Talk:Ancient Greek mathematics

Potential changes

I am going to make a few additions under the achievements header. Austinroberts3567 (talk) 17:47, 5 March 2021 (UTC)

I also added an addition under achievements about the Sector theorem. — Preceding unsigned comment added by SouryaMo (talk • contribs) 18:03, 5 March 2021 (UTC)

SouryaMo, this section is devoted to seminal achievements, that is to achievements that have influenced mathematics for centuries. Menelaus theorem is not among them, and there are hundreds Greek theorems of a similar importance. As it is not reasonable to list them, Menelaus theorem has not its place here. So, I have reverted your addition. D.Lazard (talk) 18:44, 5 March 2021 (UTC)

I plan on adding some minor changes to the article under the Archaic and classical periods. After doing some research I found that the majority of the first paragraph was plagiarized from "A History of Mathematics" by Carl B. Boyer. I plan on rewriting most of that paragraph and adding the proper references to his work. Austinroberts3567 (talk) 15:46, 9 April 2021 (UTC)

Added some stuff to the Hellenistic and roman period section — Preceding unsigned comment added by SouryaMo (talk • contribs) 21:11, 9 April 2021 (UTC)

Wiki Education Foundation-supported course assignment

This article was the subject of a Wiki Education Foundation-supported course assignment, between 20 January 2021 and 7 May 2021. Further details are available on the course page. Student editor(s): SouryaMo, Austinroberts3567. Peer reviewers: Aewmnw, CarricoHayden08.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 22:42, 16 January 2022 (UTC)

Sources

Just found this page. It contains a list of sources that could be useful for improving this article. Gererhyme (talk) 10:34, 15 March 2024 (UTC)

Requested move 19 April 2025

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: Moved per consistency (non-admin closure) >>> Extorc.talk 20:37, 26 April 2025 (UTC)

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Greek mathematics → Ancient Greek mathematics – consistency with Ancient Greek medicine, Ancient Greek philosophy, Ancient Greek astronomy, more clearly delineates that the subject of this article is about mathematics in the ancient Greek language during classical and late antiquity, not modern Greece. Psychastes (talk) 17:38, 19 April 2025 (UTC)

• Support for consistency. Srnec (talk) 03:52, 20 April 2025 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Netz's list of ancient authors seems to be missing a few?

I cross-referenced the 29 authors in mathematics, astronomy, and music listed in this paper by Reviel Netz with the 144 authors listed in this one (also by Netz, cited by the other one), and there are at least a few on the list of 144, including Aristotle(!) and Marinus of Neapolis, whose works do survive but are not included in his list of 29. Confusingly, he also includes some (originally) Latin authors in his list of 144, such as Apuleius and Vitruvius, who do have extant works, along with eight *anonymous* authors of works that survive! And there are extant writings by other authors (at the very least Cleonides, and also the anonymous 6th century author of Elements Book XV) that go wholly unmentioned by him in either list. So we're already at 39 surviving authors out of 146 rather than 29 out of 144. And there may be more, these are just the ones I've noticed so far in about half an hour, I haven't dug in that thoroughly.

Since both of Netz's numbers are apparently incorrect, I propose we scrap the sentence with a specific number of authors and attribution to Netz 2011, and just list out the authors whose works do survive, in parallel with the arabic list. Alternatively, if the list is really only valuable in the context of a percentage of surviving authors, we could scrap the whole list and just add surviving works to a bibliography? Or try to find another source that lists them all out. But whatever the case, I believe the current (inaccurate) numbers should be removed. Psychastes (talk) 05:05, 29 April 2025 (UTC)

Why is it confusing to include Latin authors? The titles here are "The Bibliosphere of Ancient Science" and "Classical mathematics in the classical Mediterranean". Anyhow, Netz's 1997 paper is probably the more relevant here. Some other sources citing that that might be useful:

• Netz 2002, "Greek Mathematicians: A Group Picture" doi:10.1093/acprof:oso/9780198152484.003.0011
• Keyser & Irby-Massie, eds., 2008, Encyclopedia of Ancient Natural Scientists doi:10.4324/9780203462737
• Zhmud & Kouprianov 2018, "Ancient Greek Mathēmata" doi:10.1086/699921
• Acerbi & Masià 2022, "The Greek Mathematical Corpus: a Quantitative Appraisal" doi:10.4000/histoiremesure.15779

Personally I don't think the precise numbers are that important outside the specific context of some kind of quantitative survey. It would be fine to give rough numbers / rough proportions in Wikipedia.

–jacobolus (t) 18:39, 29 April 2025 (UTC)

To clarify, it's not confusing to include the Latin authors amongst authors whose works survive (I think we should), but rather, they're *not* included in that list, but are included in the list of 144 authors, so it makes it seem like a larger proportion of works are lost than actually are.

