June 2023 (UTC)

Please correct me if I’m wrong, but all of the content about how the conventions have evolved over time is speculative, at best “original research.” I do agree that it’s good to have easily accessible information on the differing conventions, but that seems perfectly appropriate to about one paragraph’s worth of content on the separation axioms page. Instead of deletion I should have suggested merging the good content into that page (and then deletion). Gumshoe2 (talk) 00:05, 17 June 2023 (UTC)

There is nothing speculative about that. It's all a matter of looking at the sources and seeing what each author is using. It is true that not that many sources are cited in the article (maybe in 2005 the guidelines were not as strict?). But looking at all the classic textbooks for general topology (Hausdorff, Kuratowski, Dugundji, Kelley, Engelking, Bourbaki, Willard, Schechter, etc, etc) matches what's in the article. One additional reason that overall information is useful to have is that it is often confusing for newcomers to topology and it's good to spell out why Wikipedia made a certain choice and not the other one. As far as merging into separation axiom, that's a possibility, as long as we don't obliterate this useful information. PatrickR2 (talk) 00:50, 17 June 2023 (UTC)

It's all a matter of looking at the sources and seeing what each author is using. Is this not definitionally WP:SYNTH? --JBL (talk) 00:54, 17 June 2023 (UTC)

Reporting what each text says is probably OK. Speculating about why certain changes happened, or saying that there has been a general trend towards some point, would be advancing a new conclusion that no source has itself advanced first, which would be over the WP:SYNTH line. XOR'easter (talk) 14:41, 18 June 2023 (UTC)

I do not currently have any opinion on whether this information is verifiable and encyclopedic.

I do think that if it is, it is valuable, but seems to me to have a much better place on the seperation axioms page, where it is actually seen by the readers that are interested in it. Felix QW (talk) 09:34, 17 June 2023 (UTC)

Should all math articles be immediately switched from : indentation to <math display=block>?

User:Sbb (contribs) has recently been making large numbers of regular expression assisted changes to math and other technical pages, switching them in mass from : indentation style to <math display=block> instead. I asked them to stop doing this at large scale, because in my opinion it is of limited benefit, not an urgent problem to fix, and needs to be manually checked/fixed afterward which requires nontrivial effort from other editors, and is therefore unhelpful and disruptive to do quickly at wide scale. They have promised to continue such edits, saying (paraphrased) "don't tell me what to do". I'm bringing the conversation here, as the math wikiproject seems like the group of most direct interest in this topic.

User:Sbb, please desist from further edits along these lines pending some consensus here.

I have several problems with uncareful uses of <math display=block>:

• First, it often creates weird phantom vertical scroll boxes on blocks of mathematics that otherwise fit just fine on the page, and these intercept user mouse/touchpad scrolling to scroll the tiny box (which only scrolls by a pixel or two) instead of scrolling the page as intended. Tweaking the LaTeX markup to find an appropriate workaround so that these scrollbars disappear is fiddly and unpredictable, and takes a few minutes of going back and forth between preview and markup to fix each individual case. I don't know how to predict when/why this happens. Does anyone else know?

• Second, when formulas are placed to the left and floating images are placed to the right, if the content column gets narrow (e.g. in a narrow browser window), colon-indented math will be moved after the image while display=block will try to display to the left no matter how much the image and math block collide, and the block math box will get as narrow as necessary, showing a horizontal scrollbar to see the rest of the formula. If the formula is of moderate width, this is incredibly inconvenient to read. To work around this, editors often move images away from where they think would be the best spot or resize them to a non-optimal size to minimize the chance of creating a collision.

• Third, display=block always generates invalid HTML markup, because it puts a <div> inside a <p> element, but according to the HTML specification a <div> is not "phrasing content", and therefore cannot sit inside a paragraph. The browser responds by adding an implicit closing </p> immediately before the math block, and then also implicitly adds another opening <p> tag at the end of the paragraph. When block math is included in the middle of a paragraph of text this is especially problematic: the content of the paragraph after the end of the block math ends up being inserted into the HTML as a bare text node without any enclosing element, breaking CSS's ability to style it. The workaround is to always surround display=block by blank lines. The resulting HTML is still invalid (still tries to put a <div> inside a <p> element) but at least the rest of the paragraph ends up inserted into the HTML as intended. Any large-scale use of <math display=block> should adopt this workaround, pending fixes to mediawiki (don't hold your breath for fixes; this issue was reported in 2017). Otherwise editors have to come and manually add the blank lines afterward. See user:jacobolus/math block example for a bit of detail.

• Fourth (and somewhat less importantly), display=block has more vertical whitespace padding than colon-indented math, and on pages with many formulas, this is sometimes space wasting and somewhat ugly. In some cases formulas should be manually combined using \begin{align} ... \end{align}. In other cases this can be worked around using {{bi}} or the like. Again, any intentional fix takes quite a bit of manual work to do.

Overall, my impression has been that there is not any consensus at this wikiproject that all colon-indented block math in math articles must be switched to <math display=block>. I find such changes to many pages on short time scale to be distracting and unnecessary. But I am curious what other editors here think about it. –jacobolus (t) 17:51, 15 June 2023 (UTC)

Accessibility is not optional. MOS:ACCESSIBILITY demands that we not use : for indentation. Editors who improve the accessibility of our articles should not be discouraged from doing so. There are other alternatives that we can use in place of display=block or : – another that I often use is {{bi|left=1.6| ...math... }}. All three of these alternatives are problematic in different ways but that can be laid at the feet of the Wikimedia developers who refuse to put any effort into improving our mathematics capabilities. —David Eppstein (talk) 19:05, 15 June 2023 (UTC)

Unfortunately {{bi|left=1.6|<math>..</math>}} turns out to cause its own problems: it creates a box that gets cut off on the right in a narrow browser view and isn't scrollable at all, leaving especially some mobile readers unable to see the whole equation. Is there some other workaround? Can we make some alternative indentation template?

What is the precise accessibility issue with colon indentation? Something about screen readers speaking? Can someone demonstrate concretely what the difference is between math with vs. without colon indentation? Are the display=block formulas actually accessible by screen readers? How are they rendered in speech? Is it coherent and legible? Are there other ways to add explicit fallbacks that are directly intended for clear audio rendering? –jacobolus (t) 19:16, 15 June 2023 (UTC)

The accessibility issue is that it gets marked up in html as the definition of an entry within a list of definitions rather than as an indented piece of content. So content readers based on the semantic markup of an entity rather than on the visual rendered appearance will not be likely to handle it correctly, because the semantic markup says that it has a different purpose than its actual purpose. —David Eppstein (talk) 19:24, 15 June 2023 (UTC)

Is there a concrete example of what screen readers actually do with each version? What is the actual spoken content in each case? –jacobolus (t) 19:40, 15 June 2023 (UTC)

I knew it. Based on the discussion at my talk page, I sensed User:jacobolus wasn't going to represent the discussion fairly or honestly. It is a flat-out smear to summarize the discussion as They have promised to continue such edits, saying (paraphrased) "don't tell me what to do".

For some reason, User:jacobolus is concerned that I use a regex to find colon-indented math blocks at the beginning of a line. He noted it here (regular expression assisted changes), and twice characterized it as script changes, when I specifically reiterated, multiple times, that I specifically read each pattern match before replacing, to make sure I don't include apparent block-math with following wikitext (such as refs, equation numbers, etc.).

As I summarized in that discussion, both MOS:INDENT and MOS:INDENTGAP say don't abuse colon-indent, as well as Help:Displaying a formula#Block stating <math display="block"> is the way to do it. Yes, poor HTML5 is produced with display="block", but that can be fixed in the Math plugin code. Conversely, the colon-indent will never be fixed in the wikitext parser.

As I stated, I am absolutely willing to also make more substantial edits to articles. But I am primarily a gnomish editor, and User:jacobolus can't berate and brigade me because he doesn't like what I edit, when they are all constructive edits. I'm pretty sure this forum isn't the place for this; my edits are constructive, and it's not up to any individual user to require me to get consensus from a WikiProject, when I'm not violating WP:PRESERVE.  — sbb (talk) 19:17, 15 June 2023 (UTC)

That was intended as a quick summary not a "smear". Please stop with your own personal attacks. I will directly quote you if it helps. I politely asked you to please stop making many such edits in quick succession, pending a discussion arriving at some wider consensus, and you said:

IMO, replacing invalid HTML5 markup–generating wikitext with recommended best practice doesn't need consensus. And I'm going to continue WP:BOLDly fixing them. [...] At any rate, respectfully, no, I don't intend to stop. [...] I'm not going to ask you for permission before I edit. [...] I'm not going to justify my edits, where I choose to focus my efforts, to you. Stop asking me to defer to what you want. [...] Do what you need to do. I'm going to continue to edit where I think it's necessary.

I thought that "don't tell me what to do" was a reasonable one-sentence paraphrase of the above. But again, you trying to turn this into some kind of personal tit-for-tat is all an off topic digression from the subject of this conversation. My point here is to reach some kind of community consensus about how block math should be treated and whether it should be changed at wide scale right now instead of handled gradually case by case in the course of other edits, not to start some kind of personal dispute. A request to reach community consensus before making sweeping changes is a fundamental norm of Wikipedia collaboration, not intended to be a personal attack. This Wikiproject is the most appropriate venue for this discussion (see WP:SEEKHELP), not "brigading". –jacobolus (t) 19:25, 15 June 2023 (UTC)

I really don't want to go back and forth with you. But your I thought that "don't tell me what to do" was a reasonable one-sentence paraphrase of the above is not at all a reasonable summary of the discussion, when I continually said that I was absolutely willing to make more edits to those articles, or other steps you might suggest. But your one-sentence summary paints me as unwilling to discuss, interact, or come to a compromise. And when you kept mischaracterizing my edits as "script assisted", and damned me with faint praise by comparing me to another bot-mimicking user who has now wasted thousands of hours of volunteer cleanup effort... . And yet I'm the one making personal attacks? No, I am not.

I agree, the back-and-forth tit-for-tat must stop. I hoped it would have stopped on my talk page. But don't you dare try to open a topic like this here a project talk like you did, with absolutely ZERO WP:GOODFAITH in my intentions or contributions, like you did. I'm done conversing with you about this, I don't think there's anything more productive you and I can say to each other in this matter.  — sbb (talk) 19:46, 15 June 2023 (UTC)

Yikes. Please try to re-read more charitably, and not try to imagine a personal attack in every part of every comment. I swear to you that not a single one is intended.

I'm sorry, it is unfair of me to take my frustration with other script-assisted editors making large-scale changes (who have cost other Wikipedians thousands of hours and me tens of hours of cleanup) out on you. I was not trying to directly associate you with those other scripts or editors; my point bringing it up was just that semi-automated changes are relatively cheap while coming back and manually inspecting/undoing such edits if necessary takes dramatically disproportionally more effort. Therefore, I think it's important to be extra careful to get it right up front.

continually said that I was absolutely willing to make more edits – I just wanted to have some kind of community discussion about the best approach forward before you invest a huge amount of time into making changes and before I invest a huge amount of time into trying to check them one by one. We can together as a community decide if such effort is helpful/necessary, and perhaps collectively we can come up with some solutions to any problems created. I am not trying to question your motives or belittle your effort.

I wish I had a clear idea of extra steps you could take to not get phantom scrollbars (which have showed up on many of the pages you changed); does anyone know an easy way to avoid them? My method of adding weird LaTeX spacing tweaks to work around the problem is not reliable and takes a lot of fiddling.

One concrete thing I would ask, if you insist on changing block math at scale: would you please add a blank line after any block math formula that you turn to? Otherwise the text content afterward gets inserted into the HTML as a blank text node, not inside any paragraph. This makes it completely impossible for anyone to style it with CSS. –jacobolus (t) 20:09, 15 June 2023 (UTC)

I'm sorry, it is unfair of me to take my frustration with other script-assisted editors making large-scale changes ... "other script-assisted editors", but not me. I see. Please, police your wording if you're actually apologizing. Again, I'm not a script-assisted editor, so "other" means nothing in this context.

(who have cost other Wikipedians thousands of hours and me tens of hours of cleanup) out on you. I was not trying to directly associate you with those other scripts or editors; ... Yet, you keep lumping me, in your set-associative language (with "those other, but not you" (meaning, me) ...), but still characterizing me as a script-editor that you seem to hold with disdain or derisiveness.

Look, it's quite simple: I, or any other editor, script-using or not, am not making/requiring you to do anything. You don't have to edit WP. You don't have to review a single one of their, or my, edits. You keep talking about "thousands of hours" (eyeroll of eyerolls) that you and your fellow put-upon guardians against the chaos (this is the subtext I read from you, with little exaggeration) must endure. You don't have to do anything. Please stop victimizing yourself with my WP editing. Please!

my point bringing it up was just that semi-automated changes are relatively cheap while coming back and manually inspecting/undoing such edits if necessary takes dramatically disproportionally more effort. Therefore, I think it's important to be extra careful to get it right up front. To the extent that doing semi-automated changes (which, I'm not), yes, it's important to get it right. And in this case, I'm sorry to say that you aren't correct. Rather, you and I differ on opinion; and I'm totally backed by MOS and documentary direction. Nowhere in MOS / MOS:Accessibilty does it say that editors should hack wikitext to achieve visual goals at the expense of semantic correctness (for as much as wikitext (and/or template wrapping) provides semantic correctness).

I just wanted to have some kind of community discussion about the best approach forward before you invest a huge amount of time... my time is my time, please. No need to presume to speak for me. ... into making changes and before I invest a huge amount of time into trying to check them one by one. What you choose to do with your time, likewise, is up to you.

We can together as a community decide if such effort is helpful/necessary, and perhaps collectively we can come up with some solutions to any problems created. Consider this: I'm not doing anything wrong. You have chosen to allow yourself to be put out by me. In that reframing, do you not see that you are the one making "any problems created"? Again, you don't have to check me. At all. You can choose to just... not.

I am not trying to question your motives or belittle your effort. Sincerely, and without snark, thank you. And in the grand scheme of things, truly, I don't think you are, AT ALL. But I do think you're convinced that you're so right, that you need me to stop editing, until you're convinced that I'm actually making semantic improvments to wikitext. Here's the thing: it might be that neither of us are objectively right or wrong in our positions. Where does that leave us? Frankly, it leaves us with you doing your thing, and me doing mine. And hopefully, we can try to come to a mutual understanding. Speaking of which, let's address that...

I wish I had a clear idea of extra steps you could take to not get phantom scrollbars (which have showed up on many of the pages you changed) I appreciate that, and while they suck, I have to admit, I'm not very concerned about them. By that, and let me be clear, I intend on making better semantic improvements to wikitext, with less concern towards mitigating specific browser bugs, etc. I spent a lot of my earlier programming career HTML & CSS hacking to get around IE/FF discrepancies in presentation, and I'm done with it. My job as Wikipedian is to produce the best possible wikitext, with the least sacrifices to accessibility, with the faith that eventually parsing and presentation bugs get fixed in the MW engine and plugins. But tweaking wikitext to massage presentation is a fool's errand, and I won't cotton to it. I just won't. I've been around that block waaaay too many times. It's a de-stabilizing effort, to accede to poor input just to mollify the existing bugs in software. Commit to correct input, and thereby lampshade and shine a light on how the system isn't producing the right output, rather than hide the bugs with workarounds and mollycoddling.

One concrete thing I would ask, if you insist on changing block math at scale: would you please add a blank line after any block math formula that you turn to? Otherwise the text content afterward gets inserted into the HTML as a blank text node, not inside any paragraph. This makes it completely impossible for anyone to style it with CSS Finally, after many repeated offers and requests by me, have you suggested compromise or meeting you halfway. This is a reasonable request, truly. However, I'm initially inclined to deny it, at least prior to discussion and consideration. Let me explain...

I have been making article-wide changes by mass-replacing colon-indented math blocks, but aside from that, trying to minimize my additional impact. Ideally, in those changes, literally all you would see is s/^: *(\<math)/$1 display="block"/ -type changes (if you're sed-saavy). Many articles with <math> tags with prepended ":" don't have blank lines around those math block; many other articles do have blank lines around them.

• Semantically speaking, from a wiki-text–parsing standpoint, there shouldn't be blank lines around block-displaying <math>. This is because, although presentationally-speaking, the CSS is displaying them as blocks, linguistically/syntactically, they're not separate paragraph objects. They are absolutely part of the sentence(s)/fragments that lead and/or follow them. So normally speaking, wikitext blank lines indicate paragraph breaks.
• However... I fully realize and understand what's happening with blank lines (or the lack thereof) around <math> blocks. And yes, the behavior is different when disply="block" is applied. I get that. And no, it shouldn't be, I agree.

So... to that end, I'd absolutely like to know, what is the suggested path to take with regards to <math display="block">? Should those blocks be separated by blank wikitext lines, or not? IMHO, I'd prefer they would be separated by blank lines, trusting the Math-plugin parser to be fixed to not introduce empty <p> tags before/after, like "works" with :<math> surrounded by blank lines.

But inasmuch as this has become a huge distraction for me, when I truly try to minimize the additional edits I make, I'm a bit hesitant to go adding blank lines around colon-indented math blocks, simply because I'd prefer to just minimize other changes, for fear of going through the sturm und drang like we're doing now.

I'll happily submit to larger input, and blank-line pad my math block edits, if there's a hint of consensus which way it should be in semantic wikitext. Truly and respectfully.  — sbb (talk) 02:59, 16 June 2023 (UTC)

I'm not very concerned about [ugly phantom scrollbars that hijack users' attempts to scroll the page] [...] My job as Wikipedian is to produce the best possible wikitext, with the least sacrifices to accessibility, with the faith that eventually parsing and presentation bugs get fixed in the MW engine and plugins.

We should be very concerned with those. Wikipedia exists for readers, not for some kind of platonic ideal machine ingesting markup to reach enlightenment. We should try our best not to generate pages that are worse for nearly all readers today (except possibly some screen reader users whose specific problems I still do not have a clear understanding of) in the hopes that they might be better for some hypothetical readers in an uncertain future.

We could just as well wait until "eventually parsing and presentation bugs get fixed", whereupon we can all together have a barn raising effort to fully adopt a working solution site-wide. I'd be happy to contribute substantially to that. But it seems just as likely that these bugs will not get fixed for years or perhaps ever, and then by making a mass switch all of our readers will just be indefinitely stuck with result which is worse than the previous version.

Wikitext markup isn't what is shown to readers. What readers see is HTML as rendered by their user agents (browsers or other tools).

"Semantic" purity of Wikitext (or any other document format or other kind of nontrivial human or machine interface in use ever anywhere) is an impossible pipe dream. Rendering legible (and yes, accessible) pages requires piles of workarounds and hacks, just as there are piles of workarounds and hacks at every level from bare machine metal on up – you'd be amazed at the impurity compiler writers, language implementors, network hardware/software, browsers, display driver authors, etc. have to put in so that you can [mostly] not have to think about how much stuff is happening for you to read this page – and web authors including wiki authors are sadly are not exempt from that.

Many articles with <math> tags with prepended ":" don't have blank lines around those math block; many other articles do have blank lines around them.

