Talk:Archimedes

Arcamidus was born in siracuse Sicily was not greek

The following discussion 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.

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arcamidus was born in siracuse Sicily was Sicilian 51.155.64.194 (talk) 09:05, 15 May 2024 (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.

FA Criteria

This article is deeply below FA standards, and unless immense and extensive improvements are made, it should go to WP:FAR. This may all sound harsh, but that's because the issues are so woven into the article's structure that most, if not all, sections would need to be completely rewritten to meet FA standards. I understand that various editors have attempted to maintain this page over the yeas, but its existing structure from the 2007 nomination has deeply limited such efforts.

There is poor sourcing all throughout; aside from non-existent citation formatting and sporadic page numbers, random web sources of highly variable notability are consistently prioritized over academic scholarship. In fact, I can't see that a single contemporary book-length survey of Archimedes is even touched, let a lone used extensively—why are they all in the further reading!

There are way too many references in the lead (see WP:LEADCITE), which seems to imply that the lead and the body are not matched at all. The lead includes no biographical information, and its structure is very difficult to follow.

The Biography section pulls directly and extensively from ancient sources, without any filtering through modern commentary. Citations are sporadic and inconsistent. The discoveries and mathematics sections are extremely choppy and brief. Every single work of his does not need its own subsection just to include two (usually uncited) sentences. The legacy section is merely a list of length quotes and random trivia; no information on his actual influence into later mathematics is explained.

There is much more to say, but in conclusion I'm afraid the issues are rather extreme. Aza24 (talk) 20:20, 27 June 2024 (UTC)

We don't know much about the life of Archimedes and everything we do know was written long after his death; the article makes this clear. I'm not sure how "filtering through modern commentary" would help, as he has been dead for over two thousand years. This is a weird argument to make.--♦IanMacM♦ ^{(talk to me)} 08:03, 28 June 2024 (UTC)

Hi there, this is a rather revealing point to harp on, and I highly recommend you take a look at some recent FAs (Leucippus, for instance) and read WP:Primary. Every featured article needs to be "a thorough and representative survey of the relevant literature; claims are verifiable against high-quality reliable sources and are supported by inline citations where appropriate". Primary sources are simply not allowed in place of suitable secondary ones. You can disagree with this all you like, but you will find that no reviewers will agree. The aforementioned Leucippus, for example, has a biography section only citing academic articles and books from the last 20 years (albeit a single one from 1979).

Yes, "he has been dead for over two thousand years"—exactly! So scholars have had two thousand years to analyze, update and revise his biography! Would you really claim that there are no scholars which have altered, changed, updated, reinterpreted his biography from 2000 year old accounts?

I understand it is easy to see my comments as "[weird] argument[s]", but this is a misunderstanding. I am citing real and rather egregious issues, after having review hundreds of articles for FAC & FAR, in content and source reviews. This article falls extremely flat, and defending it will take you no where, unfortunately. Aza24 (talk) 18:07, 28 June 2024 (UTC)

Sorry, this is still a weird argument. We know very little about the life of Archimedes other than what was said by Roman historians many years after his death. I'm not sure what these "modern sources" are supposed to be, perhaps you could find them if it is such a problem. I don't have access to specialist academic libraries or paywalled academic resources, so it is hard for me to know exactly what you want here. We know that many of the things said by the Roman historians are likely to be apocryphal, which is why they are treated with caution.--♦IanMacM♦ ^{(talk to me)} 18:28, 28 June 2024 (UTC)

"which is why they are treated with caution" — they shouldn't be treated at all... that's WP:Original Research, please read WP:Primary, we do not interpret primary sources on Wikipedia. This is a tertiary encyclopedia that summarizes secondary sources. We don't cite from Roman sources directly, period, and we definitely do not in featured articles.

