Talk:History of algebra

Confusion between branch of maths and European name

If this article is about a branch of mathematics then the emphasis should be on the branch rather than on the name. Indians for example call this Beeja-Ganita or the 'seed mathematics'. The man behind the name algebra is al-kearizmi. He studied and translated Indian works of Beeja-Ganita earlier. Then etymology will have to include etymology of what others call it as well like in China, India. I will add Beeja-Ganita. Other who know what it is called please add the names. ~rAGU (talk)

Hlo the article about beeja ganita was written by bhaskaracharya 2 who lived in 12th century but al khwarzimi lived in 9th century.He didn't translate work of indians as he lived at the time beeja ganita wasn't even written at all. Obiwana (talk) 03:19, 28 December 2022 (UTC)

Alexandrian University?

I've removed a reference to the "university" at Alexandria. While technically, I suppose the various schools of Alexandria shared resemblance to what we would now term a "University," but the description is anachronistic, and gives the false impression that some sort of tradition of "universities" originated with the Greeks that is directly linked to the modern institutions of that name. Obviously, the word university, is not even Greek in origin, and was coined long after Hellenistic civilization collapsed. Semantic issues aside, Alexandria contained many schools, not a single unified one.

Omar Khayyam and algebraic geometry

I have removed the sentence:

Another Persian mathematician, Omar Khayyam, developed algebraic geometry.

Since it is not sourced and also because there is evidence to the contrary:

Boyer, Carl B. (1991). "The Arabic Hegemony". A History of Mathematics (Second Edition ed.). John Wiley & Sons, Inc. pp. 241–242. ISBN 0471543977. One of the most fruitful contributions of Arabic eclecticism was the tendency to close the gap between numerical and geometric algebra. The decisive step in this direction came much later with Descartes, but Omar Khayyam was moving in this direction when he wrote, "Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras are geometric facts which are proved." {{cite book}}: |edition= has extra text (help)

So although Omar Khayyam was moving in the right direction he did not actually get to the destination and so he did not "create" algebraic geometry. selfworm 23:30, 20 February 2007 (UTC)

What, no Descartes?

A history of algebra with nary a mention of René Descartes? How's that? Is his invention of analytic geometry not considered part of the history of algebra? -GTBacchus^(talk) 21:13, 7 September 2007 (UTC)

Don't worry, there'll soon be mention of him. Just give me about one to two weeks. selfworm^Talk) 00:33, 8 September 2007 (UTC)

Removed incorrect citation

I have removed the sentence "is initiated by Abū al-Hasan ibn Alī al-Qalasādī and" since this is not what the source says. The source clearly says that he "took the first steps toward the introduction of algebraic symbolism." A look at his notaion will reveal that although his notation was closer to symbolic algebra than that of Diophantus or Brahmagupta, he did not have symbolic algebra since he used abbreviations such as the following,

j from jadah meaning "root"

[...]
m from mal for x²
k form kab for x³
al-Qalasadi

which are not considered as being a part of symbolic algebra.

That he did not "initiate" it is even clearly stated in the given source:

Certainly symbols were not the invention of al-Qalasadi. Perhaps even more telling is that the particular symbols he used were not even his own invention since the same ones had been used by other Muslim mathematicians in North Africa 100 years earlier. [...] We must stress that he does not clam originality - this was the incorrect invention of historians 400 years later.al-Qalasadi

Take care. selfworm^Talk) 07:42, 13 February 2008 (UTC)

Italian Renaissance algebrists

General solution of cubic and quadratic equations were obtained by italian algebrists (Scipione Del Ferro...) in the XVI century. It represented a major breaktrough in the history of algebra (and maths). Shouldn't they deserve to be mentioned? —Preceding unsigned comment added by Magnagr (talk • contribs) 19:39, 27 January 2010 (UTC)

Greek geometric algebra

The section cites Boyer promoting algebra in Greek geometry. In Routes of Learning (2009) Ivor Grattan-Guinness takes on this subject, indicating its roots in works by Nesselmann (1847), Hieronymus Georg Zeuthen (1886) and Paul Tannery (1882). He says

They interpreted much of the Elements, and some other Greek mathematics, as 'geometric(al) algebra' (their phrase): that is , common algebra with variables, roughly after the manner of Descartes though without necessarily anticipating his exact concerns, and limited to three geometrical dimensions.(page 172)

He goes on to make an explict case against this interpretation of Euclid. In fact, he develops a contrast between history and heritage, indicating that Nesselmann, Zeuthen, and Tannery were muddling in heritage. Thus for the History of Elementary Algebra, the article should not overstate Greek contribution.Rgdboer (talk) 23:19, 18 October 2010 (UTC)