A line-leading : is always interpreted in mediawiki as starting a new block-level element, and new block elements in mediawiki such as lists, headings, etc. are indifferent to separation by (zero or one) blank lines. So adding or removing blank lines around :<math>...</math> makes absolutely no difference to the HTML rendered as output, and presence or absence of blank lines does not express any kind of authorial intent one way or the other. This is just the same as the way I can add double spaces after sentences or pad section headings like either == Heading == or ==Heading== without any effect. Ideally the mediawiki software would also output well-formed HTML when encountering <math display=block> irrespective of the preceding or following text. But sadly it does not.

linguistically/syntactically, they're not separate paragraph objects.

This is true in a certain very pedantic sense, but that's because mathematical typography (and in general text with intra-paragraph block elements) has conventions which are not at all aligned with the basic design choices of HTML. There's a mixup of two different things here, first the logical structure of the text, and second the presentational structure (a tree structure consisting of boxes positioned relatively to each-other) browsers use to render the page.

Ideally any table, block quotation, figure, list, formula, etc. could be stuck into the middle of a "semantic paragraph" while still rendering as a separate block, and the user agent would know that the block element should be pulled out of the ordinary flow and rendered on a separate line (optionally centered, indented, boxed, or whatever else), but that inline content afterward should subsequently continue as ordinary following lines, not treated as the beginning of a new paragraph.

Unfortunately, HTML was not ever designed to work that way, and in practice effectively never does work that way. Instead, it has a strict distinction between "phrasing" vs. "block" content, and the latter is not allowed in paragraphs. Nearly everyone who outputs HTML, including every mediawiki author, is stuck expressing their block-presenting elements as separate blocks, and using the content within multiple <p> elements to implicitly create "semantic" units across markup-element boundaries. This applies not only to math content but also to lists, tables, figures, etc.

Feel free to take it up with the original creators of HTML and CSS. –jacobolus (t) 06:41, 16 June 2023 (UTC)

re: [ugly phantom scrollbars that hijack users' attempts to scroll the page]: We should be very concerned with those. Wikipedia exists for readers, not for some kind of platonic ideal machine ingesting markup to reach enlightenment. I am concerned with them, yes, to the extent that I want those issues to be fixed. But I am not willing to commit to hacking wikitext to get it done. The correct place to fix it is in the Math extension parser/generator.

We could just as well wait until "eventually parsing and presentation bugs get fixed", whereupon we can all together have a barn raising effort to fully adopt a working solution site-wide. I'd be happy to contribute substantially to that. That's not how this wiki project has ever really worked. We write and edit IAW what the parser, MOS, and Help pages advertise and suggest. That's what I'm working with and towards.

Wikitext markup isn't what is shown to readers. What readers see is HTML as rendered by their user agents (browsers or other tools). Correct, absolutely. And in order to help the parser & plugins generate the best possible HTML+CSS, we should try our best to create the best possible wikitext as input. Clarity of intent (input) helps drive better improvement and fixes to the output. We shouldn't be trying to fuzz the parser with production content in order to massage the best output. That leaves cruft and clutter around for years when the parser bugs eventually get fixed. That's why metric boatloads of inline <math> content have trailing "\, " in order to pad them out from surrounding inline text, when instead, it should have been (and eventually was) fixed in either the generated math output or the math CSS.

"Semantic" purity of Wikitext (or any other document format or other kind of nontrivial human or machine interface in use ever anywhere) is an impossible pipe dream. As an absolute, sure, it'll never be 100%. But let's don't dismiss all of the tools that marginally improve semanticness. There are a lot of words in MOS:EMPHASIS to explain several ways to italicize text, but they explain clearly, using the word "semantic" frequently, to not use '' or <i>...</i> to italicize text that is meant to indicate emphasis, and rather to use {{em}} or <em>...</em> to semantically mark up the content, which also happens to italicize it. Etc., etc., for everything else in wikitext that needs to be indicated with semantic meaning.

Rendering legible (and yes, accessible) pages requires piles of workarounds and hacks, just as there are piles of workarounds and hacks at every level from bare machine metal on up – you'd be amazed at the impurity compiler writers, language implementors, network hardware/software, browsers, display driver authors, etc. have to put in so that you can [mostly] not have to think about how much stuff is happening for you to read this page – and web authors including wiki authors are sadly are not exempt from that. Spare me. I've designed circuits, written entire parsers with metatemplate programming, written hypervisors and emulators, network stacks, and hardware drivers. I know what's involved. And in every case, every layer is an abstraction to hide the tough and gritty details, to make it cleaner and easier for the next person up the stack to use.

Wiki editors are not web developers; we shouldn't be asked to be, nor should we rely on our lower-level knowledge to hack the wikitext to massage the output, when instead we should report bugs, and let the development process work. When you put on your wiki-editor hat, you are committing to producing wiki content. You might know what's going on under the hood, which is great. But bodging wikitext as a matter of practice is not something we should be doing. And it's certainly not something we should be trying to build sub-community consensus around.

Community consensus should be aimed at best practices. Best practices don't always yield perfect results, but they produce consistently better results than without them. The metric of "consistently better", of course, is up to community judgement. There's compromise involved, and faith and judgement that the tools' bugs will get fixed. Without that faith, we might as well just drop back to nested table layouts and pixel twiddling. We're not going to do that, and I'll fight such inclinations, or their analogues, every step of the way.

Many articles with <math> tags with prepended ":" don't have blank lines around those math block; many other articles do have blank lines around them. A line-leading : is always interpreted in mediawiki as starting a new block-level element... Immaterial. I'm removing colon-indent math blocks as I go, leaving it semantically better.

and presence or absence of blank lines does not express any kind of authorial intent one way or the other. This is just the same as the way I can add double spaces after sentences or pad section headings like either == Heading == or ==Heading== without any effect. You're missing my point about blank lines. You're talking about blank lines separating block-level content. In wikitext, consecutive lines of text, without blanks in between them, become a single HTML (and conceptual) paragraph. Editors writing sentences with block-layout math interspersed, if they don't put blank lines surrounding the <math display="block">...</math> tags, aren't doing anything wrong. Yes, the Math extension is generating poor HTML, as you have noted (and has nothing to do with [taking] it up with the original creators of HTML and CSS). But that needs to be fixed in the extension. I don't think it's justifiable to make a consensus policy against legitimate, should-work-as-advertised wikitext, just because some of us might be fatalistic about the bug ever getting fixed.  — sbb (talk) 14:53, 16 June 2023 (UTC)

concerned with them, yes, to the extent that I want those issues to be fixed. But I am not willing to commit to hacking wikitext ... – It sounds like your alternative plan is to leave them strewn across all technical articles on the site and shrug about it, vaguely hoping someone else will eventually deal with it. Are there other concrete steps we can take here as a community to push on this? I personally find these scrollbars very ugly and annoying, and I think they make Wikipedia seem unprofessional.

That leaves cruft and clutter around for years when the parser bugs eventually get fixed. That's why metric boatloads of inline <math> content have trailing "\, " in order to pad them out from surrounding inline text, when instead, it should have been (and eventually was) fixed in either the generated math output or the math CSS. – This supposed "cruft and clutter" has never harmed anyone throughout its lifetime, but its inclusion meant that for many years (a decade?) the content appeared as intended despite poor technical choices in the platform. It is excellent that authors adopted such "cruft" to fix their pages as a workaround for technical shortcomings; as a result readers were able to read pages with better, more consistent typography – both when they were written and still today – instead of living with wonky rendering inconsistencies violating authors' intentions. Once the technical issue has been resolved resolved it's fine to now eliminate vestigial "cruft" at leisure, a bit at a time, but there's no particular hurry because it doesn't cause any significant problem to just let it continue to sit doing nothing.

You're talking about blank lines separating block-level content. In wikitext, consecutive lines of text, without blanks in between them, become a single HTML (and conceptual) paragraph. ...

In wikitext, a line beginning with : always indicates a new block-level element. Whether or not it is offset by blank lines does not make any difference to the output. Whether authors add blank lines around their :<math>...</math> lines is not inherently meaningful, and should not be interpreted to mean any particular thing.

But that is all somewhat irrelevant. As a general rule, in mathematical typography, block math is semantically part of the previous sentence. Readers can infer this from the punctuation and phrasing used. But in HTML (both at Wikipedia and pretty much everywhere else on the internet), block math is encoded in markup using separate block level elements, with text afterward encoded as a separate paragraph.

Or sometimes, as in the wiki bug I am complaining about, authors write it using invalid markup as a <p> element with a block-level element nested inside which the browser proceeds to break by implicitly closing the <p> before the block element and then inserting any trailing part of the paragraph as a bare text node not inside any <p> element. Then the authors are left puzzled if they ever try to style their paragraphs with CSS and some part of their content is left unstyled because their markup is broken.

If you want to "fix" this so that "pure semantic HTML" is properly interpreted, feel free to go tell Google, Mozilla, Apple, and the W3C that their HTML specifications are all broken and they should change this behavior which has been baked into browsers for decades because it is incorrect and you aren't willing to "hack" your HTML to work in browsers because you intend for someone external to eventually fix it so that you can continue to purely convey your intentions. They will ignore you, or if you are lucky they will patiently explain that backwards compatibility prevents such a fundamental change to browser parsing. –jacobolus (t) 15:42, 16 June 2023 (UTC)

It sounds like your alternative plan is to leave them strewn across all technical articles on the site and shrug about it, vaguely hoping someone else will eventually deal with it. You seem bound and determined to undermine what little common ground to discuss this we've built, by going back to passive-aggressive and undercutting barbs. Please stop.

Are there other concrete steps we can take here as a community to push on this? Yes. The Phab ticket(s) you linked to (or opened, I can't recall, and really ATM, I can't be bothered) are a great place to get people to ping the devs about the issue. Advocate for that. I'm on board. I'll try to carve out time later to figure out what I have to do to chime in on Phabricator.

In wikitext, a line beginning with : always indicates ... Please, stop talking down to me about block content. I know what block content is. In wikitext, a line beginning with a : always results in a <dl><dd>, full-stop. And that's not going to change. The base wikitext parser has been immutable on that score, and it's safe to assume it always will be. Ignore the colon, because standalone colons (i.e., not part of a description list) are going away. That's the whole entire reason for this conversation you dragged me into against my will. Follow the MOS and documentation.

If you want to "fix" this so that "pure semantic HTML" is properly interpreted, feel free to go tell Google, Mozilla, Apple, and the W3C... Stop telling me to "feel free" to contact orgs outside of WP. That's the 2nd time you did that, in a row. I don't have a problem with browser devs, WhatWG, or even MW devs for that matter. They aren't my problem.

This discussion has gone on long enough. We're back to arguing round and round. Either get your consensus to enjoin me from editing IAW MOS:INDENT, MOS:INDENTGAP, and Help:Displaying a formula#Block, or drop it.

With regards to adding blank lines around <math>...</math> blocks where none existed before, as I said earlier, that's a reasonable request, but I'm not convinced of the merits of it. I will consider it.  — sbb (talk) 16:19, 16 June 2023 (UTC)

Nobody is talking down to you. I repeated my previous point again because you ignored it the first time and talked past me. And now you have ignored it again a second time.

The point is, when you look at existing wiki pages with the intention of switching colon indentation to <math display=block>, you cannot (and should not try to) draw any meaningful inferences about author intent from whether or not there are blank lines surrounding block math. Those do not now (and should not in the future either, once this bug is fixed) make any difference to HTML output, which should ideally be something like:

<p>some leading text</p><div class=math><svg>... formula ...</svg></div><p>some trailing text.</p>

Until this bug is fixed, adding blank lines after math blocks makes the HTML output significantly less broken than not adding them (though still slightly broken). Once the bug is fixed – years from now if ever – those blank lines will no longer make any practical difference to the HTML output and will at that point only be an aid to legibility of the markup. That's just fine. –jacobolus (t) 16:37, 16 June 2023 (UTC)

I have ignored your digression about HTML phrasing and flow elements, because you're assuming it must always present breaking <p>...</p> tags around math blocks. There's no reason to presume that the Math extension fix won't use nested <span> tags (like is currently done for non–display=block math) with the inner one using class="mwe-math-mathml-block" instead of class="mwe-math-mathml-inline".

It can be made to emit correct HTML5, and made to respect blank wikitext lines before, after, both, or neither, around the <math> block. All other navel-gazing about it is not productive here. These details need to be hashed out at Phab.  — sbb (talk) 19:16, 16 June 2023 (UTC)

I am assuming that Wikipedia body copy should be inside <p> elements, that is correct. That is how all ordinary text on the web is marked up and how HTML/browsers were designed to work.

I am also suggesting that block content should be marked up as HTML block elements. This is also fundamentally part of the design of HTML.

Whether you like it or not, block content is not in HTML allowed to nest inside of paragraphs (which only allow "phrasing" content).

The most semantically explicit HTML markup accurately conveying author intent would be something like:

<div class=paragraph><p>...</p><div class=math>...</div><p>...</p></div>

The alternative, of having elements (math, lists, tables, figures, ...) intended to be displayed as a block but as a hacky workaround marked up using <span> elements instead of divs, lists, figures, etc. so that you can stick them into a paragraph is a gross abuse of the <span> element which does not actually work very well in practice because browsers are not intended to work that way.

There's no reason to presume that the Math extension fix won't use nested <span> tags (like is currently done for non–display=block math) – there is a very good reason to presume that. The reason is that block math is intended to be displayed as a block, whereas inline math is intended to be displayed inline ("phrasing content"). It is supposed to be separated from the paragraph, centered or indented, with padding on top and bottom, not rendered within the body copy but pulled out as a block... i.e. precisely the intended use of HTML block elements. This is just the same as literally every other kind of block element (lists, tables, etc.). For every kind of block element, sometimes the author's intent is to have a semantic "paragraph" wrap the block with part before and part after. However, HTML as designed does not and never will accommodate this. The mental model around which HTML is designed is in fundamental conflict with a mental model which holds that "semantic paragraphs" should wrap block content. Those decisions were made decades ago and there's absolutely nothing we can do about it now or ever in the future. –jacobolus (t) 20:33, 16 June 2023 (UTC)

Whether you like it or not, block content is not in HTML allowed to nest inside of paragraphs (which only allow "phrasing" content). The most semantically explicit HTML markup accurately conveying author intent would be something like... It has nothing to do with whether I like it or not. Flow element content (i.e., <span>) with "block" presentational attributes (display=block or display=inline-block) is specifically allowed accommodated for in HTML+CSS. It's entirely semantically-explicit to have a paragraph (<p>) with flow elements with block display attributes within.

The most semantically explicit HTML markup accurately conveying author intent would be something like: [stuff with <div>s, etc. ...] Pure opinion. If it needs to be inline flow content with block-style breaking and indentation purely for display/formatting reasons, it's perfectly semantically correct to represent it in <span>s.

them into a paragraph is a gross abuse of the <span> element which does not actually work very well in practice because browsers are not intended to work that way. [[citation needed]]. Balderdash. HTML+CSS provides fairly little semantic structure, but block and flow level content can definitely be structured on top of it by a pre-processed language... such as Wikitext. HTML+CSS can absolutely provide as much semantic information as required by the authors, or the meta-authors with language translation tools. That's the very flexibility of HTML+CSS once we abandoned pre–HTML 4.

there is a very good reason to presume that. The reason is that block math is intended to be displayed as a block, whereas inline math is intended to be displayed inline ("phrasing content"). I have news for you: MW/WP's <math> isn't HTML5. It's re-interpreted (i.e., pre-parsed and rewritten) for MW/WP's Math extension's own purposes.

And what's more, "The <math> MathML element is the top-level MathML element, used to write a single mathematical formula. It can be placed in HTML content where flow content is permitted." (directly quoting MDN). Meaning, <math> is a flow-content tag every bit as much as <span>. They can both be "promoted" to block-style presentation via CSS.

For every kind of block element, sometimes the author's intent is to have a semantic "paragraph" wrap the block with part before and part after. However, HTML as designed does not and never will accommodate this. The mental model around which HTML is designed is in fundamental conflict with a mental model which holds that "semantic paragraphs" should wrap block content. Those decisions were made decades ago and there's absolutely nothing we can do about it now or ever in the future. Now you're just talking out of your ass, with a weird fatalism, and without apparent understanding of how HTML was initially conceived and developed from SGML, through standards with XHTML via hard work from W3C and WhatWG, and ultimately settled fairly rationally by WhatWG in HTML5.

I'm not trying to disparage you now. But what I see is simply floundering; your ego is defensively reaching to claw some sense of a "win" from this fight. From this windmill-tilting. And it's not going well. Again... all of these "points" (such as they are, and they're not strong) should be developed and brought up at the Phab ticket to potentially solve the Math extension's bug. But this dead horse has been beaten and bloodied. There's no more traction here.  — sbb (talk) 22:25, 16 June 2023 (UTC)

not trying to disparage you – haha. yes you are, as you have been since the beginning of this conversation, which from your end has consisted of a mix of aggressive insults, passive aggressive insults, false claims about my statements and intentions, whining about my good faith efforts to engage with you, and now preposterous disclaimers about how your insults aren't meant to be insulting (lol). All of which I have been largely ignoring because responding in kind to rudeness is a fool's game on the internet. As they say about mud wrestling pigs...

Your comments about <math> elements meaning MathML are all off topic and irrelevant to what we are discussing here. Wikipedia does not currently (and as far as I know is not planning to) emit MathML.

Spans are inline elements intended to be used, when inside a paragraph, as "phrasing content" and only allowing "phrasing content" nested inside them. If you want to stick any kind of "block level content" (such as new paragraphs, headings, ordered lists, unordered lists, definition lists, tables, blockquotes, figures, ...) inside a span inside a paragraph, you are entirely out of luck. HTML does not allow it – instead your browser will implicitly close the paragraph. HTML is designed in such a way that block elements are not intended to fit inside paragraphs (or spans inside paragraphs).

You can if you want override the display style of a span to make it render as a block, but it's an abuse and in my experience putting a block display element in the middle of a paragraph doesn't work very well and is a pain to style with CSS in such a way that the text on both sides of the block actually does what you want, because browsers aren't really expecting that to be done. (Disclaimer: most of my CSS experience was 10–20 years ago.)

Why don't you make an example page (off wiki) showing of the HTML markup and CSS you think Wikipedia should use for block math embedded in a paragraph, demonstrate how you think it should render, and we can test it in the common browsers, and then we can all try to pitch the developers to adopt that preference in what they emit, ASAP. If such markup works effectively and such a change lands in the code (and especially if someone fixes the phantom scrollbar bug and slightly reduces the vertical padding of <math display=block>) I'll be more than happy to leave all of the block math crammed inline into paragraphs of markup. I don't think it's going to work very well but am happy to be proven wrong. In the mean time, please don't emit such markup, because as of today it results in completely broken HTML. –jacobolus (t) 23:54, 16 June 2023 (UTC)

Your comments about <math> elements meaning MathML are all off topic and irrelevant to what we are discussing here. No, they're not. You said, and I quote, block math is intended to be displayed as a block, whereas inline math is intended to be displayed inline ('phrasing content'). I don't know how you can square the circle you've painted yourself in, but MW's Math plugin allows us to specify block display vs. inline display. Both can be done, with a flow container (<span>). With flow oriented HTML tags, if the bug is fixed. So don't presume to assume that MW has decided to override HTML+CSS intent for all time.