Where are the modern sources? How about the huge Further reading section that includes multiple major recent surveys? Why is not a single one of them included? How can this be "a thorough and representative survey of the relevant literature; claims are verifiable against high-quality reliable sources and are supported by inline citations where appropriate"? Aza24 (talk) 18:44, 28 June 2024 (UTC)

A lot of the sourcing in Leucippus seems to be from specialist academic sources. I don't have easy access to this type of material and people who want to read the sources for themselves would also have this problem. However, I accept your point on this.--♦IanMacM♦ ^{(talk to me)} 18:57, 28 June 2024 (UTC)

I appreciate that. Certainly that material is more difficult to access, but nowadays there are more resources for that. GoogleBooks includes extensive previews, and Archive.org is a goldmine for academic sources. You'll see that the further reading section already includes quite a few links to archive.org copies, which are freely available to borrow (sometimes a free registration is needed). Aza24 (talk) 19:17, 28 June 2024 (UTC)

@Aza24, @Ianmacm. Sounds like a heated discussion is occurring. I pinged both WP:WPM and WP:PHY for more opinions. Dedhert.Jr (talk) 02:30, 29 June 2024 (UTC)

It would help if someone dug up recent scholarly work that evaluated the traditional tales and checked them for consistency, plausibility, etc. Something like what the Stanford Encyclopedia of Philosophy does for Pythagoras. I don't see a fundamental problem with our reporting "Cicero said..." as long as we have further, modern sources to contextualize that. Nothing in the WP:NOR policy forbids judicious use of primary sources. (Indeed, I'd actually fault the Leucippus article for not giving direct pointers to editions/translations of the ancient sources; that's mildly inconvenient! When we say, for example, Plato explored cosmological ideas similar to those of Leucippus in the dialogue Timaeus, a reader shouldn't have to get a paywalled journal article to find which sections of the Timaeus are relevant.) XOR'easter (talk) 04:54, 29 June 2024 (UTC)

Leucippus doesn't even try to link to the source texts where its claims originate. This does a disservice to readers, because it makes them jump through hoops to figure out what was actually said. I imagine in most if not all cases there are online scans of these texts and probably also translations. Frankly I am not impressed. All of the content is along the lines of "So-and-so says Leucippus says XYZ" where so-and-so was writing a few centuries after Leucippus, but then the link shows that Wikipedia's text is a paraphrase of some paywalled academic paper where the author paraphrased an earlier Greek/Roman source who was paraphrasing Leucippus, so what Wikipedia readers are getting is 4 steps removed from the original. This helps tick off FA boxes, and might help scholars looking for a list of recent works to cite, but readers would probably be better off with a direct quotation of the oldest extant work or a translation. –jacobolus (t) 04:54, 29 June 2024 (UTC)

The sourcing in Leucippus has a high gloss sheen, but if someone wanted to actually read and verify the cites it would be very difficult. I have tried to stick to easy to follow cites, not what someone said about it on page 336 of an obscure or paywalled academic work.--♦IanMacM♦ ^{(talk to me)} 06:43, 29 June 2024 (UTC)

I agree overall with jacobolus and Ian, and appreciate the "high gloss sheen" comment in particular. I think there is no problem citing ancient sources appropriately in the biographical sections. While I haven't looked that closely, everything I looked at sourced to an ancient source also had a secondary source nearby. E.g., Something about ancient source [ footnote to ancient source ]. Another sentence or two.[ footnote to secondary source ]

There are some sourcing issues to be sure (which are very easy to fix!) The mathematics section needs better sources, as there are some paragraphs lacking footnotes. But this material is so standard as to be found in tertiary sources like Kline, or Boyer and Merzbach. Perhaps the sections in Archimedes works each should be individually referenced with a footnote to the Heath source (which provides commentary, and therefore is a secondary source on the works of Archimedes), as this remains the standard modern reference for Archimedes works. Only the palimpsest, which post-dates Heath, needs to be referenced separately (which it is). In any case, concerns over the lack of sourcing of this section are overwrought, considering the extremely high quality references Knorr and Sato that are very explicitly intended to support the section as a whole.

The "Legacy" section is also very weak. It's hard to overstate the continuing legacy of Archimedes in mathematics: one could go so far as to say that he invented mathematics as we know it. The section doesn't even try. Tito Omburo (talk) 11:46, 29 June 2024 (UTC)

Primary sources are not the main problem here. It is the lack of academic secondary sources (which extends to the entire article). The FA criteria are explicit in asking for "a thorough and representative survey of the relevant literature". Outside of the lead, there is a single book on Archimedes sourced. The result is highly noticeable in the article, as you point out, the mathematics sections and legacy are surprisingly sparse, and the reliance on solely primary sources (or not sources) for large swathes of text is not ideal.