This should indeed be incorporated. Blasjö, in a recent overview article referencing among others Grattan-Guinness, takes the opposite view. He argues that all the arguments that have been advanced against the geometrical algebra hypothesis, properly understood, are invalid, and that it should be reinstated as a viable historical hypothesis. He does not go so far as to advocate for its correctness. https://link.springer.com/article/10.1007/s00407-015-0169-5 Martijn Meijering (talk) 22:57, 14 December 2019 (UTC)

Name and subject of this article

This article named "History of elementary algebra" is entirely devoted to the history of algebra until 17th century (there are only 6 lines on more recent evolution of the field). It must be expanded to cover the history of algebra during 18th, 19th and early 20th centuries. I will therefor tag it with {{incomplete}} template.

It has nothing to do with "elementary algebra" because the discoveries that are described were not elementary at their time. Therefore, I will rename it with its old name "History of algebra".

D.Lazard (talk) 14:04, 20 February 2013 (UTC)

But it really looks like elementary algebra! Ancient Rome wasnt ancient Rome when the people were living there, but now it is. Christian75 (talk) 21:11, 21 June 2014 (UTC)

I agree, though it was not seen as elementary during that time, it can be viewed as elementary now. It is important to note that the foundations were laid, and the complexity of algebra and other forms of mathematics increased over time. Berryfeet (talk) 15:55, 17 September 2023 (UTC)

Removed assertion

I have removed the sentence Al-Khwarizmi's work established algebra as a mathematical discipline that is independent of geometry and arithmetic from the section "The father of algebra", with the edit summary rm controversial content based on a non notable source. It appears that, although the editor of the source is not notable, its author is notable. Nevertheless, this is a controversial opinion, which would need an explicit quotation. Most authors date the start of algebra, as a distinct discipline, from François Viète. — D.Lazard (talk) 16:55, 18 November 2014 (UTC)

What is odd about this page is that its discussion of the three-part division into rhetorical, syncopated, and symbolic does not mention Viete at all. Surely he came before Descartes :-) Tkuvho (talk) 12:52, 19 November 2014 (UTC)

I have fixed this, clarified the contribution of Descartes, and removed the peacock term "culminated". D.Lazard (talk) 14:26, 19 November 2014 (UTC)

Proposed new article

Dear Historians of Algebra, I have drafted a new article, "Origins of algebraic x" <https://en.wikipedia.org/wiki/User:Kotabatubara/sandbox>, which I am considering uploading to Wikipedia. I would like to have your advice as to whether such an article is warranted, any errors I have made in terminology or concepts, and your suggestions for improving it. Kotabatubara (talk) 23:18, 31 December 2015 (UTC)

Good to see many sources, but La Geometrie (1637) should be cited with page references (see links in main article). It almost appeared that you had Enestrom on-line, which would be a prize. There may be questions of topic significance (it could be absorbed into La Geometrie). — Rgdboer (talk) 21:27, 2 January 2016 (UTC)

Thanks for your comments. Eneström is online. Both of his contributions appear in the same note on pp. 316-317 of the source that is linked from my bibliography. Kotabatubara (talk) 19:16, 3 January 2016 (UTC)

Do you mean this reference ? It comes up "This item is not available on-line" for me. The Biblioteca Mathematica that Enestrom produced is often referred to, but so far it seems elusive. HathiTrust has uncovered many sources, but this link doesn't serve here! — Rgdboer (talk) 23:14, 3 January 2016 (UTC)

Sentence fragment

This appears in the section about etymology: "reuniter of broken bones" or "bonesetter". YoPienso (talk) 07:46, 22 August 2016 (UTC)

Single Source

I have come across many articles on Wikipedia with an editorial note complaining of it relying too much on a single source. This article as written commits the same error, being far too reliant on Boyer's book, A History of Mathematics. The footnotes might almost violate copyright, they reproduce so much of Boyer's book. It's worth noting, too, there's an updated version of the book from 2011 with a co-author named Merzbach. Hard to believe, but the 1991 edition is 25 years old now. But I think the article could benefit from another perspective. History, even math history, is not nearly as cut and dried as it is presented from a single author's viewpoint.

The last paragraph presents the case for Al Khwarizmi, but not the case for Diophantus, and is thus heavily slanted toward one particular opinion.71.48.255.7 (talk) 00:04, 16 January 2017 (UTC)

I agree. However this article has many other weaknesses.