It's really simple. We can generate whatever content we want, assuming we pressure the devs to generate it correctly. So the focus and fight isn't here, in this alreaddy overly digressed thread. The fight is with the devs over at Phab.

I'm not, nor ever have been, trying to disparage you. You picked a fight, went passive aggressive early (c.f., the title of this ENTIRE subject, et al, dismissively cheap characterization of our initial conversation, etc.), and are trying to back out of the personal fight you picked.

Stop. Breathe. Recognize that in the big picture,

1. colon-indent anything, including math blocks, is never going to be supported by the parser. (BTW, colon-indent is 100% presentational markup, completely in violation of separation of content from presentation. Other lang wikis either center or left-align math blocks. Don't dictate indentation when it isn't semantic).
2. <math> can be emitted 100% as flow content, within <span>, if we have the MW Math plugin devs recognize the need to fix the emitted HTML.
3. CSS display=block is 100% legitimate, and not encumbered by semantic constraints, for flow tags like <span>.

 — sbb (talk) 00:25, 17 June 2023 (UTC)

trying to back out of the personal fight – yes that is correct, I never wanted a fight, and now I would like to back out. –jacobolus (t) 00:48, 17 June 2023 (UTC)

Agreed. Handshake, honestly and wholeheartedly. 🤝  — sbb (talk) 01:29, 17 June 2023 (UTC)

As an aside, in my opinion wiki markup with block elements (lists, math, figures, headings ...) clearly separated by blank lines is more legible than when they are crammed together, even in cases where the extra whitespace does not affect parsing. Separating mathematics blocks (and sometimes writing the LaTeX markup across several lines) makes it easier for source readers/authors to see that there is a block-level element and the appearance in markup matches the appearance in the output. This also encodes one kind of semantic intent – not intent about sentence grouping, but intent about whether an element should be visibly separated from the rest of the paragraph.

If I write:

The formula for such-and-such,

<math display=block>
f(x) = ...,
</math>

is so-and-so.

That is much more legible as markup, and IMO better conveys both semantic author intent and expected output, than:

The formula for such-and-such, <math display=block>f(x) = ...,</math> is so-and-so.

Which is just a big distracting wall of illegible markup overhead. –jacobolus (t) 16:21, 16 June 2023 (UTC)

In some contexts it is an absolute necessity to format the source of the display=block math as part of a paragraph of source, rather than setting it off by blank lines. For instance, in any kind of list environment, a blank line would interrupt the list, indent the math by the wrong amount (not accounting for its inclusion in a list), and start a new list.

More generally, your proposed multi-line format is semantically wrong. Again. —David Eppstein (talk) 17:37, 16 June 2023 (UTC)

In those contexts there is no need for a blank line because they are not output as HTML <p> elements, they have no restriction to only allow "phrasing" content nested inside, so there is no issue including block content inside. In such cases mediawiki does not emit invalid HTML and browsers are able to interpret it just fine. So they are somewhat of a tangent. I agree that given the way mediawiki markup is parsed, block math (or other block content) should not be put on a separate line in such cases.

"your proposed multi-line format is semantically wrong" – "Semantically right" output does not accord with the design of HTML. Block elements (whether formulas, figures, tables, lists, etc.) are not allowed in the middle of HTML <p> elements, full stop. It is simply impossible in HTML to "correctly" put block content in the middle of paragraphs. You can try to shoehorn block elements in using <span> elements that are then styled as separate blocks with CSS, but this is an abuse of the inline elements and is also somewhat buggy in results.

For better or worse, the design of HTML forces authors to encode separate chunks of "phrasing content" (i.e. prose and other objects that flow like prose) on either side of block elements as separate paragraphs with a separate block element in between.

The semantic structure of the text then does not precisely match the tree structure of the HTML markup, but that's the best we can do. –jacobolus (t) 18:00, 16 June 2023 (UTC)

The incorrect output semantics is merely a bug in rendering. It is your input that is semantically wrong, by formatting something whose intended meaning is one continuous paragraph of text (including a block formula) using a format that means three separate paragraphs. One cannot hope to get correct output semantics from incorrect input semantics. GIGO. You are encouraging our input to be garbage. —David Eppstein (talk) 18:09, 16 June 2023 (UTC)

One cannot hope to get correct "output semantics" no matter what one does. HTML does not allow it. But if we pretend and try to cram everything into a paragraph, what we get instead is completely broken invalid HTML that cannot be styled in CSS. If and when this bug is ever "fixed", the output is necessarily going to be what you call "garbage". So basically your preference amounts to, a bit snarkily phrased, "we should intentionally emit garbage on fire today because someday Mediawiki might be smart enough to put out the fire and emit mere garbage". –jacobolus (t) 18:12, 16 June 2023 (UTC)

What pretending? It really is a paragraph in its meaning. All else is hackery to work around formatting bugs. —David Eppstein (talk) 19:19, 16 June 2023 (UTC)

The fundamental issue is not "formatting bugs". The fundamental issue is that HTML was designed to never allow block content nested inside paragraphs. So in short: your mental model of how the markup should be structured is fundamentally in sharp conflict with what HTML is designed to accept / what browsers are designed to display. –jacobolus (t) 20:23, 16 June 2023 (UTC)

That is a matter for the back-end translation from markup to html. If we do not provide meaningful front-end markup, we cannot hope for the rendered appearance to correctly reflect our meaning. —David Eppstein (talk) 20:38, 16 June 2023 (UTC)

The rendered appearance should be as 2 separate paragraphs with block math in the middle. If we wanted to get fancy we can e.g. wrap the whole thing in an extra <div class=paragraph> or we can add an additional style to the trailing-content paragraph, say <p class=trailing> so that stylesheets can intentionally style the start of the paragraph differently from the end of the paragraph. If you want to accomplish this today you can emit that markup explicitly, instead of writing ordinary wiki-syntax paragraphs, though I would recommend against it.

One way or another, emitting a <p> element with any kind of block content wrapped inside is fundamentally broken and will never not be broken. It is mangled invalid HTML which does not render properly in readers' browsers. It just isn't how HTML works however much you might wish otherwise. –jacobolus (t) 20:47, 16 June 2023 (UTC)

INCORRECT. The rendered appearance should be as one paragraph consisting of three blocks of text, math, text. A paragraph is a semantic unit describing a meaningful sequence of text sentences. A rendered block of content in the visual appearance is a different thing. You should separate the meaning from the appearance rather than conflating the two.

This may seem like a subtlety but it does make a visual difference. For instance, in a style where the starting line of each paragraph is indented, the third block (second text block) should not have its starting line indented. —David Eppstein (talk) 21:13, 16 June 2023 (UTC)

The "correct" way to achieve a rendered appearance of "one paragraph consisting of three blocks of text, math, text" in HTML is by using the three HTML elements, <p>..</p> <div>..</div> <p>..</p>, optionally wrapped in a top-level <div> container or with distinct classes for the two <p> elements so they can be styled independently.

Trying to wrap the "internal blocks" of a paragraph inside a <p> element is always and inevitably broken invalid markup, not allowed by the HTML specification and not rendered properly by browsers.

You are trying to hammer a round peg ("semantic purity") into a square hole ("how HTML is specified to function"). –jacobolus (t) 21:28, 16 June 2023 (UTC)

The 'correct' way to achieve a rendered appearance of "one paragraph consisting of three blocks of text, math, text" in HTML is by using the three HTML elements, <p>...</p> <div>...</div> <p>...</p>, optionally wrapped in a top-level <div> container or with distinct classes for the two <p> elements so they can be styled independently. ... or, just as "correctly" (as in, 100% legitimate HTML, no abuse of the language), <p><span display="block">...</span></p>. 100% correct, supported by HTML+CSS, no problem at all. et voila, no need to hammer a round peg ('semantic purity') into a square hole, as you put it. And thus, no need to require wikitext to have blank lines around <math display="block"> blocks.  — sbb (talk) 23:38, 16 June 2023 (UTC)

I don't know anything about HTML and don't really care to, but certainly David Eppstein is correct about the semantic content. --JBL (talk) 00:14, 17 June 2023 (UTC)

100% agreed.  — sbb (talk) 00:17, 17 June 2023 (UTC)

Nobody thinks that mediawiki markup should be require[d] to have blank lines. The primary problem is that when the blank lines are not included, for the past 6+ years, the result has been broken HTML, and there is no sign that this bug will be fixed (the HTML is also slightly broken when the blank lines are included, but in a less harmful way). The secondary question is how precisely the bug should be fixed. Personally I expect the result would be better (easier for browsers and stylesheet authors) if mediawiki emitted separate paragraphs with an intermediate div. But I would be happy if the bug were fixed in whatever way more or less works. –jacobolus (t) 00:26, 17 June 2023 (UTC)

So we're back to assuming fatalism w.r.t. getting the bug fixed? This has has been... a lot of back-and-forth, just to get back to that point. So let's wrap this up: what else needs to be said, that hasn't been said, regarding this specific topic to enjoin me from making edits? Sincerely, I'm asking. ???  — sbb (talk) 00:33, 17 June 2023 (UTC)

This is not "fatalism". I'm cautiously optimistic that this might someday be fixed. I'm just not willing to put up with all of our technical pages having broken output in the mean time, especially since I have no evidence that any such fix is on the way. –jacobolus (t) 00:41, 17 June 2023 (UTC)

According to a Mediawiki developer "This cannot be done from the math extension as it does not know the context of the math element. So this can not be implemented in the near future." That doesn't sound particularly hopeful for any kind of prompt fix. In the (indefinite) mean time I would recommend we ask authors to put a blank line after every instance of <math display=block> as part of a top-level paragraph on Wikipedia. –jacobolus (t) 19:24, 20 June 2023 (UTC)

If you're going to recommend hacky workarounds, wouldn't it make more sense to wrap problematic paragraphs in <div> ... </div> and then NOT put artificial paragraph breaks within them, so that the math block div ends up nested inside another div (where it works) instead of nested inside a p (which breaks the html syntax)? See Special:Diff/1161125998 for an example. —David Eppstein (talk) 20:22, 20 June 2023 (UTC)

If you instead want to do something like:

<div class=paragraph><p>Leading text, </p><math>...</math><p>trailing text.</p></div> that would also be fine. But I doubt many Wikipedia authors want to put such a bunch of illegible markup overhead in the middle of their page. Even if we can wrap it in a template it's going to be kind of a pain.

By comparison, adding a blank line is pretty trivial, and if anything makes the source appear more like the rendered output. –jacobolus (t) 01:22, 21 June 2023 (UTC)

The biggest problem with your example is that you need to more explicitly tell stylesheets/user agents that your div is standing in for a paragraph. The most effective way to do this would be by adding explicit paragraph elements inside as I suggested just above. You could alternately try to establish some convention for a "class" to apply to the p-like div, and then advise everyone else on Wikipedia to adopt that one, so that stylesheet authors would know which divs were really supposed to represent paragraphs. One slight issue is that it's then a bit hard to style those "fake paragraphs" one way but style the math or other block elements contained inside them a different way that properly spills out of the paragraph container. I think the CSS may be achievable, but it's going to require some experimentation and maybe some annoying CSS hacks. –jacobolus (t) 01:31, 21 June 2023 (UTC)

@David Eppstein you might find the blank lines less unsavory if you mentally reinterpret the <p> to mean "contiguous block of prose" rather than "paragraph" per se. This interpretation accords much more closely with how browsers actually interpret (and web authors actually use) the <p> element in practice.  :-) –jacobolus (t) 01:36, 21 June 2023 (UTC)

Here is a single contiguous block of prose:

"An affine permutation is a list $[u_{1},\ldots ,u_{n}]$ of $n$ integers such that

$$u_{1}+\ldots +u_{n}={\binom {n+1}{2}}$$

and exactly one $u_{i}$ is conjugate to $j$ modulo $n$ for each $j$."

Indeed, it is a single sentence. As I said, I don't know much about HTML, but it seems obvious to me that any good outcome necessarily must respect that structure. I don't see any point in doing formatting hacks if the result is not going to be compatible with a good outcome; it's like how lots of equations all over WP have ridiculous \, in them still because once upon a time a decade ago that forced PNG or SVG or something. --JBL (talk) 17:33, 21 June 2023 (UTC)

This is very clearly not a contiguous block of prose. It is three separate visual blocks, two consisting of prose and one consisting of an indented and whitespace padded mathematical equation. Every typesetting system on the planet, whether chalkboard, pen and paper, hand-set metal in a printing press, MS Word, Indesign, or LaTeX treats this as 3 separate visual blocks. (Some systems have a richer set of primitives which treat "paragraphs" and "blocks of prose" as separate kinds of objects. HTML conflates the two, and the "p" tag is closer to representing the latter than the former.) –jacobolus (t) 19:06, 21 June 2023 (UTC)

Thanks for fixing the weird problems the reply-tool caused. As I say, I don't know at the level of the machine what's going on, but semantically what I have written it is a single block and this is certainly recognized by LaTeX, which would (correctly!) interpret the stuff following the displayed equation as part of the same paragraph as the stuff before it. A good system should involve me writing semantically sensible things and having the output work correctly; LaTeX does this right. You are arguing that the fix to a problem I personally cannot see is that instead people should write things that are semantically wrong; I think it would make more sense for you to think about, among all semantically correct ways for people to write, which one produces the best outcome (either now or in some future where something I don't understand is changed by the developers, whoever they are), and argue that people do that. At least, I personally would take such an argument much more seriously -- I am tired of deleting absurd \, from equations, and ten years from now I would not like to be tired from deleting [hopefully what will then be seen as] absurd blank lines around displayed equations. --JBL (talk) 19:22, 21 June 2023 (UTC)

problem I personally cannot see – the problem here is that there's a bunch of generated prose in the generated markup that is not included in any paragraph, which makes it completely impossible for CSS to style it. If you never try to apply a stylesheet to Wikipedia that tries to style paragraphs, you will see no difference. But if you do want to style paragraphs, you're completely out of luck. –jacobolus (t) 20:13, 21 June 2023 (UTC)

If you do want to style paragraphs under your proposed workaround of breaking everything into little marked-up-as-paragraph sentence fragments, you're still completely out of luck, because you will be styling them as whole paragraphs (for instance indenting the first line if that is your style) when they are not really intended as whole paragraphs. —David Eppstein (talk) 20:45, 21 June 2023 (UTC)

From my perspective, your argument can be more or less paraphased as "we should emit completely invalid malformed HTML because emitting more-or-less-okay HTML still wouldn't be perfect." I think that's a crummy place to come down, and I have a personal interest because this completely breaks my own stylesheet (in my logged-in browser, your experiment removing all the <p> elements at Sophie Germain's identity makes it now the least legible page on Wikipedia.) But YMMV. –jacobolus (t) 21:33, 21 June 2023 (UTC)

your experiment removing all the <p> elements at Sophie Germain's identity makes it now the least legible page on Wikipedia [...] But YMMV. Please, let's calm down and de-escalated. Saying a page that is 2 days old is the "least legible page on WP" is a bit hyperbolic, don't you think? Let's all step back and breathe a bit on this. I'm as guilty as you for having getting heated, but let's slow down. Please.  — sbb (talk) 00:32, 22 June 2023 (UTC)

In my browser, yes, it is the least legible, because (unlike nearly any other page on wikipedia) it breaks my browser's ability to style paragraphs. This is not intended to be an "escalation", I am just reporting my experience. –jacobolus (t) 16:54, 22 June 2023 (UTC)

That is an incorrect and uncharitable paraphrase of my argument. My argument is actually that both the semantically-correct wikimarkup (paragraphs with displayed equations within them) and the hacky split-up-into-fragments workaround that you are pushing so hard are broken, in different ways, but both legible. Given that it is impossible to produce non-broken output now, we should prioritize getting the wikimarkup correct, in the hope that it will eventually become unbroken (by using spans instead of divs). Your alternative would leave us with permanently broken wikimarkup and a big messy cleanup job that you are leaving as a debt of work for later editors. —David Eppstein (talk) 01:59, 22 June 2023 (UTC)

I think you are missing my main point though.

Currently most block math on Wikipedia uses colon indention, which results in the HTML elements (p, dd, p). This is technically an abuse of the dd element, but it has been more or less working for nearly all readers since the beginning of Wikipedia, and matches the way every other kind of block element is handled on Wikipedia. It works with all of the major browsers, user stylesheets, other tooling, etc. but unfortunately some screen readers don't deal with it well. (Aside: It's still not clear to me what their issue is and whether our alternatives are accessible.)

If we find/replace every example of colon indentation and replace it with display=block, the result is instead (p, div, orphan text fragment), which is broken (today) given a technical failure which has existed since the beginning of display=block and whose back-end solution has no clear timeline.

This is a clear regression (among 2–3 other problems with display=block which I laid out above), so I am asking in this thread if we can hold off on doing this mass find/replace job until the technical problem that causes the issue is fixed (and ideally the other issues as well). If such a mass find–replace is done, every single technical article on Wikipedia will become significantly less readable for me, making my Wikipedia browsing experience dramatically less pleasant. The phantom scroll bar and poor floating image collision handling issues also impact a substantial number of pages switched to display=block, and are a significant regression in experience for literally every reader of Wikipedia.

As a workaround for the first issue, I suggested we could instead add a blank line after every instance of display=block, which would instead result in (p, div, p). This would be effectively the same structural HTML (but with a div instead of dd element) as the original colon indentation. So if we do the find–replace of colon indentation for display=block but add this workaround, there is at least one of the three significant regressions that will be avoided.

My impression of your argument is "I don't think regressions in reader browsing experience matter in comparison to the 'semantic purity' of the wiki markup (with eventual technical fix someday in the indefinite future)". Which seems like a very reader-hostile take to me. But YMMV. –jacobolus (t) 17:06, 22 June 2023 (UTC)

Again, you are misreading my argument, after it has been explained to you several times, starting to rise to the level of WP:IDONTHEARTHAT. All current variations are broken, in different ways. Indenting with a : is broken. Breaking up sentences into fragments by blank lines is broken. All current variations produce somewhat-legible output, especially if you don't run custom scripts that interact who-knows-how with Wikimedia. Given that there is no current way of producing output that is not broken in some way, and no serious harm to readers in choosing whichever way we choose, we should go with the way that preserves the most hope of eventual non-broken output, which is to mark up the input with the intended semantic meaning. —David Eppstein (talk) 17:38, 22 June 2023 (UTC)

Breaking up sentences into fragments is not "broken" and calling it "broken" is "uncharitable" at best. This markup just aligns the markup with the visual structure of the document – for better or worse, the way HTML has always been designed to work, and the same way every other block element in HTML also works – rather than the sentence structure (the way you personally imagine wiki markup to work, without any obvious rationale). Your problem is with the creators of HTML from the 1990s, but as a result you are trying to pound a round peg into a square hole.

What you are recommending causes nontrivial harm to readers today for no discernible benefit today, based on a hope in some future benefit which may never materialize.

no current way of producing output that is not broken in some way – then we should favor the status quo ante (colon indentation), which is currently working for most readers and tools, instead of allowing significant regressions.