These academic sources are not niche or hard-to-acess. Archimedes#Further reading lists multiple works by clearly established historians, and includes direct links to archive.org which is freely available. If one wants to actually engage in a "thorough and representative survey of the relevant literature", this will include academic sources which are sometimes difficult to access. That's why Wikipedia exists, to make such information more accessible.

If I only used web/non-academic sources when I wrote the now-FA Cai Lun, it would have been a paragraph long, maybe two. You'll see that I linked almost every page number to google books: readers can click on any one and immediately find the information. How is this difficult to access? By the way, I regularly used plenty of primary sources in Cai Lun and found no issues at FAC; this is because I paired each one with a secondary source, which is certainly more advisable (and productive) than sole reliance on primary sources.

In any case, there seems to be some confusion. I'm not saying this is a bad article, or even that the sourcing is bad, I'm saying that it does not match the Featured article criteria. Alas, these are two very different things, and you are all welcome to (rather bizarrely) dig on Leucippus all you want, but it reflects the reality of what FAs are now a-days. Aza24 (talk) 18:18, 29 June 2024 (UTC)

Where is there reliance exclusively on primary sources? Tag some specific problems, please. A side note is that many of the sources listed in further reading are very pulpy. E.g., Netz and Noel is not a scholarly or academic source, and some of the others are, rather more obviously, probably not good references. Boyer is a tertiary source, generally good (I suggested above for the mathematics section), but there are better secondary sources. Clagett is a very good source, but also specifically focuses on mathematics in the middle ages, and is incredibly detailed: we already cite his survey article on this topic. I think the Dijksterhuis is a good source, particularly for the life of Archimedes, that could be used for some of the history section, and also for the mathematics section. Tito Omburo (talk) 18:45, 29 June 2024 (UTC)

Almost the entire biography is exclusively relying on primary sources; please note that these "Rorres, Chris" citations are just a web page with a public domain translation of Greek authors.

• The biography's first paragraph does not have primary sources; it includes a source from 1897 (?), a 1975 journal article and a dictionary entry, the latter two being some of the only scholarship in the whole section. The last sentence is uncited.
• The biography's second paragraph is only primary sources
• The biography's third paragraph is only primary sources (save for the line "He also mentions that Marcellus brought to Rome two planetariums Archimedes built")
• The biography's fourth paragraph is only primary sources, save for the its last line (I checked the Jaeger source and it only covers the last line).
• The biography's final paragraph is only primary sources

Now this is just a single section, I suspect there are plenty of others. Other examples (from a glance) include the first paragraph of the Heat ray section and the second paragraph of the Astronomical instruments. – Aza24 (talk) 18:59, 29 June 2024 (UTC)

Sorry, I'm not trying to rag on Leucippus, which is certainly above average for Wikipedia articles; it was just your example of exceptional citation formatting, but I don't really like the style with a plethora of footnotes often crammed together but none of them giving any detail or quotations, and in my opinion the primary sources are essential to cite in this kind of article, but there are missing. Your focus on sources from the past decade or two also seems misplaced. To my knowledge Archimedes isn't a subject of such rapid historiographical change that commentary from 50, 100, or 1000 years ago is necessarily obsolete.

In any event, it's a somewhat apples-to-oranges comparison because Archimedes is a dramatically more productive, known-about, and influential figure than Leucippus. I agree with you that this article is far from comprehensive, but on the other hand if it were expanded to the level of detail found in Leucippus or Cai Lun relative to the amount of available material about Archimedes, it would be probably 5x longer than currently – the mathematics section alone would be longer than the current article – and we'd have people complaining that GA/FAs need to be short enough to read in one sitting or whatever.

Anyway... Do you have some specific recommended recent literature that you think should be added here? One thing I'd like to see in particular is some discussion of Archimedes' influence on the mathematics and science of the medieval Islamic world, which is currently unmentioned. –jacobolus (t) 20:25, 29 June 2024 (UTC)

One source people may want to look at with some counterfactual speculation about Archimedes' influence is the recent issue of Interdisciplinary Science Reviews (Volume 47 Issue 3-4, 2022), edited by Chemla, which involved a paper by Netz, "The place of Archimedes in world history", accompanied by responses from 13 other scholars. Wikipedia editors with moderate experience can access these via Wikipedia:The Wikipedia Library at https://journals-sagepub-com.wikipedialibrary.idm.oclc.org/toc/idsa/47/3-4 –jacobolus (t) 00:22, 30 June 2024 (UTC)