My main concern with a rough number here is that we can't really say e.g. "there are roughly 29 authors whose works survive" and then list significantly more than 30 people, but I think a rough proportion would probably work. Looks like Acerbi & Masià 2022 have a figure of roughly 30% (and also observe that Netz's methods are incorrect, which we probably don't need to mention in the article but I think helps justify removing him), any objections to using that 30% figure? Psychastes (talk) 20:11, 29 April 2025 (UTC)

I've updated it to use the less exact figure from Acerbi and Masià. Psychastes (talk) 16:14, 3 May 2025 (UTC)

Expansion/Rewrite

I've been working on rewriting this page over the past couple weeks and just published a large update. here's a summary of the main changes:

• Expansion of the narrative on early Greek mathematics, much more detail about the connection to Egyptian and Babylonian mathematics and early developments
• Much more critical approach to Thales and Pythagoras; it seems like there's a consensus among modern scholars (e.g. Netz, Knorr, Fowler, Huffman, Burkert, Schofield, etc) that this tradition should be viewed more critically. There a few holdouts (Zhmud) but it seems like they're a dwindling minority. This is not just a "scholarship thinks these are myths" though, I've tried to explain the *why* as well, the reasons why these traditions are seen as dubious now even if some earlier modern historians accepted them.
• much more on the mathematics of Plato's academy, presocratic philosophy, and Theaetetus, Eudoxus, and Hippocrates of Chios. This is mostly from Netz 2022, some from Fowler. a lot more can be gleaned from those sources and also Knorr 1975.
• hellenistic mathematics - a lot more topic-based arrangements discussing developments in geometry, arithmetic, astronomy, etc. There's almost nothing about music yet, and very little about mechanics/applied mathematics, which are probably the main omissions, though more could still be added about nearly any topic. mostly from Acerbi 2018, a few other sources.
• a lot more commentators from late antiquity. this is mostly a list of names and book titles at this point but it can certainly be expanded in detail further.
• the lead is expanded to reflect the changes to the article
• i've added many sources to the "further reading" that i think would help improve the article further.

Psychastes (talk) 03:03, 4 May 2025 (UTC)

Thanks! And thanks to Guillermind81 for ongoing copyediting and tightening efforts.

Some other things that could be added, off the top of my head:

• A map of the eastern Mediterranean from this time period with the hometowns / workplaces of various mathematicians plotted. (Maybe showing at least part of Mesopotamia over to part of Italy)
• Some discussion of the origin of straightedge and compass constructions and deductive geometry coming from architecture / masonry
• More discussion of pre-Ptolemaic astronomy, with more about Eudoxus about a bit more explicit discussion of the Spherics of Theodosius and Menelaus
• More about the structural form of deductive mathematics in Euclid and contemporary work
  • A more explicit discussion of axioms, theorems and their proofs, etc.
  • A description of the typical structure of a proposition statement and proof
  • A prominent mention of the centrality of lettered diagrams
  • A mention of the way proven propositions build on each-other, with previously proven theorems invoked by more or less copy/pasting their statements with appropriate substitutions into the proofs of subsequent theorems
• An explicit subsection about Euclid's Elements with a quick summary of its content
• A more explicit discussion of the theory of proportions and the way Greek geometry carefully avoids conflating (lengths of) line segments and (areas of) plane regions with numbers
• A discussion of the scholarly controversy about whether the early parts of the Elements can be interpreted as a kind of algebra
• Some mention of Conics having a kind of coordinate geometry, long before Descartes and Fermat
• Some discussion of Greek numeral systems
• At least a mention of "Egyptian fractions"
• A mention that computations in Ancient Greece were done by finger counting or with counting boards rather than using written arithmetic
• Much more about the transmission and influence of Greek texts in medieval India, the Islamic World, etc.
• Perhaps some discussion of limitations or particularities of Greek methods which led to their modification or replacement by later methods which were more convenient for one reason or another

Anything else I'm missing here? –jacobolus (t) 17:29, 23 May 2025 (UTC)

Thanks for the feedback. I feel most of these items are too specific to belong to a general overview of Greek mathematics and probably are suited to their respective articles, e.g., a explicit discussion of the Spherics of Theodosius and Menelaus belongs to Ancient Greek astronomy rather than here. Ditto about whether Book II of the Elements can be interpreted as a kind of algebra-if that needs to be anywhere, it most certainly should be in the Euclid's Elements article. We should try avoid throwing everything and the kitchen sink here. Guillermind81 (talk) 20:48, 23 May 2025 (UTC)

A discussion of the evolution of spherical geometry (explicitly an abstract theoretical topic) most assuredly belongs in a page about "mathematics". I will agree with you that we should (also) have much more extensive discussion about the Elements at its page, which is currently very limited and frankly pretty mediocre. –jacobolus (t) 07:23, 24 May 2025 (UTC)