If we are concerned about accessibility, we should directly solicit advice from readers / screen reader software creators who currently have a problem with it (which, again, has still not been described), and design a solution which actually works for them. As far as I can tell the switch from colon indentation to display=block does not actually make the resulting HTML markup accessible to screen readers. It's still an opaque blob of LaTeX code. We shouldn't vaguely handwave toward "accessibility" to justify regressions in everyone else's experience. –jacobolus (t) 18:04, 22 June 2023 (UTC)

without any obvious rationale Surely it is obvious that this is an encyclopedia, written in natural language, and the basic units of meaningful natural language are the sentence and the paragraph? I mean I guess we could insist that editors put a line-break after every word, or after every punctuation mark, or ..., but that would be insane. --JBL (talk) 18:43, 22 June 2023 (UTC)

Let me phrase this a different way: Why should block mathematics be treated differently from every other kind of block content (list, quotation, table, figure) in Mediawiki markup and in HTML everywhere else on the web? Any of these kinds of blocks can be meaningly inserted in the middle of a paragraph (or sentence even), but none of them is allowed to be included in an HTML <p> element, or ever has been. You can argue that this is a bad design, but it makes clear what the internal mental model was for the creators of HTML: the <p> element was designed to represent a contiguous block of inline prose, rather than a "paragraph" per se. –jacobolus (t) 20:49, 22 June 2023 (UTC)

Let me guess: You also use plain TeX and advocate the abolishment of LaTeX, because manually formatting everything rather than describing its semantics and letting the formatter do the formatting is closer to the mental model from Knuth's original design? —David Eppstein (talk) 20:52, 22 June 2023 (UTC)

You may have intended that as a snarky jab, but in the name of comity, I'll answer your question frankly:

I generally use plain text with implicit formatting encoded in the visual structure, because I think it's an incredible pain to deal with fiddly markup languages, which for most uses are overkill.

Where that text needs to be turned into some kind of publishable structured output, my first preference would be to use InDesign or a similar tool that gives a user simple visual control over the output because I have very high standards and making LaTeX output truly excellent instead of kinda-sorta-acceptable-if-you-squint is always a gigantic pain in the rear.

For light-duty uses, markdown is much more pleasant than LaTeX (or HTML, or Mediawiki markup). But I can use LaTeX where necessary for collaboration. All the best. –jacobolus (t) 20:59, 22 June 2023 (UTC)

Well, that explains your attitude, at least. As you say, "making LaTeX do what I want is always a gigantic pain in the rear". It is a pain in the rear because it is a mistake. If that is how you are using LaTeX, you are doing it wrong. The right way to use LaTeX is to describe the semantic structure of your document and let LaTeX do what it wants to format it. Using LaTeX in that way becomes much easier. If you have to achieve a specific appearance rather than a canned one, you can hack up the style file instead, but that's something of a black art.

Frequently for situations where LaTeX is appropriate (scientific publication) you are going to have to follow the publication's formatting design rather than your own, anyway, and semantic markup rather than format-based markup is a much more robust way to make your document flexible enough to handle formatting changes, without having to do all the same work over again when you want a different format.

Similar responsiveness to formatting changes is also necessary for Wikipedia, where we have many different skins available for different readers, not to mention users of screen readers and the differences in formatting in browser versus mobile views. For that reason, using a semantic markup rather than a format-based markup is a good idea, so that the conversion to the reader's desired view can be done on a format-by-format basis. The alternative approach, in which editors hack up the source in whatever way they can find to optimize the appearance to their taste, risks unknowingly making it worse for everyone else reading under different skins, or even under future versions of the same skin. —David Eppstein (talk) 21:25, 22 June 2023 (UTC)

Also "everyone else" here apparently is just you: maybe there is another editor who experiences this problem, but you're the only person I've ever seen assert it. Perhaps you over-estimate how common it is for readers to use personalized CSS or whatever when viewing Wikipedia. --JBL (talk) 18:45, 22 June 2023 (UTC)

I do actually use custom CSS from my Wikipedia preferences, also, but not in a way that is affected by this. (Mine bumps the font size to 110% and makes {{orphan}} banners visible.) —David Eppstein (talk) 19:06, 22 June 2023 (UTC)

Yeah please read an implicit "that is affected by this issue" into my comment. --JBL (talk) 20:43, 22 June 2023 (UTC)

The fundamental problem is that <p> is broken by the requirement of compatibility with old old html that failed to close its tags, and is therefore unable to contain nested block-level content. Like the oldest of html tags, it is a bad mix of semantics and formatting locked together. The solution is to replace it by something like <div class="paragraph"> that can handle multiple interior blocks, with divs nested inside it for each block if necessary, and with css to make it otherwise behave like <p> There is no technical reason why the mediawiki conversion from wikimarkup to html could not do it this way. Nobody will care that their paragraphs are marked up as divs instead of ps. —David Eppstein (talk) 01:15, 17 June 2023 (UTC)

Honestly, I'm not sure this is the case (that <p> tags aren't closed by the MW parser, at least as an attempt, in the whole). I've been through the parser engine, and it seems MW parser tries to close <p> tags as much as possible (probably because of XHTML days' strict XML-based open/closed philosophy, which IMO is a noble effort).  — sbb (talk) 01:28, 17 June 2023 (UTC)

Oh, the issue of p tags not being closed has nothing to do with Wikimedia. It is an issue with old-days html when html was hand-coded and people didn't close some tags. I still have lots of more or less hand-coded pages where that is the case. But because of that issue, p has been defined to be auto-closed when any other of various block-level tags starts. I'm not sure whether it is actually impossible to nest a block-level tag within a p, or whether it can be done by using a non-standard tag that you have set to be block-level, but it definitely doesn't work to nest a div within a p, by definition in the html standards. On the other hand, nesting a div within a div is non-problematic. —David Eppstein (talk) 06:26, 17 June 2023 (UTC)

The implicit closing is done by the browser, not the Mediawiki parser. Mediawiki emits malformed HTML such as

<p>Here is a formula, <div class="mwe-math-element">...</div> and here is text afterward.</p>

then when the browser sees that, it implicitly closes the <p> tag before the <div> and turns it instead into:

<p>Here is a formula,</p><div class="mwe-math-element"> ... </div> and here is text afterward. <p></p>

See User:Jacobolus/math block example for slightly more detail. –jacobolus (t) 14:00, 17 June 2023 (UTC)

As an aside, the Mediawiki parser will do (what I would call) the "right thing" if you try to nest some other kind of block element inside a paragraph. If you explicitly add the following raw HTML to a wiki page:

<p>Here is a list, <ul><li>one</li><li>two</li></ul> and some trailing text.</p>

it gets turned into:

<p>Here is a list, </p><ul><li>one</li><li>two</li></ul><p> and some trailing text.</p>

with two separate paragraphs and the block element in between. My proposal for a bug fix for block math in a paragraph would be for Mediawiki to do exactly the same thing with block math that it already does with any other block element put in the same place. –jacobolus (t) 14:10, 17 June 2023 (UTC)

that can be fixed in the Math plugin code – it is not reasonable to rely on some future fix from the Mediawiki developers, who have in general made it clear that they don't care very much about either math rendering or accessibility. We should try to find the best available workaround solutions today using the currently available technical tools as possible (including e.g. making new templates) instead of hanging our hopes on potential changes that might happen years down the line. –jacobolus (t) 19:31, 15 June 2023 (UTC)

Disagreed. I don't think that's charitable of the developers. Bugs don't fixed if they're shown the light of day. In the meantime, I strongly believe that we should write the best wikitext we can, based on WP:MOS and Help guidelines, rather than hack too much with templates. <math display="block"> is the officially-supported way forward for the time being (since around 2015 or so), and are not so bad as to require poor work-arounds, IMO.  — sbb (talk) 19:52, 15 June 2023 (UTC)

The ideal technical fix would be for the Mediawiki developers to recruit some group consisting of users and/or developers of screen readers or other accessibility tools and math wikipedia authors and figure out how to make both a block math mode and an inline math mode that render well on desktop, mobile, and in screen readers, including designing features for whatever accessibility fallbacks are required to make the pages fully accessible, helping us write documentation for authors to take advantage of those features, and trying to roll them out on technical pages. Ideally there should e.g. be a way to specify separate output depending on the width of the window, so that a wide formula could have additional line breaks when viewed in a mobile browser. Ideally they would adopt Mathjax or KaTeX and expose the full feature set of those implementations, instead of Wikipedia having its own limited LaTeX implementation that requires piles of workarounds to achieve basic formulas. But I don't see this kind of thing happening.

The quickest and most painless technical fix for this more limited issue would be for the mediawiki parser to interpret : starting a line without a preceding ; line to mean "indent this text" rather than "definition in a definition list". It could be inserted into the HTML as e.g. <div class="indented"> with the appropriate indentation style defined in CSS instead of as a <dl><dd>. That would have the side benefit of also fixing the longstanding problems with using colons for indentation in talk pages, and would stop complaints about "invalidity" of HTML. But that also seems unlikely to happen.

In the mean time, I wonder if anyone is interested in experimenting with other potential templates for indentation. –jacobolus (t) 20:23, 15 June 2023 (UTC)

I suspect the developers would be even less interested in your "quickest and most painless technical fix" than they are with fixing math markup: because it doesn't advance their goal of making the markup carry semantic meaning both on the wikicode side and on the html-to-browser side. Mixing two unrelated meanings of : doesn't do that. —David Eppstein (talk) 00:02, 16 June 2023 (UTC)

Fair enough, but : has implicitly carried the meaning of "indent this text" on Wikipedia (esp. talk pages, but also article pages) since the beginning of the site, because it was easily available and alternative methods of achieving the same (basic and obviously necessary) task were inferior or impossible. Making that user- and community-friendly technical change would be an example of paving the cowpaths, recognizing an obvious need that Wiki contributors surfaced organically and making it convenient and retroactively "correct". –jacobolus (t) 00:58, 16 June 2023 (UTC)

Unfortunately, this is simply what must happen. It's clear that WP (by that, I mean MOS/Help pages) are willing to cede Talk: namespace to the colon-devil (because, frankly, MW markup is horrible as a chat/messaging format, but having multiple markups in the engine depending upon namespace is objectively a worse solution). But from the standpoint of "what would hypothetically generate the best possible print version of WP", clean semantic & accessible markup in article space is the guidestone, and anything less should be at most begrudginly tolerated. IMO.  — sbb (talk) 03:04, 16 June 2023 (UTC)

If generating the best possible print version of Wikipedia were the highest priority, we certainly wouldn't be using "straight quotes" everywhere. –jacobolus (t) 06:43, 16 June 2023 (UTC)

Curly quotes seems like a tangent. Let's keep this on subject.  — sbb (talk) 13:50, 16 June 2023 (UTC)

Poking at straight quotes is somewhat flippant, and is a bit of a cheap shot because straight quotes are ugly as sin, but there's a serious point lurking under the snark, which is that Wikipedia is about compromise between a wide range of conflicting interests, not any kind of absolute correctness. Anyone who knows the first thing about typography will tell you that straight quotes are unacceptable to use in any serious context. But here at Wikipedia we nonetheless settled on them (largely by consensus!) for convenient input on the widest range of author keyboard input methods (whose conventions were established by typewriters of the 19th century and have nothing to do with "print" of any kind, and certainly not "the best possible print"). –jacobolus (t) 01:24, 17 June 2023 (UTC)

Off-topic. Please keep this on topic for WP:Math. Thanks.  — sbb (talk) 00:06, 22 June 2023 (UTC)

I created two new bug reports, https://phabricator.wikimedia.org/T339996 and https://phabricator.wikimedia.org/T339999 after not finding these problems reported before. ––jacobolus (t) 00:52, 21 June 2023 (UTC)

I am having a hard time trying to follow the argument here. I usually use ":" when I want to indent for a paragraph, display equation, or quotation. and follow that with a blank line to prevent additional text from being sucked into the structure. I mostly find myself in agreement with "jacobolus" (he may not want my support since I am ignorant of this topic). JRSpriggs (talk) 00:25, 23 June 2023 (UTC)

@JRSpriggs The issue with using : for indentation is that it doesn't officially mean "indent this content". What it actually does is creates a new "definition list" with no terms to define, only definitions (<dd>, "description details" elements). This works alright in practice for most wiki authors and readers, but formally it is an abuse of the definition list element to do something it was not originally intended to do, and some screen readers (web browsers for blind people) apparently make weird noises when they encounter such a list. Years ago the <math display=block> mode was added to the math plugin to make "indent this block of math" part of the core tool instead of hacking that effect via definition lists, but there are some bugs and adoption has been slow, so most math on Wikipedia is still indented using the : method.

I'm still not really clear on which screen readers have an issue (all of them? some of them? some old ones from 10 years ago that nobody uses anymore?), precisely what issue they have, or whether the display=block generates output that is at all accessible to users of screen readers. But I would love to hear from someone who knows more about this, because I definitely want to make our technical articles as accessible as we reasonably can do given available volunteer resources. –jacobolus (t) 00:53, 23 June 2023 (UTC)

Tuple

There has been some edit-warring going on at Tuple between User:D.Lazard and an anonymous editor. I've temporarily semi-protected it (probably in the wrong version), and I assume Lazard knows not to violate 3RR, but this could use the attention of other editors. See also discussion at Talk:Tuple#Names for tuples of specific lengths. —David Eppstein (talk) 00:57, 24 June 2023 (UTC)

Template:Infobox mathematical statement

This template is apparently around since 2019, but I just became aware of it recently (due to user systematically adding it to math articles). Has their been any discussion or agreement how and whether to use that template? After all it affects potentially every theorem and lemma.--Kmhkmh (talk) 12:27, 24 June 2023 (UTC)

Can you give an example of where this template has been added, so we know what it looks like and what we are talking about? PatrickR2 (talk) 18:59, 24 June 2023 (UTC)

Special:WhatLinksHere/Template:Infobox mathematical statement. —David Eppstein (talk) 19:03, 24 June 2023 (UTC)

I vaguely remember arguing against ever including such an infobox long ago, on the basis of WP:DISINFOBOX: there is no room for subtlety or nuance in an infobox. It assumes that every statement can have at most three discrete events in its history: someone stated it at some precise time, someone conjectured it at some precise time, and then someone proved it at some precise time. For that matter, even the example infobox given in the template documentation is bad: its image is unintelligable and its image caption is a whole paragraph of text. I'm not sure where to find that past discussion. I would still argue against ever using this. —David Eppstein (talk) 19:02, 24 June 2023 (UTC)

I'd like to add that there may exist important 'mathematical statements' which are not proven and will never be, because they have been disproven already. As such, they could not be correctly described with the template in question. For example, a so-called Borsuk's conjecture. --CiaPan (talk) 21:17, 24 June 2023 (UTC)

I'd generally recommend removing these infoboxes from the articles I have seen them used in. They are redundant to the immediately adjacent text and have little if any benefit, while adding metadata that is often largely trivial or obvious and taking up space/reader attention. If someone thinks it's helpful to put an outline around a theorem statement, go ahead and just include it in the version in the text. Even add a pale background color if you want to go all out (subject to consensus from other authors of each specific page).

As an example, there is one in Goldbach's conjecture. The article leads with "Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory..." then continues in the first section "On 7 June 1742, the German mathematician Christian Goldbach wrote a letter to Leonhard Euler...". The infobox repeats this as: "Field: Number theory; Conjectured by: Christian Goldbach; Conjectured in: 1742; Open problem: Yes ...". –jacobolus (t) 19:55, 24 June 2023 (UTC)

I'm just seeing now that the template was already proposed for deletion at some point, but there was no consensus to delete it:

• Wikipedia:Templates_for_discussion/Log/2019_February_24#Template:Infobox_mathematical_statement

Nevertheless there was clearly no consensus for its use either. Personally I'm not opposed to infoboxes in principal, in some areas they are well established and somewhat useful (for instance movies, countries, cities, etc.), but I dislike the "trend" to push infoboxes into any article and in particular adding it to all the math articles about theorems and lemmata strikes me as a bad idea. Maybe we could add a note to the template, pointing out that its use is somewhat controversial/not encouraged? Otherwise its mere existence might lead (well meaning) Wikignomes astray. --Kmhkmh (talk) 21:25, 24 June 2023 (UTC)

Peer Review for Po-Shen Loh

I think y'all at Wikiproject Mathematics may be interested in looking into this peer review - I am planning to get a quick check before a GAN to see what else I may need to do before starting a GAN. — Prodraxis {talk • contributions} (she/her) 16:45, 28 June 2023 (UTC)

Math notation accessibility

Does anyone here know whether and where there has been previous discussion of accessibility of formulas on Wikipedia, or what the general best practices are for accessibility of mathematical notation online? Where would be the best place to find readers who need assistive technologies to read Wikipedia to ask them about their current experience? I'm especially thinking about screen readers here, but also happy to discuss other tools.

My speculation (based on a total lack of understanding or experience) is that screen readers would choke badly on formulas, whether expressed as LaTeX or math templates. Is that an accurate guess, or are there some screen readers smart enough to make sense of math notation? How are formulas rendered in practice by screen readers and other alternative user agents?

If mathematical notation is an accessibility problem, is there some way wiki authors can provide a fallback formula written as plain text that screen readers would read to the standard math notation? It would be a ton of work to spell out English pronunciation for every bit of mathematical notation on Wikipedia, but if the technical means were available I'd at least consider trying to add such a fallback on pages I'm spending a lot of work on anyway. –jacobolus (t) 20:40, 22 June 2023 (UTC)

Sorry about my total ignorance on this topic, but what are we talking about here? Is it about blind people wanting to read wikipedia? I imagine for regular non-math articles, there would be text to speech and they can listen to that. For mathematical formulas, not sure. I apologize in advance for my lack of sensitivity, but are there really many blind people who would need to read complicated mathematical formulas while on their own, i.e., who don't have access to other people to read and explain the formulas to them? PatrickR2 (talk) 05:11, 23 June 2023 (UTC)

I imagine Latex formulas enclosed in <math> and </math> would be easier to process automatically. One more argument for using that, and not the manual formatting solutions proposed earlier by Michael Hardy. PatrickR2 (talk) 05:15, 23 June 2023 (UTC)

@PatrickR2: I find it strange that someone thinks I expressed a preference for "manual formatting solutions" over LaTeX. Michael Hardy (talk) 21:06, 26 June 2023 (UTC)

@Michael Hardy I was referring to the earlier discussion "Why can't mathematicians spell?". You expressed (and edited articles showing) your preference for the use of manually fiddling with "& nbsp;" instead of relying on LaTeX surrounded by "<math></math>". PatrickR2 (talk) 21:47, 26 June 2023 (UTC)

@PatrickR2: No, I did not. Michael Hardy (talk) 00:36, 29 June 2023 (UTC)

Yes I am talking about blind people wanting to read Wikipedia. A purported problem that screen readers have with <dd> elements is the primary reason we are supposed to eliminate the use of : indentation (the claim is "colon indentation is not accessible"), but I noticed that I haven't ever actually heard from any screen reader listeners about math article accessibility. So I am curious if our formulas are in fact at all accessible.