Another possibly useful source relevant to Archimedes' influence is the 2010 conference proceedings The Genius of Archimedes doi:10.1007/978-90-481-9091-1 edited by Paipetis and Ceccarelli. –jacobolus (t) 02:25, 2 July 2024 (UTC)

Does anyone have the energy to find page numbers in Dijksterhuis, Heath, etc.? Citing these long books without more specifics seems a bit mean to readers. –jacobolus (t) 01:45, 30 June 2024 (UTC)

Here are my two cents: Netz has been publishing and translating Archimedes for over two decades, but almost everything worth reading from him is behind paywalls and he believes writing a "biography" of Archimedes is pointless. Knorr is better overall but his work is behind even more impenetrable paywalls. Heath is terribly outdated and should be used with caution, while Dijksterhuis is about the best your regular, "I don't work for academia" person could have access right now. Believer or not, Heiberg's work still holds on and its packed with lots of good textual and biographical information but you'll have to read German (and Latin!) to make sense of it. Bottom line, the best sources are the most esoteric, hard to reach ones, while the popular sources are often worth crap.

I do agree the article needs a major Enterprise "refit" to keep it FA worthy, just wanted you to know what we might be up against.

-- Guillermind81 (talk) 04:43, 2 July 2024 (UTC)

Dijksterhuis (which I only skimmed parts of) seems like an excellent source, and the consensus seems to be that it is the best available biography. I think we should pull it out in a new section of "Works Cited" or whatever, and then liberally add footnotes citing specific chapters and pages for every currently unsourced section of this article. It's kind of a lot of grunt work, but especially if we include links to a scan (the IA scan is unfortunately "borrow unavailable, presumably by request of Princeton Univ. Press) should be at least moderately helpful to readers, and might satisfy some of the footnote police. –jacobolus (t) 05:29, 2 July 2024 (UTC)

Having now gone through the article and attempted to verify claims with Dijksterhuis's work, I have to concur with @Aza24's initial concerns here. The problems with this article are severe; Dijksterhuis is hardly the most skeptical historian and a more recent book would undoubtedly take a more critical approach with primary sources, and yet nearly all of the claims from less historically-minded sources have turned out to be either outright fabrications which he provides the context to debunk, or mischaracterizations and misinterpretations of the primary sources so severe that I've had to scrap an entire section of the article on "discoveries and inventions" because Archimedes can't plausibly be credited with discovering or inventing any of them! I've removed a lot of OR or material from self-published sources that repeats the same errors; And there is still a lot of work to be done, just looking at the mathematics section Archimedes is already credited with discoveries (such as the method of exhaustion) that I know are now attributed to earlier mathematicians by historians. Frankly I think this is a stark representation of *why* we require secondary sources, and why we prefer WP:SCHOLARSHIP; when editors attempt to interpret primary sources themselves or rely on self-published fanpages of ancient historical figures, things will inevitably go badly wrong.

I still intend to make more improvements to the article, but even if all of the concerns with WP:OR were addressed, I've already rewritten enough that I believe it ought to go through the entire WP:FAC process again regardless, so I think it would be productive to do a WP:FAR at this point. Psychastes (talk) 06:31, 30 April 2025 (UTC)

You just took out like 20% of the article's content by byte count, especially removing a lot of sources, in a way that after cursory spot checks seems heavy handed and arbitrary and a disservice to readers. (As an example, you took out the link to Alexander Bogomolny's excellent page showing interactive diagrams for each proposition in the Book of Lemmas, for no apparent reason.) Some of the folks who originally wrote and sourced material should probably do a careful double check of the removed material. It's a big job that I don't really have the bandwidth to tackle right now. –jacobolus (t) 18:03, 30 April 2025 (UTC)

Unfortunately, the removal of a lot of that material was necessary, because it's largely an amateur (i.e. by mathematicians and engineers, not by historians) misrepresentation of historical sources. For example, we were crediting Archimedes with three different inventions (block and tackle, windlass, lever) for the apocryphal ship story, without even making it clear that they all derive from the ship story, or that they're all almost certainly false. Much of the mathematics credited to him in this article is also in Euclid's Elements, which predates him, and so while it makes sense to discuss it, it's wrong to credit him with it.