• Firstly, except in the lead, it is confusing about what belongs to algebra and what does not belongs. In fact, as the term algebra is modern (17th century, I believe), attributing earlier work to algebra needs a definition of the term. The problem is that the meaning of algebra has changed over the time: from 17th to 19th century, it meant theory of equations, while the modern meaning is roughly "computing with symbols as if they where numbers". The confusion between these two definitions makes the whole article confusing, even if this has been clarified (rather recently) in the lead.
• Even if restricting algebra to the theory of equations, the article is incomplete and biased: the main contributions (more recent than 16th century) to the theory of equations are ignored or minimized: Cardano and Ludovico Ferrari, the fundamental theorem of algebra, Fermat for Fermat's Last Theorem, Lagrange, Ruffini, Niels Abel, and, overall, Évariste Galois, who finished to solve the main problem of the theory of equations. Also Hilbert's tenth problem and its solution (by a proof of impossibility) are completely ignored.
• About algebra as symbolic manipulation, things are even worse: the introduction of the algebraic notation by François Viète is ignored, the the section about modern algebra is simply ridiculous: apparently, the author(s) of this section believe that algebra exists only in education, and that there is no modern research in algebra. D.Lazard (talk) 08:56, 16 January 2017 (UTC)

Can we ask a moderator or administrator to review these references for copyright violations. Some of the references quote more than is necessary and can be culled.selfworm^Talk) 18:19, 14 July 2017 (UTC)

Some better Sources

I noticed that a lot of this article relies on Boyer, which in my opinion is very outdated scholar. I've read the work of Jeffrey Oaks and Jens Høyrup like , , , and it paints a very different picture. This is quite a fascinating read. Apparently neither Diophantus, nor al-Khwarizmi invented algebra. It existed orally, as "sub scientific tradition" among merchants and practitioners. Moreover as Oaks stressed it, medieval algebra was ultimately an art for problem solving, that existed along side with double false position and the rule of three methods, and not a science that this article implies. Moreover it remained an art throughout entire middle ages! It was only in 16 and 17 centuries algebra will become a science.
Diophantus learned it, probably from merchants, and use algebra to solve problems in arithmetic, while al-Khwarizmi wrote a first complete book on it, see , for instance. There are also a lot of extremely interesting information there, like huge conceptual differences between modern and medieval algebras, slow emergence of symbolism, Italian vernacular algebra and it's influence on development of modern algebra. I consider Oaks to be much better source that Boyer. I feel this article could benefit from significant rewriting/modification. DMKR2005 (talk) 22:31, 28 December 2020 (UTC)

References

It is amazing that the article and your comment talk of "algebra" several centuries before the introduction of the term, without giving any definition of the term. Moreover, it seems that the term has at a very different meanings for historians and for mathematicians. From your post, it seems that, for you (and for a part of the article), algebra is the art of solving problems by computing. In mathematics, this is called arithmetic. On the other hand, in mathematics algebra means essentially the art of manipulating formulas whose not all elements have an explicit numerical value (variables and parameters). This is essentially this which was new in al Kwarizmi's work (the title of his work refers to such methods of formula transformation). So please, stop talking of Diophantus' algebra and Medieval algebra without a reliably-sourced definition of "algebra". D.Lazard (talk) 10:24, 29 December 2020 (UTC)

You very clearly haven't read any of the sources that I posted. Please read the [1]. This a an article published in academic journal by two professional historians of mathematics. They explain very clearly the similarities between al-Khwarizmi and Diophantus and what algebra means in medieval and ancient context. See especially Conclusion section in that paper. Your claim that al-Khwarizmi's algebra is about formulas manipulation is wrong. Al-Khwarizmi work is essentially practical manual for numerical problem solving, using technique of al-jabr. Again see [2], written by Oaks for The Oxford Encyclopedia of Islam and Philosophy, Science, and Technology.The algebra that you are referring to only emerged in early modern period. As for introduction of the term algebra, well the term mathematics and astronomy where coined by Greeks, but mathematics and astronomy precedes Greek civilization. DMKR2005 (talk) 18:23, 29 December 2020 (UTC)

Ok. I added some info about Diophantus, as it was mainly based on Boyer who is very dated.I also plan to rewrite section on al-Khwarizmi based on Oaks. Plus I am probably gonna write about Viete as he is central to transitioning from pre-modern to modern algebra DMKR2005 (talk) 22:18, 3 July 2023 (UTC)

Orientalism/Eurocentrism

"Ancient Egyptian algebra dealt mainly with linear equations while the Babylonians found these equations too elementary, and developed mathematics to a higher level than the Egyptians.[7]" How does a comment about the Babylonians have a place in the section on Ancient Egyptian algebra? Why does Ancient Egypt need to be denigrated in favor of Babylonia? 2001:1C00:1E20:D900:9FC:37E1:276A:946D (talk) 05:02, 12 January 2023 (UTC)