I just tried the Mac VoiceOver tool (which has no problem whatsoever with colon indentation), and in my opinion our LaTeX formulas are not at all accessible using that tool, unless maybe to an extremely committed and experienced listener willing to make a lot of inferences.

Numerical exponents and coefficients are read identically, square roots are not read, fractions are not indicated and there is no audio distinction between numerator and denominator, in multiline equations it is difficult to understand the intended alignment of different parts, various irrelevant features of the markup are read out, etc.

I'm skeptical that our LaTeX formulas can be made at all sensible without some kind of explicit fallback text, but I admit I am largely ignorant about this whole subject. –jacobolus (t) 05:44, 23 June 2023 (UTC)

Blind people definitely use LaTeX for mathematics and we should stick with that. I don't think it is up to WikiMedia to invent some new way of outputting it to blind people but if there is som good software out there they could be asked to incorporate it. Otherwise it is up to whatever is the blind persons favourite reader and we provide the LaTeX. No I do not think fallback text is a good idea to pursue. NadVolum (talk) 15:53, 24 June 2023 (UTC)

Can blind people make sense of Wikipedia's current formulas using their commonly used screen readers, is my question? If not, are there ways we could make that output more accessible?

I am a sighted person with basically no screen reader experience, so my experience should not be taken as meaningfully conclusive, but my impression trying to look at Wikipedia articles with the Mac VoiceOver tool was that our current mathematical notation output is largely useless and inaccessible.

As a related question: what is the current industry best practice for making websites with mathematical notation accessible? Are there any good examples of accessible mathematical web pages that we could look at or take inspiration from? –jacobolus (t) 19:44, 24 June 2023 (UTC)

I'd suspect Latex in doubt makes it easier for sight impaired people, because whatever additional tools you might to create audio or braille for formulas, those are probably are more likely to work with Latex (as the widely adopted standard) than with a mix of wikipedia templates.

Aside from the accessibilty for sight impaired, I personally prefer Latex to template solutions, as it provides one standard pretty much anybody writing math texts is already familiar with and which is used across all language wikipedias, whereas that is not true for various template solution. I regard that as more important than templates yielding currently slightly better renderings.--Kmhkmh (talk) 17:25, 24 June 2023 (UTC)

Jul 2023

Significant digits

73.254.227.172 (talk · contribs) claims to have an unusual superstition about the number of digits in decimal fractions, that they "should have 6 or not more than 3 sig. digits", and is edit-warring to add unnecessary digits in order to enforce their avoidance of 5-digit fractions at Reuleaux triangle. More eyes welcome. Also welcome: other opinions about a good number of digits to standardize on. Currently most of the decimal approximations in that article are 5-digit, but there are a couple of 6-digit ones (not caused by the IP edits) and a couple of 4-digit ones. I'm not convinced that the extra digits and variation in numbers of digits are necessary; 4 or even 3 might be good enough. —David Eppstein (talk) 00:42, 10 July 2023 (UTC)

In the context of this article, which is heavy on discussion of physical objects, I would go for 3 significant digits. Nothing more precise is going to be either useful to readers or physically realizable. –jacobolus (t) 02:25, 10 July 2023 (UTC)

I agree with Jacobolus. Students of physics, chemistry, engineering and economics are taught to perform calculations using 4 or even 5 significant figures but to give answers using no more than 3 significant figures. Any more than 3 significant figures is most likely just false precision. Dolphin (t) 02:39, 10 July 2023 (UTC)

It always depends on context. Really what decides sig figs, rigourously, is the uncertainty. In practice, it's how many do you really need. You can manufacture a bike wheel to 30.00 +/- 0.01 cm tolerance. But if you had a 30.49 cm bike wheel... would that really change your biking experience? Unless your a top athlete, the answer is likely no.

For this article, anywhere from 3 to 6 seems reasonable. I would err on the higher side here, since there are machining applications, and machining can be done at very high precision levels. There's certainly no reason why 5 is verbotten though. Headbomb {t · c · p · b} 03:59, 10 July 2023 (UTC)

Anyone who cares enough to need more than 3 digits of precision can trivially get as many digits as they want from the exact expressions. The question for this Wiki article should be: "How many digits are meaningful for most readers?" Even 3 digits is more than enough. –jacobolus (t) 04:04, 10 July 2023 (UTC)

Yes, the presence of the exact expressions (rather than "this is a root of the following transcendental equation", for instance) is one reason I tend to lean to fewer digits over more. —David Eppstein (talk) 06:29, 10 July 2023 (UTC)

Artificial intelligence in mathematics

Artificial intelligence in mathematics is nominated for deletion since 3 July at WP:Articles for deletion/Artificial intelligence in mathematics‎‎. Apparently very few of the participants of the discussion are mathematicians. So the opinions of the participants of this project are welcome. D.Lazard (talk) 11:50, 11 July 2023 (UTC)

Block display in dark mode

I cannot view mathematical expressions in dark mode when <math display="block"> is used. I can view it fine when the markup is simply <math> without the display="block". I can see math just fine on Unit hyperbola but I cannot see most mathematical expressions on Hyperbolic functions. I would guess that display="block" formats text to be black rather than using the default text color. Nine hundred ninety-nine (talk) 03:14, 10 July 2023 (UTC)

It probably depends on something more detailed than just display=block + dark mode. For me, using the built in dark mode gadget, vector2022 style, math rendering preference set to svg, Firefox, and OS X, display=block formulas look fine, including the ones on hyperbolic functions. But there are a lot of variables there that might make a difference. —David Eppstein (talk) 06:38, 10 July 2023 (UTC)

Yes that is what the default would be and it worked fine for me. A thing I did notice that surprised me was that the formatting of the page changed slightly between dark and light mode. I'll see if I can spot why. NadVolum (talk) 18:51, 10 July 2023 (UTC)

In dark mode the images are 2 pixels smaller each way! There can't be any good reason for that! NadVolum (talk) 19:23, 10 July 2023 (UTC)

It seems like there are a number of bug reports related to dark mode. The main one seems to be T268279 which is closed and resolved. T326122 is explicitly about <math display=block> but its marked as a duplicate of the first. If this is still broken we can reopen the task. To do so, we would need a bit more details: in particular what settings you are using to enable dark mode. For me looking at https://en.wikipedia.org/wiki/Hyperbolic_functions?withgadget=dark-mode works fine for me.--Salix alba (talk): 20:31, 10 July 2023 (UTC)

I am using Zorin OS (based on Ubuntu) and Firefox. Under Preferences > Appearance, I have Skin set to Vector Legacy and math set to SVG. Under Gadgets > Appearance, I have Use a black background with green text and Dark mode toggle: Enable a toggle for using a light text on dark background color scheme checked. No other item under Gadgets > Appearance is checked. Even when I toggle to light mode, I still cannot see the mathematical expressions on hyperbolic functions. Nine hundred ninety-nine (talk) 19:45, 11 July 2023 (UTC)

Theta function

Over the last six weeks or so, Reformbenediktiner has massively expanded the article Theta function; in bytes, it is now (current version) between 2 and 3 times larger than it was at the beginning of June. I have only glanced over the changes; some of them bear references to obviously reliable sources, but there are also several new references to stackexchange websites, and others that are marginal at best (OEIS, MathWorld, something on researchgate). There are other respects in which the changes are superficially worrying -- see the use of color in the new section Theta function#Elliptic nome, for example. I hope that someone with more expertise (or free time) than I have can take a look. --JBL (talk) 23:33, 15 July 2023 (UTC)

I strongly dislike the colors. They are tacky and substantially illegible. Color should be used sparingly in mathematical formulas or table backgrounds, if at all, and wherever used it is used, choices should be conservative: think plum, maroon, navy for foreground colors rather than lime or hot pink, or gray, pale blue or ivory for backgrounds colors. –jacobolus (t) 01:02, 16 July 2023 (UTC)

More strongly than personal taste, several of the color pairings fail Wikipedia:Manual of Style/Accessibility § Color. For instance, cornflowerblue text (#6495ED) on greenyellow background (#ADFF2F) or on yellow background (#FFFF00) are both far from the minimum WCAG AA level of accessibility, according to [6], let alone meeting the AAA level that we should be aiming for. Forest green (#228B22) on the default gray Wikitable background (#F9F9F9) again fails AA, for the text size used. —David Eppstein (talk) 01:31, 16 July 2023 (UTC)

And if you want a better guideline than the profoundly flawed WCAG 2.0, under Myndex's APCA metric, that first combination has contrast 42.7, when for ordinary font size/weight we should be aiming for contrast of 90+. –jacobolus (t) 02:25, 16 July 2023 (UTC)

Paired data (= paired samples?)

According to the talk, there seems to be an issue with the current definition of that lemma. Also, Paired sample redirects there, even though this – fairly poor – article doesn't deal with sampling as such. Does this redirect make sense, yet? If yes, shouldn't Dependent sample and Independent sample redirect there as well, or rather to Sampling (statistics), even though these important terms are not discussed there by now? Hildeoc (talk) 17:44, 10 July 2023 (UTC)

I fixed the article to an extremely basic level of competence. It's still a stub, and reliable sources are badly needed. I'll respond at that talk page. Mgnbar (talk) 19:06, 10 July 2023 (UTC)

Thanks a lot for looking into this. Apart from the deplorable state of that article, I think we should have some kind of content for the two red links I invoked above. IMHO, the proper place for these terms would be at Sampling (statistics) then. What do you think? Hildeoc (talk) 19:20, 10 July 2023 (UTC)

I tried to address this at Talk:Paired data, but: I am not a statistician, but: I don't know what the term independent sample means. Does it mean a sample that is IID? (By which I mean a data set {x1, ..., xn} that is a realization of random variables X1, ..., Xn that are IID.) Mgnbar (talk) 19:33, 10 July 2023 (UTC)

See, for instance, here. Hildeoc (talk) 20:19, 10 July 2023 (UTC)

Okay, so paired samples are an extreme form of dependent samples. And is this terminology in common use? And is it not covered anywhere on Wikipedia? I could imagine this kind of dependence being treated at confounding or something like that. If it's nowhere, then it seems that it might merit an article. (And I hope my questions above convince you that some readers are going to confuse independent samples with samples that are IID. So present it carefully.) Good luck. Mgnbar (talk) 20:27, 10 July 2023 (UTC)

In this case, I guess I'd rather not get my fingers burned here – I'm no professional either. Hildeoc (talk) 22:34, 10 July 2023 (UTC)

This article does not belong to mathematics, it's about statistics. Is there a WikiProject for statistics, where you would get more feedback on this? PatrickR2 (talk) 20:40, 12 July 2023 (UTC)

See Wikipedia talk:WikiProject Statistics. However, the project may be moribund. JRSpriggs (talk) 18:14, 13 July 2023 (UTC)

At some point I will add more to this article. I tentatively think that "paired sample" would be a better title for the article. Michael Hardy (talk) 16:04, 13 July 2023 (UTC)

@Michael Hardy: That would be really great, especially as you are an expert on the field in question! For consistency, what do you think about the concepts dependent sample and independent sample? Wouldn't they fit best under Sampling (statistics)? Hildeoc (talk) 23:07, 13 July 2023 (UTC)

PS: Just for reasons of completeness and transparency, I also realized we're lacking sample coverage (possible redirect lemma Coverage (sampling)), as defined here, as well as the related concepts undercoverage and overcoverage. Any ideas? Hildeoc (talk) 22:10, 16 July 2023 (UTC)

PPS: We do have Statistical coverage and Coverage (statistical), both merely redirecting to Coverage probability, though. Does that make sense? Hildeoc (talk) 14:03, 18 July 2023 (UTC)

Formula Wikidata association

Stegmujo adds links of math formulas to new Wikidata pages (28, sofar), by changing "<math>" into "<math qid=...>" This is not useful, and not very harmful, except when users click on the formula, where a page is displayed with information that is confusing because of lack of context.

If our project agrees, I suggest that these edits are reverted, and Stegmujo stops their disruptive edits. D.Lazard (talk) 12:46, 14 July 2023 (UTC)

Hello @D.Lazardit would be nice keep these annotations. These allow accessibility systems to understand the context of a formula through the annotated formula definitions. Stegmujo (talk) 13:12, 14 July 2023 (UTC)

I disagree with your above assertion, that is only your opinion. In any case, I'll not revert your edits if there will be no consensus for that on this page. D.Lazard (talk) 16:08, 14 July 2023 (UTC)

@Stegmujo: could you explain the meaning of the sentence These allow accessibility systems to understand the context of a formula through the annotated formula definitions? I am not familiar with the various pieces of jargon. What, for example, are some concrete examples of situations in which you think this would be helpful to someone? How are you selecting equations to add this to? How far do you imagine this kind of labeling extending? --JBL (talk) 17:27, 14 July 2023 (UTC)

Which accessibility system are you thinking of?

If there's going to be a link pointing to an extended explanation of a formula, I would recommend putting an ordinary wiki-link in the prose before or after the formula (that is, a name styled so readers can obviously tell it is clickable) pointing to an article about the formula. For example, "applying the quadratic formula, ${\textstyle x={\bigl (}{-b}\pm {\sqrt {b^{2}-4ac}}{\bigr )}{\big /}2a,}$ we obtain ..."

I don't really see what benefit readers are going to get from Wikidata entries for formulas. I agree that these don't seem like they provide much if any useful information, and readers accidentally clicking a formula may end up confused. –jacobolus (t) 18:45, 14 July 2023 (UTC)

I agree that these are unhelpful and should be reverted (I reverted one that showed up on my watchlist already). More, there is general opposition to Wikidata links in English Wikipedia articles; for instance, interwiki links through {{ill}} can technically be made to link to Wikidata for topics that exist there but not here, but that tends to get reverted as well. —David Eppstein (talk) 18:05, 14 July 2023 (UTC)

I'm all for accessibility (making our material more useful to those with screen-readers, for example), but I am not sure how these tags do that. They seem more like an attempt to make a semantic wiki. If I'm missing something, I'd like to hear what. From a user-interface design perspective, making some formulas clickable and not others without any visual clue seems a poor move. XOR'easter (talk) 20:33, 14 July 2023 (UTC)

The information obtained from structured data from Wikidata linked to a formula in a Wikipedia article provides the formula disambiguation for screenreaders which are used by visually impaired or blind people.

The W3C proposes the intent-attribute towards the disambiguation of mathematical formulas for screen readers for blind or visually impaired people. I'm a developer for the mediawiki-math-extension, currently we are aiming to create native MathML support within PHP within this extension. This will also enable us to integrate upcoming features for MathML v4 such as the intent-attribute. The intent-attribute is an new markup element in MathML. For its generation from LaTeX-Math, additional structured data is required, Wikidata provides an ideal structure for creating, maintaining and retrieving linked annotations to formula. From the retrieved info, intents can be generated and screenreaders will be able to synthesize the correct speech output.

A very simple example how this can be helpful. From "hbar" in LateX the generated MathML would usually look like:

mathml1 = '<mathml><mi>ℏ</mi></mathml>'

With additional information from annotated wikidata items it can be identified automatically as planck constant and this info can be added to the MathML as inent-attribute:

mathml2 = '<mathml><mi intent="planck-constant">ℏ</mi></mathml>'

In the first mathml item (generated from tex), the screenreaders would read "h with an hat" or similar, in the second item, with the additional info from intent, the item can be read as "planck constant".

For further reading about intent-attribute, check https://www.w3.org/TR/mathml4/#mixing_intent

As already mentioned it does no harm when formulas are clicked. It can even present explanations for the mathematical symbols in a quick and structured way searching for parts in the article.

The plan is to annotate around 100 formulas which are selected based on their usability with intent-attributes. These can be used as first examples for the usage with accessibility components with blind-people.

I would appreciate the support of the Wikipedia community in realizing accessibility features for Wikipedia Stegmujo (talk) 14:28, 17 July 2023 (UTC)

@Stegmujo did you solicit feedback/ideas from this community or from users of assistive technologies before starting in on this implementation?

Having to associate every formula with a wikidata entry and go add information in a separate page away from the article and outside Wikipedia per se to make it accessible seems like a very steep hurdle that few authors are ever going to attempt for the vast majority of formulas, which will leave this feature as a cute demo rather than a practically valuable addition to the project. I think it seems like a waste of limited developer attention.

does no harm when formulas are clicked – this seems wrong. Sending an unsuspecting reader off-site to a weird kind of page they have never seen before when they accidentally click something that doesn't look like a link is a serious harm.

Is there a way to add the same additional metadata locally within the page? (For example, by typing <math intent="Planck's constant">\hbar</math>.) That would be a much better approach in my opinion. Wikidata does not seem to me like the appropriate venue for this. –jacobolus (t) 14:58, 17 July 2023 (UTC)

I would have thought that a screenreader should say "h bar", the way that physicists actually do when reading formulas as they write them on a blackboard. Saying "Planck's constant" is longer by a syllable and more ambiguous by a factor of $2\pi$. More generally, it might be useful to provide some semantic data about a symbol, but that data isn't always useful to read aloud! For example, lots of physics equations use $c$ to denote the speed of light. When we read them, we typically say the letter $c$, rather than saying "the speed of light". This is not a hard-and-fast rule — one might say "speed of light" to emphasize that it is light we are concerned with at the moment, rather than the speed of anything else — but one generally goes with just $c$. Alternatively, consider the letter $\pi$. It frequently stands for the ratio of a circle's circumference to its diameter, which is the sense in which I used it a few sentences ago. But it can also denote a permutation of a set, the prime-counting function, and so on. It might be helpful in some applications to tag instances of the symbol $\pi$ with semantic data that disambiguates its use (e.g., in an online textbook with a feature that lets the reader jump to the point where a notation is first introduced). But when reading a formula out loud, saying "ratio of circle circumference to diameter" instead of "pi" adds syllables while keeping the clarity at best neutral.

I am concerned that this is metadata for metadata's sake. XOR'easter (talk) 17:15, 17 July 2023 (UTC)

Without going in as much detail, I too do not consider this to be useful. If it's important to know that something is say, Pythagoras' theorem, then it will be mention in the article directly. There's no need to associated specific formulas, wheter it's $a^{2}+b^{2}=c^{2}$, $x^{2}+y^{2}+z^{2}=r^{2}$, or $r^{2}+l^{2}=h^{2}$ with a qid here. Likewise, ℏ is universally pronounced h-bar when reading formulas, rather than "the (reduced) Plank constant". Headbomb {t · c · p · b} 17:20, 17 July 2023 (UTC)

Although I completely agree for unassisted readers — this is the point of hypertext — the issue here seems to be users who are assisted by screen readers and other accessibility tools. The claim (as far as I understand it) seems to be Wikidata is the right place to provide the metadata needed to make accessibility work. Mgnbar (talk) 17:31, 17 July 2023 (UTC)

Someone should fully articulate what their vision/plan is then, and what kind of support they are expecting from volunteers. If the vision is that every formula on every page on Wikipedia should have its own wikidata entry (my current impression, but maybe that's inaccurate), that just seems like a pipe dream. –jacobolus (t) 17:39, 17 July 2023 (UTC)

I think we need specific examples of how existing accessibility technology fails and how this metadata can fix those problems. Right now, it is not clear whether existing software can make use of this metadata, or if hopes are being pinned on future software development. Nor is it clear on a more fundamental level that these WikiData entries actually can provide the right information.