As for the Book of Lemmas, I was under the impression that the translation it provides was still in copyright? That page you linked cites the Great Books of the Western World translation, which was published in 1952. If that's *not* the case, I don't think it would hurt any just any to re-add it; the Book of Lemmas may not be Archimedes' work but it's probably based on one of his. Psychastes (talk) 18:18, 30 April 2025 (UTC)

Also, if you're looking for more information on why many of these sources are such a problem, I'd recommend reading the essay WP:CLPRIM, which explains what the WP:BESTSOURCES are for this type of material and also runs through a lot of the pitfalls that occur from using other sources. I think especially the section on "Secondary sources mirroring primary ones" is relevant here. Psychastes (talk) 18:31, 30 April 2025 (UTC)

I don't understand what you mean by "Much of the mathematics credited to him in this article is also in Euclid's Elements, which predates him," – can you be specific? –jacobolus (t) 19:28, 30 April 2025 (UTC)

I've written a bit more below but the method of exhaustion (outlined in Book X.1, used heavily in book XII) is the most common misattribution. Psychastes (talk) 19:44, 30 April 2025 (UTC)

It was nowhere claimed that Archimedes originated the method of exhaustion. I don't see any such "misattribution" in the previous version of the article. Adding a bit of extra context might be helpful, but your claim on this topic in this discussion seems clearly inaccurate to me. You are implying that there are multiple further "misattributions" involved. Can you list them? –jacobolus (t) 23:25, 30 April 2025 (UTC)

But I think it's supportable to give Archimedes quite a bit of credit on this score. E.g. Stillwell in Mathematics and its History says "The method of exhaustion was brought to full maturity by Archimedes". Our article Method of exhaustion could definitely use significant help, e.g. it should say more clearly that the relevant content from Elements XII is believed to come from Eudoxus. Both there and here we should be clearer that the Quadrature of the Parabola is an example of the method of exhaustion (our summary here is a bit anachronistic). –jacobolus (t) 23:32, 30 April 2025 (UTC)

Stillwell is a mathematician, not a historian; he's a nonspecialist writing a general study for a broad audience and can be expected to repeat common misconceptions (i.e. "Secondary sources mirroring primary ones"), which is certainly not WP:BESTSOURCES. Compare Acerbi in Hellenistic mathematics: In the prefaces to Sph. cyl. 1 and Method (AOO 1, 4; 2, 430), Archimedes expressly ascribes to Eudoxus the proof of results that we read as the corollary to Elements 12.7 and as 12.10. In Quadrature of the Parabola he asserts that what we now read in Elements 12.2 was proved by resorting to the lemma that “the excess by which the greater of two unequal regions exceed the lesser, if added to itself, can exceed any given bounded region,” and what we now read in Elements 12.18, the corollary to 12.7, and 12.10, by resorting to a “similar” lemma (AOO 2, 264). Archimedes does not mention Eudoxus about Elements 12.2 and 18: this suggests these results were proved by other geometers. Book 12 of the Elements is the first sustained application of the so-called method of exhaustion. (i.e. the method of exhaustion as outlined in book XII is not necessarily due to Eudoxus, so we shouldn't say that) and also: In the rest of the mathematical corpus, most notably in Archimedes, the technique admits subtle variations. which is certainly a far cry from "brought to full maturity" of Stillwell, the nonspecialist. Archimedes is merely applying a technique that's been well-established for a century! Psychastes (talk) 00:22, 1 May 2025 (UTC)

I didn't mean to imply that Eudoxus originated the method of exhaustion, nor is the precise history or attribution for each specific example very clear. It's certainly plausible that a few of the propositions found in Elements XII predate Eudoxus, and also plausible that authors after Eudoxus polished or rewrote some of his arguments. "first sustained application" here implicitly needs "extant" in front, since the preceding material does not survive and our knowledge of its content and form is substantially speculative. But Stillwell's opinion in not in any contradiction with Acerbi; one person's "full maturity" is another person's "notable subtle variations". But in any case, please feel free to cite Acerbi and expand the relevant parts of Method of exhaustion. As I said our treatment there is not very complete or careful. As I also said above, I think it would be fine to add some additional context in our mention of the method of exhaustion here at Archimedes. –jacobolus (t) 02:18, 1 May 2025 (UTC)