I'd tend to think that instead of trying to specify "intent", the way to make screenreaders say something useful when they hit an equation is to tell them what to say. For example, <math phonetic="a squared plus b squared equals c squared">a^2 + b^2 = c^2</math> would be rendered as $a^{2}+b^{2}=c^{2}$ and read as "a squared plus b squared equals c squared". Yes, this would be work, but not necessarily more work than inserting "intent" indicators, and perhaps not necessary on every math expression, depending on how good the reader software is. XOR'easter (talk) 18:06, 17 July 2023 (UTC)

More strongly, attaching hardcoded wikidata entities to formulas is a recipe for getting the wrong wikidata item attached to the formula when people edit the formula, or when they copy-and-paste a formula and then edit it. If there is any utility to using wikidata in this way at all (something that remains to be demonstrated) it must be done from the formula itself and not from attaching auxiliary data that will inevitably become unsynched from the formula. —David Eppstein (talk) 18:07, 17 July 2023 (UTC)

The proposal seems unworkable for most mathematical expressions, including the one-off expressions that serve as intermediate steps/lemmas in bigger arguments. It might be workable for expressions that rarely change, because they are established elements of the canon — maybe something like Schrödinger equation or Mayer-Vietoris sequence? But I don't see a big accessibility benefit from tagging just those relatively static, canonized expressions.

To be clear, I'm not advocating for this proposal. I have the same worries that others here have. I was just trying to steer us away from the "this is already handled by wikilinking" argument. Mgnbar (talk) 18:37, 17 July 2023 (UTC)

Yes, absolutely agreed. Having metadata hosted on a completely separate page is a deeply flawed idea. I would expect software developers to have encountered this before: keeping specification, code implementation, tests, documentation, etc. all in sync when they are hosted on separate pages or platforms is one of the most pervasive problems in software development, a hard challenge even for the most dedicated and organized teams of paid professionals. (It's often hard to even keep comments in sync with code written on the same line!) Trying to get an army of pseudonymous, untrained, often non-technical or marginally engaged volunteers to keep tens of thousands of formulas (or likely more) synchronized with detailed metadata hosted at Wikidata one page per formula is going to be a hopeless mess. –jacobolus (t) 20:56, 17 July 2023 (UTC)

@Stegmujo: Instead of rushing to do whatever current implementation you have started or picking 100 formulas to make Wikidata entries for, my recommendation – based on my modest but certainly non-expert experience with user interface design and user experience testing – would be:

Pick one very math-heavy pages (ideally including formulas with nested fractions, continued fractions, square roots, piecewise functions, matrices, etc.) and find some mathematically sophisticated user(s) of assistive technologies, and then watch over their shoulder as they use their existing screen reading software to navigate and make sense of the page. At first just watch as they try to go through the article once, and then ask them questions about the symbolic mathematical content to see if they were actually able to make sense of it.

Then if you have an idea for improvements, make a copy of that page as a plain HTML page (i.e. not changing the Mediawiki software yet) and make whatever markup changes you want to experiment with, whether "intents" or "phonetic alternatives" or better MathML output or off-site links to Wikidata or whatever, and again watch as an actual user of the assistive technologies you are targeting tries to navigate the "improved" page, and see if they have a better time. Until you have that demo in hand, don't bother making speculative changes to Mediawiki itself, or you'll be wasting most of your time. –jacobolus (t) 21:27, 17 July 2023 (UTC)

Thanks for the proposal for annotating speech directly in the math-tags in Wikitext. I think it would be the only alternative currently to add the necessary data for speech disambiguation, but I don't think it is practical....

Wikidata is edited by the Wikimedia community as well as Wikipedia is. The special-page-links don't point at any mysterious and very dangerous webpage, but a knowledge graph for storing open data created and maintained by the Wikimedia Foundation, which has an editorial process similar to Wikipedia. Wikidata has been used for several years for annotations on Wikipedia for a vast number of wikipages. In example, in similar cases for geographic locations with the P625 property. More examples of annotations can be found here.

A speech annotation with only Wikitext will create lots of redundant data. One Wikidata item holds labels in multiple languages and can be used as a reference on multiple pages. This reduces the maintenance effort in comparison to an approach that would annotate the speech-hints directly in Wikitext. Every language page would have to contain a specific annotation. This makes the information very redundant, given the huge number of languages available. On the other hand, in Wikidata a formula that occurs multiple times would only be maintained once. Also, the annotation itself with symbolic references is language-independent, and automatic recommendations appear in the annotators' language.

Using speech annotations (for disambiguation, like W3C-intent) in the Wikipedia Wikitext editor (i.e. in the math-tag) would require introducing a new syntax to the Math-parsing components and the Wikipedia authors. Intent is an attribute of MathML, not for LaTeX math. Requiring authors to manually create annotations in a newly introduced markup increases the probability of rendering errors and typos, or requires extra time in the implementation of automated checks for the new syntax. Wikidata already offers a structure and an editor for creating formula annotations. Why rebuild the capabilities of such a tool on Wikipedia? Wikipedia also offers automated recommendations for the annotation of mathematical equations. These appear when editing the values assigned to 'symbol represents' property in the 'in defining formula statement'. A predefined 'vocabulary' with symbol representations won't be available when annotating speech hints directly on Wikipedia.

By design, Wikipedia and Wikidata should be editable by non-technical users, introducing a Wikipedia-specific annotation markup would create a steep hurdle in annotating mathematical equations.

I agree with some of the precautions for the statement that every formula variation has to have a dedicated Wikdata-Item. This is unfortunately currently the case, but I am sure a technical solution by defining a new property which allows multiple formulas in one item and making the annotated formula selectable in each annotion ( like math qid=Q12345.id123) can solve this issue.

Also, I think the clickability of the math pop-ups would rather contribute to the readers' understanding than their confusion. A widely used similar example in would be about persons. Stegmujo (talk) 16:29, 20 July 2023 (UTC)

Annotating a formula is pure nonsense. For example $|x|$ may mean "absolute value" is $x$ is a number, "norm" if $x$ is a vector, cardinality if $x$ is a set, etc. So formula annotations that are independent of a specified article cannot be mathematically correct, and are confusing by design. D.Lazard (talk) 17:26, 20 July 2023 (UTC)

@Stegmujo before you rush ahead with this, will you please please please pick a few highly technical articles with a significant number of formulas of wide variety, and try implementing your idea outside of Mediawiki proper, say just as a static website, and then directly perform some user testing on some readers with visual impairments (i.e. recruit someone, then physically go stand next to them while they try to use the page). All of your ideas seem wildly idealistic to me, and my baseline expectation is that on your current trajectory you are going to waste a whole lot of your own and other people's time, then end up with nothing to show for it.

but I don't think it is practical.... In my opinion your current proposal is completely impractical. I think you would be able to clearly see why if you tried testing your idea with some off-site experiments or gathering feedback from article authors.

Wikidata is edited by the Wikimedia community as well as Wikipedia is. – No it isn't. In my impression, Wikipedia is a hugely popular site with mass public reading and significant community engagement, while Wikidata is a niche hobby project of that the vast majority of Wikipedia authors and readers ignore to the extent possible, don't care about at all, and are confused when accidentally dumped there. This is another thing that user testing can surface. If you can recruit a few mathematically sophisticated but low-engagement (sighted) readers who mainly interact with Wikipedia by reading articles or maybe occasionally fixing typos, and sit them down in front of a demanding technical article, you can directly watch what happens when they get dumped on Wikidata. As a pretty heavily engaged editor, I find it baffling and annoying; it must be worse than that for the median reader.

One Wikidata item holds labels in multiple languages and can be used as a reference on multiple pages. – this makes matters worse, because it increases complexity and makes it more likely that the wrong annotations will be attached to the wrong formulas across projects.

would require introducing a new syntax to the Math-parsing components and the Wikipedia authors – definitely don't do that. I thought we were all talking about an annotation separate from the LaTeX markup? Please don't try to mix annotations inline in the LaTeX.

Wikidata already offers a structure and an editor for creating formula annotations – do you have a concrete example of a highly complex piece of mathematical notation so annotated which we can look at? For example, an algebraic proof with several steps, including piecewise functions, matrices, nested fractions, etc., annotated in a way that visually impaired readers using their existing screen readers find accessible?

Wikipedia also offers automated recommendations for the annotation of mathematical equations. These appear when editing the values assigned to 'symbol represents' property in the 'in defining formula statement'. – I don't know what you are talking about. Do you have a link?

... every formula variation has to have a dedicated Wikdata-Item. This is unfortunately currently the case, but I am sure a technical solution by defining a new property which allows multiple formulas in one item and making the annotated formula selectable in each annotion ... can solve this issue. – this is handwaving away the entire problem and punting solutions to the indefinite future.

–jacobolus (t) 19:35, 20 July 2023 (UTC)

The essence of tuples: notation versus mathematical concept

I am not entirely please with the beginning of the article titled Tuple. It says:

In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, which are called the elements of the tuple.

I think this confuses that which is essential to the mere notation with that which is essential to the mathematical concept.

Tuples are conventionally written with the elements in a particular order and it matters which order they're in. However, suppose we write:

barometric pressure = 1,013 millibars

relative humitity = 62%

temperature = 22 °C

and also:

relative humitity = 62%

temperature = 22 °C

barometric pressure = 1,013 millibars

These are written in two different orders, but they are both the same tuple. By contrast, in a sequence rather than a tuple, the order is essential not only to the notation, but to the mathematical concept, and usually its elements are things of the same kind; for example: the temperatures at noon on three consecutive days.

Should the article titled Tuple explain this? Michael Hardy (talk) 14:16, 8 July 2023 (UTC)

Your example is clearly some kind of ordered or indexed set (computer programmers might call this a "record" or "structure" or "named tuple"). Instead of using a counting number for your index, you are using several field names. But if you mixed the different values up and assigned them to different indices (temperature: 62%, ...), it would entirely change the meaning of your object. –jacobolus (t) 14:45, 8 July 2023 (UTC)

I agree with Jacobolus. Your key-value-pairs version of tuples is endowing them with more semantics than they usually have. Mgnbar (talk) 19:11, 8 July 2023 (UTC)

@Mgnbar: I don't understand how your comment constitutes agreement with jacobolus. At any rate, I think the account that says a tuple is always an ordered list endows them with more meaning that they properly have, whereas my account doesn't. It doesn't appear that jacobolus disgreed with anything that I wrote. Michael Hardy (talk) 19:35, 8 July 2023 (UTC)

What you describe is an instance of the dictionary problem in data structures: an association between a finite set of one kind (identities of certain parameters) and another set (the values of those parameters). If we had an article on finite functions, instead of a redirect to something unrelated, it would belong there. It is not a tuple. The distinction is clear in Python programming (where dictionaries and tuples are two different basic data structures) and I think is more or less the same as the distinction in mathematics. —David Eppstein (talk) 19:45, 8 July 2023 (UTC)

Python has a "namedtuple" constructor in the standard library which adds names to tuples (because as Michael Hardy pointed out in his example, names are often more legible to use as indices than numerical positions). A namedtuple is semantically different than a dictionary (in that the keys are pre-specified rather than arbitrarily extended at runtime), and should generally be used like a C "struct". The relevant Wikipedia article is Record (computer science). Despite the use of names, this kind of object is still conceptually quite similar to a tuple indexed by position. –jacobolus (t) 20:41, 8 July 2023 (UTC)

The issue here is that you've doubled specified the meaning whereas in a usual mathematical tuple, ordering implies meaning, and it's in that sense that the ordering matters.

For example, (0, -9, 8) normally means x=0, y=-9, z=9 in the traditional Cartesian coordinate system. You could say that this is the same as (x=0, y=-9, z=9) is the same as (x=0, z=9, y=-9), is the same as (z=9, x=0, y=-9), but plug z=9 into x, x=0 into y, and y=-9 into z and you've got nonsense. Headbomb {t · c · p · b} 19:47, 8 July 2023 (UTC)

[Edit conflict] @Michael Hardy: My sense (which agrees with the article as currently written) is that an n-tuple is essentially a function with domain {1, ..., n} (or sometimes {0, ..., n - 1}). It corresponds to an array in computer programming. Jacobolus called this situation "a counting number for your index".

Your examples are essentially functions with domain {pressure, humidity, temperature}. They correspond to associative arrays in computer programming. An associative array is a list of key-value pairs, which are also known as name-value pairs. That is, it is a list of names paired with values. Jacobolus called this situation indexing by "names". Mgnbar (talk) 20:00, 8 July 2023 (UTC)

I did disagree with what you wrote. The crux of the matter is: you are talking about an indexed data structure, not an unordered set. Usually a "tuple" is considered to be indexed by numerical position, but if you want to you can consider it to be indexed by some other kind of object (e.g. in Headbomb's example about using basis vectors as your indices). –jacobolus (t) 20:43, 8 July 2023 (UTC)

@Jacobolus: I certainly never said a tuple is an unordered set. How do you find that in anything I wrote? Michael Hardy (talk) 20:59, 8 July 2023 (UTC)

You directly claimed that the order is not essential to the mathematical concept of a tuple. I think that is wrong. If we were to qualify that by saying e.g. "it is possible to replace positional order by some other unique index scheme and end up with a closely related concept", that seems like an unnecessarily tricky semantic game, not particularly helpful to readers of the article about tuples. –jacobolus (t) 21:05, 8 July 2023 (UTC)

However, I do agree with your original observation that a tuple and a list (sequence, array, whatever you want to call it) are two conceptually different kinds of objects. –jacobolus (t) 21:08, 8 July 2023 (UTC)

@Jacobolus: My claim that order is not what is essential is not at all the same as saying a tuple is an unordered set. If you don't see that, I wonder whether you know what an unordered set is. Michael Hardy (talk) 03:02, 26 July 2023 (UTC)

@Michael Hardy – we were previously using two different concepts of "order", as I have said repeatedly. By "order" I meant something like "structure", whereas by "order" you meant "a linear sequence"; when you said that you thought a tuple didn't need order I took that to mean "unstructured", but what you apparently really meant is "we can replace one kind of structure with a slightly different equivalent variant". Which... okay I think everyone agrees. I thought we already cleared this up previously. I'm not quite sure what you are still trying to argue about. –jacobolus (t) 03:08, 26 July 2023 (UTC)

@Jacobolus: That's very far from claiming a tuple is an unordered set. The only structure in an unordered set is which things are members and which are not. In my characterization of tuples, the components have distinct roles. In an unordered set they do not. Michael Hardy (talk) 06:09, 22 July 2023 (UTC)

The way "tuple" is conventionally defined in every source I have seen, your "distinct roles" are explicitly indicated by numerical sequence order. But of course you could accomplish the same goal by specifying them some other way (which I would also consider to be a kind of "order"). Whether you consider that to be a different "kind" of object or not is a philosophical question, not a mathematical one. –jacobolus (t) 06:23, 22 July 2023 (UTC)

@Michael Hardy: Certainly not. In mathematics a three-element tuple $(S,+,\cdot )$ may define a ring as a set $S$ with binary operations $+$ and $\cdot$, which by no means is equivalent to $(\cdot ,S,+).$ As another example, an ordered pair (a two-element tuple) of numbers (2,5) defines a point in Cartesian coordinates different from (5,2). --CiaPan (talk) 21:01, 8 July 2023 (UTC)

@CiaPan: What I wrote does not imply the the ring denoted (S,+,·) is equivalent to anything denoted (·,S,+). Rather, what I wrote implies that the notation (S,+,·) is equivlanent to "the ring with binary operations '+' and '·' on the underlying set S." Michael Hardy (talk) 21:18, 8 July 2023 (UTC)

You have replaced a concise formal notation with some less formal written prose expressing roughly the same idea. There are 2 ways to look at this: either (a) you are saying precisely the same thing and calling on the same "tuple" abstraction, in which case you would still have an order involved, but have just left it implicit for now; or (b) you are invoking a less formally specified concept of a ring not built on the tuple concept per se, but which could be rewritten that way if anyone cared whereupon there would be an order involved. –jacobolus (t) 22:37, 8 July 2023 (UTC)

We might have some higher level meaning for the n-tuples in a particular circumstance which would allow us to name the elements - but tuples don't have names for the elements without that extra level which isn't part of the tuple itself. So (3,4) might be an (x,y) coordinate - but the tuple (3,4) doesn't of itself have elements named x or y. NadVolum (talk) 23:45, 8 July 2023 (UTC)

@NadVolum: We may not have words other than x-coordinate and y-coordinate or first component of the pair and second component of the pair, but the two components have two distinct roles, so that the pair (3,4) is not the same as the pair (4,3), just as the three numbers specifying the temperature, the humidity, and the barometric pressure have three distinct roles and the numbers cannot be interchanged freely. All tuples have those distinct roles, whether we have names for them or not. Michael Hardy (talk) 18:58, 9 July 2023 (UTC)

If, as the lead states, the article is about Mathematics, then the use of the term in various programming languages is irrelevant. In Mathematics, a tuple is a finite ordered list, defined in various ways, e.g., recursive ordered pairs. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 02:03, 9 July 2023 (UTC)

Draft:Kirchhoff graph

A review is being requested of this draft. Should it be accepted? I am noting that the author of the draft is the author or co-author of all the references. I haven't yet checked the policies to see whether this is considered a conflict of interest. It is not original research because the papers being cited have been peer-reviewed. Should the draft be accepted? Robert McClenon (talk) 04:31, 26 July 2023 (UTC)

I don't find it understandable. It is difficult to interpret it as properly defining its subject. It doesn't say what the vertices are, it doesn't say how a cut is to be interpreted as an element of the row space, and it doesn't say how a cycle is to be interpreted as an element of the null space. And it is stuffed full of technical trivialities making it difficult to find anything of substance in it. The conflict of interest problems are a problem, as is the issue that one of its references is not even properly published yet (arXiv preprints are not reliably published), but I think that readability is a bigger problem. —David Eppstein (talk) 04:55, 26 July 2023 (UTC)

It doesn't seem to be a notable topic. I don't think it should be accepted. Gumshoe2 (talk) 05:08, 26 July 2023 (UTC)

Aug 2023

Original proof of Gödel's completeness theorem

Some additional eyes would be generally appreciated at Original proof of Gödel's completeness theorem. There is some longer standing confusion about the argument itself, which is not helped by the fact that the article draws on none of the available secondary sources that are available on the topic. Felix QW (talk) 16:42, 25 July 2023 (UTC)

A lot of the mathematical notation is not well done. I've begun cleaning it up. Michael Hardy (talk) 21:00, 4 August 2023 (UTC)

Contrast these:

(it is thus of degree k-1)

(it is thus of degree k − 1)

I changed the former to the latter. Notice that (1) I expunged the bolding, (2) the k is italicized and the digit 1 is not (consistently with TeX and LaTeX style), (3) spacing before and after the minus sign (This is different in cases where a minus or a plus sign is used as a unary operator rather than as a binary operator. In those cases no such space is added. This is also consistent with what TeX and LaTeX do.) (4) the minus sign is not just a stubby little hyphen. Michael Hardy (talk) 21:07, 4 August 2023 (UTC)

Contrast these:

∀x₁∀x₂...∀x_k ∃y₁∃y₂...∃y_m φ(x₁...x_k, y₁...y_m)

∀x₁ ∀x₂ ... ∀x_k  ∃y₁ ∃y₂ ... ∃y_m φ(x₁ ... x_k, y₁ ... y_m)

Note that under WP:MOSMATH in this context one does not italicize digits or parentheses or other punctuation or things like cos, exp, det, max, sup, log, etc., but one italicizes variables. Note also that some space has been added between characters where appropriate. (Similarly, in the foregoing sentence I did not write "Notealsothatsomespacehasbeenaddedbetweencharacterswhereappropriate.") Michael Hardy (talk) 21:15, 4 August 2023 (UTC)

signed area

I just created a stub page for signed area which previously redirected to integral. This is a widely used concept which is not well described by integral and should have its own page (though it should probably eventually also be summarized in a section of area), so I created a stub for now with a basic definition.

I don't precisely know when I'll get around to expanding it, so other folks should feel free to jump in with any improvements or sources. –jacobolus (t) 18:15, 20 July 2023 (UTC)

You've just made me realize I've never actually properly considered what the area of a Möbius strip is or are there a couple of different reasonable areas :-) NadVolum (talk) 15:45, 22 July 2023 (UTC)

A Riemannian metric on any smooth manifold, oriented or not, defines a density, which can be integrated just like differential forms. This gives an unambiguous meaning to something like the volume of a Möbius strip with a particular Riemannian metric. (This is the general form of Riemannian volume, which in many textbooks is only dealt with for oriented manifolds.) Gumshoe2 (talk) 23:26, 25 July 2023 (UTC)

I've made it more general, but it still needs a lot of work. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 19:21, 25 July 2023 (UTC)

I've deleted the material you added, since the 2-form you wrote down has positive integral over every region; it's an unsigned area. A better differential-geometric generality might instead be based on interpreting the signed area 'under' the graph of y = f(x) as the integral of the 1-form y dx on R², taken over the graph curve. Gumshoe2 (talk) 23:23, 25 July 2023 (UTC)

Since circular angle is bounded there is no need for negative angles. On the other hand, hyperbolic angle and difference of slopes are doubly unbounded so they require a zero and orientation + or −. To give these three concepts a unified foundation, signed area is appropriate. See signed measure#Usage. Incorporation here of signed area as a fundamental tool for foundations is long overdue.Rgdboer (talk) 23:29, 25 July 2023 (UTC)

• In illustrations in Wikipedia articles the typesetting is generally of poor quality and cannot be edited without recreating the illustration. And in this one we see something that, although not abominable, is substandard and by reasonable standards incorrect:
  $${\begin{aligned}{\text{right: }}&\int _{a}^{b}f(x)\,dx\\[8pt]{\text{wrong (as it appears in the article): }}&\int _{a}^{b}f(x)dx\end{aligned}}$$
  Michael Hardy (talk) 16:35, 5 August 2023 (UTC)

  This figure is mediocre, but missing a thin space before the dx is the least of its problems. Feel free to make a new figure, and please include enough contrast between labels and background colors. Aside: For all your concern about typography, what's the deal with the big matrices inline in the text? It completely wrecks the leading (inter-line spacing) in body copy. –jacobolus (t) 18:41, 5 August 2023 (UTC)

• Oriented area was a redirect to Vector area. I've changed it to a disambiguation page also pointing to Signed area. Michael Hardy (talk) 16:51, 5 August 2023 (UTC)

  Vector area is a weird and confusing name. This redundant article should probably be merged into bivector. Or should at the least clarify that given any bivector in Euclidean space, the "vector area" is its dual (same magnitude but a complementary and perpendicular subspace of Euclidean 3-space, which can be found by multiplying [using the geometric product] by a unit pseudoscalar), but that bivector is a more general concept which generalizes to arbitrary dimension and works in the affine setting, which has traditionally (in Hamilton's quaternion system and Gibbs/Heaviside's vector analysis) been represented by a vector because these formalisms don't have any concept of bivectors. –jacobolus (t) 18:42, 5 August 2023 (UTC)

• One place where I forgot to mention that a particular area should be viewed as a signed area is on page 4 of this document. Referring to the illustration on that page, if μ is in the convex hull of the chord and the arc, then the area of the triangle is negative; otherwise positive. Michael Hardy (talk) 16:56, 5 August 2023 (UTC)
• Should we have a page titled Oriented volume? And perhaps incorporate this page into it and redirect Signed area to that? Michael Hardy (talk) 17:03, 5 August 2023 (UTC)

  There is a huge amount that could be written about signed area per se. I don't think it needs to be merged anywhere. –jacobolus (t) 18:54, 5 August 2023 (UTC)

Hypercomputation

The article Hypercomputation needs attention. It starts to become a confusing read at the second sentence. XOR'easter (talk) 21:58, 4 August 2023 (UTC)

In this version the lead was fine. --JBL (talk) 23:13, 4 August 2023 (UTC)

April 1 edits last year seem to be the culprit. --JBL (talk) 23:14, 4 August 2023 (UTC)

I have excised the problematic sentences; I haven't checked beyond the lead for other similar problems. --JBL (talk) 23:17, 4 August 2023 (UTC)

Will anyone be shocked to learn that the only other edits by that IP address are to Hava Siegelmann? --JBL (talk) 23:18, 4 August 2023 (UTC)

It also does not shock me to learn that someone into bio-inspired AI might also be into hypercomputation. —David Eppstein (talk) 02:14, 5 August 2023 (UTC)

Thanks for the excisions. The page is still tagged for various things; I'm guessing that this is a topic where plenty of offbeat ideas have been aired, and anything that anybody thought sounded cool eventually got added to Wikipedia. XOR'easter (talk) 22:30, 5 August 2023 (UTC)

Two math articles at WP:FAC

Two articles with substantial mathematical content are currently under consideration to become featured articles: they are Quine–Putnam indispensability argument and Affine symmetric group. (Currently, fewer than 10 articles on mathematics (as opposed to, say, mathematicians) are featured articles.) As part of the FAC process, reviews are required by members of the community. If you might be interested in reviewing one of these articles, you can follow the instructions at Wikipedia:Featured article candidates#Commenting, etc. --JBL (talk) 17:52, 3 July 2023 (UTC)

If you would like/be willing to contribute reviews of either of these articles, it would be good to do so sooner rather than later! You can comment at Wikipedia:Featured article candidates/Affine symmetric group/archive1 and Wikipedia:Featured article candidates/Quine–Putnam indispensability argument/archive1. --JBL (talk) 18:53, 24 July 2023 (UTC)

Another featured article candidate is Logic, which relates to mathematics, although it mainly deals with philosophy. See Wikipedia:Featured article candidates/Logic/archive1 for someone who interests in reviewing the article. Dedhert.Jr (talk) 10:47, 26 July 2023 (UTC)

This should be a reminder to keep Wikipedia:WikiProject Mathematics/Article alerts on your watchlist. Then you get watchlist notices of everything ongoing! Headbomb {t · c · p · b} 11:41, 26 July 2023 (UTC)

I see that Quine–Putnam indispensability argument has been promoted. Affine symmetric group looks close. XOR'easter (talk) 22:32, 5 August 2023 (UTC)

is there an article about degeneracy to an infinite/infinitesimal approximation?

I've been working on articles about spherical geometry, cartography/geodesy, etc., and one common observation/tool used, especially in practical applications, is that in the infinitesimal limit the sphere (or any other 2-dimensional Riemannian manifold for that matter) looks locally Euclidean, so that tools of affine or Euclidean geometry can be used without too much error for small areas on the sphere, or e.g. a flat map of some part of the world can be treated as a faithful enough representation. Many theorems in Euclidean geometry are degenerate limiting cases of analogous theorems in spherical or hyperbolic geometry. This is a common theme more generally, with e.g. Taylor polynomials often used as function approximations for very small arguments in numerical computations. Right now the titles much greater than and much less than redirect to Inequality (mathematics), which (a) doesn't do a very good job explaining what these mean or why they are used, and (b) seems like the wrong home for these infinite or infinitesimal approximations. We also have Degeneracy (mathematics) and Limiting case (mathematics), but these both seem much broader than what I am talking about (and are also not very good articles). We also have Small-angle approximation which is one specific example but a bit narrower in scope than I am imagining. There is also Asymptotic analysis but this seems like a distinct (albeit related) topic.

Do we have an article matching this idea? If not, would it be a good idea to add one? (I would imagine e.g. redirecting much greater than and much less than there.) What would a good title be, and can anyone think of good canonical sources? –jacobolus (t) 23:58, 5 August 2023 (UTC)

Wikipedia:Notability (academic journals) has an RFC

Wikipedia:Notability (academic journals), which is within the scope of this WikiProject, has an RFC for possible consensus. A discussion is taking place. If you would like to participate in the discussion, you are invited to add your comments on the discussion page. Thank you. Tercer (talk) 13:57, 6 August 2023 (UTC)

Proofs in math articles

Is there any general guidance about whether a proof should be given for a result stated in an article? Thanks. ByVarying (talk) 00:08, 3 August 2023 (UTC)

This is up to Wikipedians' discretion, but personally I like to see a proof or proof sketch if the article is about a theorem directly, especially if the proof is not too complicated. –jacobolus (t) 01:35, 3 August 2023 (UTC)

We've discussed this before; check the archives. My preference is to include proofs when they are separately noteworthy (as in, multiple sources have discussed that specific proof) or when the proof itself would help readers understand the topic, but not when they are just routine manipulation or don't have a proper source. —David Eppstein (talk) 01:51, 3 August 2023 (UTC)

A reference to a proof in a reliable source is always preferable. Occasionally the idea of a proof can be mentioned if it helps to understand the topic, as David Eppstein mentioned. But giving a proof for every single result in an article is not recommended and is counterproductive, as it makes the whole article hard to read and buries the overall content in minute technical details. Remember, the purpose of Wikipedia is not to "teach" a subject, but to summarize mathematical knowledge as it is present in reliable sources. PatrickR2 (talk) 03:11, 3 August 2023 (UTC)

A proof for every result in a broad article (say calculus or ellipse or group) turns it from an encyclopedia article into something more like a mathematical monograph or textbook, ballooning the content without necessarily much value to readers looking for an overview. But in the case that the result itself is the direct subject of the article, then having a proof (or sometimes several proofs) can help to explain why the result is true, why it is interesting, what connection it has to other fields, etc. For some arbitrary examples of famous relatively accessible theorems, see Pythagorean theorem, quadratic reciprocity, Chinese remainder theorem, fundamental theorem of calculus, square root of 2#Proofs of irrationality, central limit theorem, Sylow theorems, Brouwer fixed-point theorem. –jacobolus (t) 05:50, 3 August 2023 (UTC)

We are both in complete agreement. PatrickR2 (talk) 18:39, 3 August 2023 (UTC)

I think that nearly everyone would agree, as a general but non-absolute rule, that it's bad to give complete details of a proof. I agree with jacobolus that on a page for a specific theorem it's good to give, at the least, an indication of what's involved in the proof. It's easy to give more details than appropriate (and I've certainly been guilty of it!). Gumshoe2 (talk) 08:12, 3 August 2023 (UTC)

@Gumshoe2: That depends very much on the context. If the article is titled Proof that pi is irrational then the proof needs to be there. Michael Hardy (talk) 18:26, 3 August 2023 (UTC)

Agreed, that's why I say it's a non-absolute rule. There are some obvious exceptions. Gumshoe2 (talk) 18:33, 3 August 2023 (UTC)

I think that it's good to give proofs of important and notable theorems (for example, the functional equation of the Riemann zeta function). You can also make them collapsible so that they don't take up space. A1E6 (talk) 12:21, 3 August 2023 (UTC)

I'd leave out the 'important' and only have ones which are notable in themselves as proofs. And no need for the proof to be a watertight proof - what it should show is why the proof is notable. Sometime it can be worthwhile to include very simple proofs which make the article hang together without too much clicking - one or two lines. Textbooks or papers can be referred to anything more. What I've left out there is things like the multiple proofs of root 2 being irrational which I fully approve of including but haven't rationalized yet ;-) NadVolum (talk) 18:53, 3 August 2023 (UTC)

+1. Lots of important theorems have unenlightening or uncondensable proofs (the four color theorem comes to mind immediately). A good encyclopedic treatment might summarize the key ideas of the proof. --JBL (talk) 18:59, 3 August 2023 (UTC)

Of course; if a proof is too long, only summarizing its key points is appropriate. A1E6 (talk) 17:35, 4 August 2023 (UTC)

I did my best to summarize what I take to be the general attitude about this in my "So, you've decided to write about physics and/or mathematics on Wikipedia" advice page. XOR'easter (talk) 17:43, 7 August 2023 (UTC)

That's nicely put. --JBL (talk) 19:55, 7 August 2023 (UTC)

I definitely agree that important theorems, closely related to the subject of the article, generally deserve a proof or proof sketch in the text. The objective should be to show why the result is true, if possible, and to give an overview of the proof. If the proof is simple enough, a complete proof may be appropriate; in general probably proof sketches are better. - CRGreathouse (t | c) 13:51, 7 August 2023 (UTC)

Should I include a proof about the example of non-surjective epimorphism in the category of rings ? If we don't include the proof, this example might be better added to epimorphism. --SilverMatsu (talk) 02:41, 6 August 2023 (UTC)

This example is already (without proof) in Homomorphism#Epimorphism.

By the way, in this article there are proofs that, for "most" algebraic structures, "monomorphism=injection" and "epimorphism=surjection". This is a case where proofs are needed for verifiability, because, as far as I know, sources for the general cases are generally much more technical (general category theory) than the level of the article, and therefore not accessible for the common reader. D.Lazard (talk) 14:27, 6 August 2023 (UTC)

It seems that users who insert proofs into articles without references are often the ones that make the most mistakes. Something can look correct but be deeply misleading. (For instance, an editor might argue that it's common knowledge that the antiderivative of 1/x is ln|x|+C, but that ignores the fact that the two branches can have different constants). I agree with others that proofs should only be included if references are given; otherwise it is the literal definition of original research. Brirush (talk) 14:31, 6 August 2023 (UTC)

Personally, I like to see proofs when they are unusually elegant, or when they shed light on other topics. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 09:41, 8 August 2023 (UTC)

Too closely following text

On the page Projective tensor product, two sections, "Seminormed spaces" and "Examples" follow a book by Trèves on topological vector spaces very closely, basically all but verbatim. I also removed a lot from the page that I thought trivial or not notable, and these sections could very well fall under that too. I'm wondering what to do about these sections if anyone could give them a look. ByVarying (talk) 19:05, 9 August 2023 (UTC)

Oops, I forgot that the "Examples" section is cited to Schaefer and Wolff's book on topological vector spaces (of which I only have access to the older edition) but I have the same concern. ByVarying (talk) 19:45, 9 August 2023 (UTC)

@Mgkrupa: this appears to be your doing. Care to explain yourself? —David Eppstein (talk) 19:19, 9 August 2023 (UTC)

You said:

"follow a book by Trèves on topological vector spaces very closely, basically all but verbatim."

I just compared my edits with Trèves pp. 434-438 and it is not a verbatim copy.

Recall the definition of "verbatim":

verbatim (not comparable)

1. Word for word; in exactly the same words as were used originally. [quotations]

I have copied his speech verbatim, so this is exactly what he said, word for word.

Unlike my edit, the definition above was copied verbatim.

I did use much - but clearly not all (e.g. where's $\theta$?) - of the notation found in Trèves. (Is this not allowed for notation?) But please tell me what notation I should use for the tensor product of $p$ and $q$ if not $p\otimes q$? Ditto for the tensor product of sets?

And if you ignore all the content from Trèves that I didn't include and also ignore the parts that are out of order (e.g. I defined tensor products of seminorms before describing neighborhoods of the origin whereas Trèves presented neighborhoods first), then I did follow Trèves's presentation (as can be concluded from my citations to him) but nowhere did I plagiarize. Mgkrupa 02:34, 10 August 2023 (UTC)

I said "all but verbatim," not "verbatim." The point is that taking large portions of the source text and changing notation, phrasing, and order only just enough that it's not verbatim, which looks like what happened here, does not comply with policy. See WP:PARAPHRASE, which says among other things, Close paraphrasing ... when extensive (with or without in-text attribution) may also violate Wikipedia's copyright policy. ByVarying | talk 03:06, 10 August 2023 (UTC)

Thank you for clarifying that by "all but verbatim" you meant "closely paraphrasing". I just read through Wikipedia:Close paraphrasing in its entirety (thank you for the link) and although I feel that my edits are consistent with this policy (and I can argue this), I'd prefer to take the path of least resistance and instead work with you to edit the article in a way that resolves your concerns.

And since you are (presumably) better acquainted with the Wikipedia:Close paraphrasing policy than I am, perhaps you'd be willing to help me understand your concerns by discussing in detail some specific sentences that you think are problematic. I realize (based on your original post) that you think that every sentence in the section on seminormed spaces violates WP:PARAPHRASE but my paraphrasing of Prop 43.1 (for instance) is so substantially different from Trèves's statement on p. 435 that I do not see how WP:LIMITED doesn't apply since there's only so many ways you can change certain equations/definitions/facts before you start to violate some other Wikipedia policy. (For example, Trèves's definition of $p\otimes q$ that I gave in the article is clearly just the Minkowski functional of the set and that's the wording I would use, but I can't define it that way since then I'd be accused of violating WP:SYNTHESIS or WP:ORIGINAL RESEARCH).

The article's talk page (Talk:Projective tensor product) is the appropriate place to do discuss this futhure. I will start making changes once I can dedicate enough time to this, but you should please feel free to change the article as you wish (including the sentences that you consider problematic). Mgkrupa 18:13, 10 August 2023 (UTC)

Ok, thank you for being open to discussing this and I'll respond there. ByVarying | talk 18:27, 10 August 2023 (UTC)

Hilbert space pre-GAR

Hilbert space is currently designated a Good article. The GA criteria were recently tightened to require more inline citations. It would be nice if we could address this before going through the whole rigmarole of a Good Article Review. Somebody with the right textbook on their shelf could probably go through and knock out most if not all of the required footnoting in a single pass. See the Talk page for details. XOR'easter (talk) 17:51, 7 August 2023 (UTC)

And on the topic of Hilbert space, should the category be Category:Hilbert spaces or Category:Hilbert space? It was moved from the latter to the former a few months ago [7][8], seemingly without any notifications or discussion anywhere, though I might have missed something. I'd say that it should be in the singular, since it contains articles that pertain to the theme of Hilbert space but aren't about examples of Hilbert spaces. XOR'easter (talk) 00:24, 12 August 2023 (UTC)

I agree. The plural would be correct if we had lots of articles on individual Hilbert spaces, but for a category about the theory of these spaces, it should be singular. —David Eppstein (talk) 02:03, 12 August 2023 (UTC)

Affine symmetric group

Affine symmetric group is at FAC and would benefit from someone familiar with this subject inputting on the sourcing. See the bottom of the page here. Thanks. Gog the Mild (talk) 18:03, 17 August 2023 (UTC)

To be explicit about what is requested: in the section Source review, Jo-Jo Eumerus has marked six footnotes as needing to be checked by a mathematician as to whether the material to which they are attached is appropriately sourced (the footnotes support the article, the content of the sources is correctly represented in the article, the sources are reliable, etc.). Any help with this would be greatly appreciated. --JBL (talk) 20:40, 20 August 2023 (UTC)

Smith–Volterra–Cantor set

I have a concern about whether the name "Smith–Volterra–Cantor set" is in fact standard. I posted a note at talk:Smith–Volterra–Cantor set#Naming, but it's a low-traffic article and I don't really know whether anyone will notice it. Anyone who can contribute, it would be appreciated. --Trovatore (talk) 20:24, 21 August 2023 (UTC)

Lead image in Tree (set theory)

I am having a dispute with an editor of Tree (set theory) who insists on adding a lead image that depicts a graph-theoretic tree, not a set-theoretic tree (the difference is that in graph-theoretic trees every node except the root has a parent, and following parent links will eventually reach the root, but in set-theoretic trees the ancestors of any node can have arbitrary well-orderings in which not all elements have a parent). Additional informed opinions would be very welcome at Talk:Tree (set theory) and in editing the article (or maybe finding or creating a more appropriate lead illustration). —David Eppstein (talk) 04:32, 27 August 2023 (UTC)

Italics on Pentagramma mirificum

Should the title of this article be italicized? I forgot if every Latin term should be so, according to the guidelines.--ReyHahn (talk) 14:51, 25 August 2023 (UTC)

According to WP:ITALICTITLE, yes: Use italics when italics would be necessary in running text; for example, ... foreign phrases are italicized both in ordinary text and in article titles. —David Eppstein (talk) 04:36, 27 August 2023 (UTC)

It appears that it is used in italics in the article so I will carry out the italicization of the title. Be free to revert otherwise.--ReyHahn (talk) 12:29, 28 August 2023 (UTC)

Hurwitz space

I've promoted this from AFC. Its seems genuine and well referenced. I'm not a mathematician so I looked up some references to confirm its existance and to determine if there was an article on Wikipedia on the subject, but doesn't appear so. scope_creep^Talk 06:05, 31 August 2023 (UTC)

It's definitely a real thing; I am not an expert in this subject, but I am inclined to agree that it is not duplicative of existing content (at least that I could find). Thanks for promoting it. --JBL (talk) 17:22, 31 August 2023 (UTC)

Emmy Noether

Algebraically inclined editors may wish to look at Talk:Emmy Noether#WP:URFA/2020, where there is discussion of whether Emmy Noether meets current featured article standards (and if not, what must be improved). — Bilorv (talk) 17:36, 28 August 2023 (UTC)

So I don't have anything to add to that as a discussion per se but are there particular tasks that if someone did them it would be helpful for ensuring that the article stays at FA? --JBL (talk) 17:37, 31 August 2023 (UTC)

"Background on abstract algebra and begriffliche Mathematik (conceptual mathematics)" has only one reference, and the following subsection has none. The book containing the van der Waerden quote isn't a very good reference for the rest of the subsection; a textbook on abstract algebra would be more helpful there. XOR'easter (talk) 18:53, 31 August 2023 (UTC)

Where is the right place to feature request support for LaTeX macros/packages?

Wikipedia's Math/LaTeX syntax doesn't support the \rlap, \llap, \clap macros. I'd like to request feature support for these macros (perhaps in mathtools package? I'm not sure). These macros are incredibly useful to pad/align equations and terms, especially when the equations are in a column in a table and can't rely on a single align block. For instance, compare the table at Inverse trigonometric functions#Solutions to elementary trigonometric equations with its layout/markup prior to my edits. I had to use a lot of \;\,\qquad -style spacing. But instead, I could have used a more "semantic" spacing à la the following, if \rlap were available (ignore the align block; I used that in an external Latex editor to help me get the alignment):

\begin{align*}
\theta &= \rlap{(-1)^k}\phantom{(-1)^k\;}\rlap{\arcsin(y)}\phantom{arccos(x)} + \rlap{}\phantom{2\,}\pi k \\
\theta &= \rlap{(-1)^k}\phantom{(-1)^k\;}\rlap{\operatorname{arccsc}(r)}\phantom{arccos(x)} + \rlap{}\phantom{2\,}\pi k \\
\theta &= \rlap{\pm}\phantom{(-1)^k\;}\rlap{\arccos(x)}\phantom{arccos(x)} + \rlap{2}\phantom{2\,}\pi k \\
\theta &= \rlap{\pm}\phantom{(-1)^k\;}\rlap{\operatorname{arcsec}(r)}\phantom{arccos(x)} + \rlap{2}\phantom{2\,}\pi k \\
\theta &= \rlap{}\phantom{(-1)^k\;}\rlap{\arctan(s)}\phantom{arccos(x)} + \rlap{}\phantom{2\,}\pi k \\
\theta &= \rlap{}\phantom{(-1)^k\;}\rlap{\operatorname{arccot}(r)}\phantom{arccos(x)} + \rlap{}\phantom{2\,}\pi k \\
\end{align*}

Where do I lodge a feature request? Or should I lobby for it here first, and get community support for it? What's the process for Latex package addition? Thanks.  — sbb (talk) 17:53, 31 August 2023 (UTC)

You would want to use the Phabricator bug tracking system using the math tag. See https://phabricator.wikimedia.org/project/view/130/ There are other feature requests for extended maths syntax there. Don't expect a quick resolution, though.--Salix alba (talk): 18:13, 31 August 2023 (UTC)

Thank you. I completely understand not to expect a quick resolution. But it doesn't hurt to try to get reasonable requests in the queue! =)  — sbb (talk) 20:02, 31 August 2023 (UTC)

If you just care about this specific case, you could do something like:

${\begin{alignedat}{4}\theta ={}&&(-1)^{k}\,&\arcsin y&&+{\phantom {2}}\pi k,\\\theta ={}&&(-1)^{k}\,&\operatorname {arccsc} r&&+{\phantom {2}}\pi k,\\\theta ={}&&\pm \,&\arccos x&&+2\pi k,\\\theta ={}&&\pm \,&\operatorname {arcsec} r&&+2\pi k,\\\theta ={}&&&\arctan s&&+{\phantom {2}}\pi k,\\\theta ={}&&&\operatorname {arccot} r&&+{\phantom {2}}\pi k,\\\end{alignedat}}$

–jacobolus (t) 18:37, 31 August 2023 (UTC)

Thanks for that suggestion! Yeah, I always get confused about alignat positioning. I know each & demarcates an alternating left- or right-aligned column, but it still always confuses me.

But that doesn't work at all in cases where the equations are on separate rows in tables, which is what motivated my original question. Here's a reduced form of the table in the article I linked to:

Solution ​(for some $k\in \mathbb {Z}$)
$\theta =(-1)^{k}\arcsin(y)+{\phantom {2\,}}\pi k$
$\theta =(-1)^{k}\operatorname {arccsc} (r)+{\phantom {2\,}}\pi k$
$\theta ={\phantom {\quad \,\,}}\pm \arccos(x)+2\,\pi k$
$\theta ={\phantom {\quad \,\,}}\pm \,\operatorname {arcsec} (r)+2\,\pi k$
$\theta ={\phantom {(-1)\,\,}}\arctan(s)+{\phantom {2\,}}\pi k$
$\theta ={\phantom {(-1)\,\,\,}}\operatorname {arccot} (r)+{\phantom {2\,}}\pi k$

 — sbb (talk) 19:59, 31 August 2023 (UTC)

Sep 2023

COI edit request at Probability box

A COI editor has made a request for information to be added to the Applications section of this article. The requesting editor appears to be the author of the reference they are hoping to apply to the requested addition to that section. Unfortunately, Space Trajectory Optimization Asteroid Impact Monitoring State Estimation is not independently notable (nor for that matter, are many other items in the Applications section). Thus, I was hoping someone more mathematically inclined could have a look? Thank you very much for any help on this. Regards,  Spintendo  01:01, 31 August 2023 (UTC)

Wikipedia:WikiProject_Statistics may be a better fit for your query. PatrickR2 (talk) 00:20, 1 September 2023 (UTC)

Thank you  Spintendo  19:59, 1 September 2023 (UTC)

Craig S. Kaplan

• Craig S. Kaplan (edit | talk | history | protect | delete | links | watch | logs | views)

Editors are concerned about a notability tag and there is a report at ANI. The report is rather premature as there do not appear to be any comments that would generally be considered unacceptable. Please join in at Talk:Craig S. Kaplan (the ANI report won't go anywhere). If participants here consider the subject to be notable (it looks that way to me), please remove the tag and tell anyone wanting to restore it to take the article to WP:AFD. Johnuniq (talk) 03:31, 10 September 2023 (UTC)

Edit war and content dispute at Interval (mathematics)

Third-party opinion would be welcome at Talk:Interval (mathematics)#New edits by 慈居. D.Lazard (talk) 09:50, 14 September 2023 (UTC)

Draft:Aliasing (factorial experiments)

This is a long, text-book-like draft at AfC. We are having problems finding a knowledgeable editor to help the editor, Johsebb, get it into acceptable form. Help would be appreciated. StarryGrandma (talk) 16:37, 18 September 2023 (UTC)

q-pseudoconvex, q-pseudoconcave, q-complete

I am adding references to the Andreotti–Grauert theorem and I am wondering where to explain the notions called q-pseudoconvex, q-pseudoconcave, q-complete. Since these notions were introduced by Andreotti-Grauert (1962), one way is to explain them in the Andreotti-Grauert theorem. In that case, it might be better to change the title of the article to Andreotti–Grauert theory, but it seems like the lead sentence needs to be rewritten. Also, I have no ideas for the lead sentence about Andreotti–Grauert theory. Another way is to explain q-pseudoconvex with pseudoconvexity and q-complete with Stein manifold, but I don't know where to explain q-pseudoconcave. SilverMatsu (talk) 08:26, 23 September 2023 (UTC)

Simplification

Can anyone check my working at Talk:Alignments_of_random_points#Simplification, please? Perhaps I'm being obtuse, but surely the second, simplified form is a correct simplification of the first; if so, what mystifies me is why the original source wrote in it the original form. — The Anome (talk) 10:57, 30 September 2023 (UTC)

Oct 2023

Draft: Mathematical Growth

I have looked for but could not find a good overview of the different kinds of growth that could be described mathematically, so I tried to write one. The article has been reviewed and found to be lacking technical depth or adequate references. As I explained in the Talk section for the article, I was aiming the article at non-mathematicians, and more technical explanations can be found in the articles on the individual types that are linked. Can anyone give me guidance on finding and citing better references? Thanks Pbergerd (talk) 16:53, 11 October 2023 (UTC)

PS: I could search the University of Wisconsin libraries for sources, but am not sure what to look for. Pbergerd (talk) 16:59, 11 October 2023 (UTC)

I gave some suggstions on Draft talk:Mathematical growth. However, the draft appears as an informal introduction to Asymptotic analysis. So, a possibility is to use it for providing a less technical introduction of this article, and, possibly, add a new section "Motivation". In this case, Mathematical growth could be a redirect to Asymptotic analysis. This deserves to be discuted, and this is a better place than the talk page of the draft. D.Lazard (talk) 18:10, 11 October 2023 (UTC)

Good article reassessment for John von Neumann

John von Neumann has been nominated for a good article reassessment. If you are interested in the discussion, please participate by adding your comments to the reassessment page. If concerns are not addressed during the review period, the good article status may be removed from the article. Thebiguglyalien (talk) 07:21, 23 September 2023 (UTC)

There are two {{citation needed}} tags that I don't have the books on my shelf at the moment to fix immediately (but the text they're attached to doesn't seem controversial). XOR'easter (talk) 19:21, 24 September 2023 (UTC)

One {{citation needed}} yet remains. I've tried my hand at reorganizing the article to make more clear what can be trimmed. XOR'easter (talk) 17:36, 25 September 2023 (UTC)

Specifically, the question is how to source this paragraph:

With the contributions of von Neumann to sets, the axiomatic system of the theory of sets avoided the contradictions of earlier systems and became usable as a foundation for mathematics, despite the lack of a proof of its consistency. The next question was whether it provided definitive answers to all mathematical questions that could be posed in it, or whether it might be improved by adding stronger axioms that could be used to prove a broader class of theorems.

--JBL (talk) 17:46, 25 September 2023 (UTC)

This is an entirely uncontroversial claim that probably should never have been tagged "cn", but I added a source. –jacobolus (t) 19:28, 25 September 2023 (UTC)

Thanks. It did seem like a statement that could equally well be supported by any of a bajillion books. XOR'easter (talk) 20:00, 25 September 2023 (UTC)

I guess on the upside, the Stanford Encyclopedia of Philosophy page I linked there (found via googling) is a pretty good summary which talks about Von Neumann's contributions and puts them in context, so would probably be useful to a hypothetical reader interested in following up on the section here. –jacobolus (t) 01:53, 26 September 2023 (UTC)

The quote is obviously true. Completeness cannot be expected. JRSpriggs (talk) 18:45, 25 September 2023 (UTC)

Thanks for all the work that has been put into this. I don't think I'll have time to do more (and to be honest, the box-checking attitude on display has soured me the rest of the way from ever dealing with GA/FA business). XOR'easter (talk) 16:09, 29 September 2023 (UTC)

I thought some more about this and tried to identify any portions that could be split off into their own articles. The only part that seemed like it could prosper more as its own page was the list of publications (see here for further background). XOR'easter (talk) 21:14, 12 October 2023 (UTC)

C_4v point group

I'm trying to find the meaning of $C_{4v}$ point grup, a pyramidal symmetry of order 8, while in few days ago I have googled on it. My interpretation about this point group states that a solid with square base is symmetrical as one rotates for every quarter-turn of a full angle around the axis of symmetry, two vertical planes pass through diagonals of a square base, and two other vertical planes pass through the midpoints of the edges of square base. Is it correct?

I'm not actually expert at this subject. I would appreciate for the explanation or correction about my interpretation. Dedhert.Jr (talk) 06:24, 16 October 2023 (UTC)

That's correct. You just extend the symmetry group of a plane square (a dihedral group $D_{4}$ of order 8) to act on the 3-space by acting trivially on the direction orthogonal to the plane (the symmetries of the pyramid must preserve the base since it's the only square face, and they can't reverse the orthogonal direction since they have to fix the apex). The article you linked could use some editing. jraimbau (talk) 08:49, 16 October 2023 (UTC)

@Jean Raimbault Thank you. Sadly, I cannot edit the article I linked due to lack of knowledge. Hopefully someone can explain more detail about the generalization of $C_{nv}$ point group, a symmetry of order $2n$. Dedhert.Jr (talk) 09:42, 16 October 2023 (UTC)

Hindu–Arabic numeral system

There is an editorial dispute concerning possible Chinese origins for the Hindu–Arabic numeral system, please see talk:Hindu-Arabic numeral system. Paul August ☎ 21:33, 18 October 2023 (UTC)

Edit an article at first time

Hello! I'm old man enough and now try to do something useful. I'm interested in computational math and got some results on OEIS etc. So now I’m dealing with centroidal Voronoi tesselations, imho very interesting subject. The Wiki paper Centroidal_Voronoi_tessellation

- is a stub

- contains inaccuracies (stable and unstable CVT mixed)

- very outdated

So I'd like to edit it and got enough data for it, but

- feel self-doubt

- don't know is it useful

So will be very glad of any support and advice here!

UPD

Thank you very much for your support, but the question is more complicated than I thought. If ones has rights of OEIS editor please look at these drafts: https://oeis.org/draft/A363822 https://oeis.org/draft/A366544 but it's just tip of the iceberg ((

Dharmacat (talk) 18:17, 10 October 2023 (UTC)

I think it would be a good idea if you can i,prove the article (or any others). Changes should be referenced, if needed. Bubba73 ^{You talkin' to me?} 19:15, 10 October 2023 (UTC)

Is there a kind of sandbox in Wiki? Dharmacat (talk) 08:51, 11 October 2023 (UTC)

@Dharmacat: There is the main sandbox at Wikipedia:Sandbox, but you may prefer to use a personal sandbox at Special:Mypage/sandbox. —Kusma (talk) 09:32, 11 October 2023 (UTC)

Aha, many thanks! Dharmacat (talk) 11:45, 11 October 2023 (UTC)

If you need help, feel free to come back here to ask questions (or even on my Talk page). But the basic guidance here, especially when you're improving a stub article, is to be bold: make the changes that will improve things, don't worry too much about making mistakes. You can fix them or someone else may come along.

Honestly, this is probably the best way to get started (the worst would be on an established, controversial article).

- CRGreathouse (t | c) 12:56, 11 October 2023 (UTC)

Actually, if you have never edited anything on Wikipedia, I suggest to not "be bold" but instead start by doing a few small fixes on existing articles, just to get the hang of it. Could be something really simple like fixing spelling or grammar mistake, adding a reference, etc. PatrickR2 (talk) 16:40, 11 October 2023 (UTC)

I have a page of advice about writing mathematics/physics on Wikipedia that may be helpful. XOR'easter (talk) 17:58, 12 October 2023 (UTC)

I'd say that this is a very good write-up. Bubba73 ^{You talkin' to me?} 19:18, 12 October 2023 (UTC)

There is a lot of overlap between the topic of this article and of Lloyd's algorithm. So if you're going to improve the article (please do!) you might also check that the two articles divide their topic matter in the appropriate way. —David Eppstein (talk) 21:49, 12 October 2023 (UTC)

I suggest that you read Help:Wikitext, WP:Citing sources, Help:CS1 and Help:CS2; it might help to play with the templates in your sandbox. I endorse the advice to BEBOLD, at least in stub articles. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:18, 25 October 2023 (UTC)

FPSAC, and notable conferences

I notice that the International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC) has been proposed for deletion. This is a highly prestigious conference with extended abstracts, comparable in several ways to a journal; I think it is the main conference in algebraic combinatorics, broadly considered. Does WP:NJOURNALS apply? If it is not notable, does a similar argument for deletion apply to e.g. Symposium on Discrete Algorithms (SODA)? (While the SODA article is better developed, the concern of primary sourcing still holds.) I think that there may be several similar conferences around theoretical computer science and nearby areas. Disclosing that I served on the scientific committee of FPSAC the year that it was in Slovenia. Russ Woodroofe (talk) 09:05, 28 October 2023 (UTC) Addition: or alternatively, do proceedings published in well-established journals satisfy GNG? Russ Woodroofe (talk) 10:46, 28 October 2023 (UTC)

It is very difficult to source articles on conferences, even major and well-established ones, and even considering selective indexes to be sources as NJOURNALS does. They are not generally indexed except by specialized sources like DBLP (which is not very selective), it is difficult to find people who write much about them rather than merely publishing in them, and often when they do write about them it is in non-independent sources such as prefaces to the conference proceedings. For SODA, it is possible that there is something about it in SIGACT News, like a report from an instance of the conference, but as an ACM publication that might not be considered independent enough. —David Eppstein (talk) 16:54, 28 October 2023 (UTC)

Nov 2023

Wikipedia talk:WikiProject Mathematics/Archive/2023/Nov

Dec 2023

Wikipedia talk:WikiProject Mathematics/Archive/2023/Dec