Heat ray section

Quick aside [from the FA criteria discussion above], @Guillermind81 semi-reverted my direct quotation of Lucian "Archimedes 'burned the enemy ships by means of his skill' " and replaced it with just "Archimedes burned enemy ships", in § Heat ray. Personally I think the direct quotation is helpful here, since the unquoted version makes it sound like we're paraphrasing a comment talking about focusing reflectors per se, whereas the direct quotation makes it clear that Lucian didn't include any specifics other than crediting "skill" (techne) [it might even be worth quoting as "burned the enemy ships by means of his techne" or "burned the enemy ships by means of his skill"]. I understand that we're trying to keep this brief here and offload details to the (currently mediocre and incomplete) Archimedes' heat ray, but we also want to try to give readers the least misleading brief summary we can. What do other folks think? –jacobolus (t) 05:17, 2 July 2024 (UTC)

The reason why it may read like that is the preceding sentence about Diocles that was not originally there. I'm all for taking Diocles out, rather than add even more stuff to this, as I keep arguing the discussion better belongs to the Archimedes heat ray entry. Maybe our efforts should divert there if said article is not up to par.

-- Guillermind81 (talk) 05:38, 2 July 2024 (UTC)

I do appreciate your effort to keep this brief. Perhaps someone else has an idea how to make a few sentence summary that conveys that there's no contemporaneous evidence about the "heat ray" and 2nd century mentions point to some kind of incendiary (perhaps some precursor to Greek fire or the like) but by ~600 AD there was apparently an established legend about reflectors and ships. –jacobolus (t) 05:46, 2 July 2024 (UTC)

Africa 1975 (JSTOR 4348211) says: «In the Hellenistic age, scientists such as Apollonius and Diocles were interested in the theoretical aspects of burning mirrors and may have experimented with them,10 but there is no reference to the practical application of a heat ray in warfare until the second half of the second century A.D. when Lucian mentions in passing that Archimedes burned ships "with his skill" (Hippias 2). Lucian did not identify the weapon, and Galen is the first author to specify mirrors as the source of heat. II Where he picked up the story is not known, but it was commonplace among scholars of the time to attribute all manner of wonders to famed sages of the past. Galen's younger contemporary, Cassius Dio, was also aware of the mirrors, for Zonaras (9.4) mentions them in his epitome of Dio's Fifteenth Book.» But I am not sure if this is an entirely accurate summary. –jacobolus (t) 05:54, 2 July 2024 (UTC)

That's accurate as far as tracing the complicated history of a "scientific" fable goes, and yes most of the time it's a game of broken telephone. But why burden the reader with all of this? Scholars have to make a living after all, sure, but I fail to see how this information will serve the reader. Guillermind81 (talk) 06:04, 2 July 2024 (UTC)

The apocryphal story of the "heat ray" has clearly been of interest to readers, and it's worth being clear that it's a legend that is surely made up. I agree the details might be unnecessary here. I'd be fine with condensing the whole section down to a paragraph or so, delegating some details to a couple of footnotes and the rest to Archimedes' heat ray. I'm just not sure what that paragraph should say. Maybe we should be leading along the lines of, "As legend has it, Archimedes focused the light of the sun using large mirrors and set Roman ships ablaze at the siege of Syracuse..." –jacobolus (t) 06:09, 2 July 2024 (UTC)

I propose we leave the section as is for now and let others weigh in before editing any more. It's getting late and I don't want us to inadvertently start the next Great Edit War. Guillermind81 (talk) 06:15, 2 July 2024 (UTC)

I took another crack at it. Is that any better? –jacobolus (t) 10:27, 11 July 2024 (UTC)

Looks OK to me (one of the links was dead but salvageable). XOR'easter (talk) 17:30, 12 July 2024 (UTC)

Biography section

Re this edit: I'm 50:50 on whether it needs to be split into separate sections (Early life, career, death). This might work well if the biography section was longer, but it makes the subdivided sections quite short. ♦IanMacM♦ ^{(talk to me)} 18:22, 8 October 2024 (UTC)

I had the same thought, as there isn't enough material to justify breaking the Biography into 3 main sections; however, I think subheadings might accomplish the same while keeping it under 1 section but I'm open to what others have to say. -- Guillermind81 (talk) 19:34, 8 October 2024 (UTC)

Things that are credited and not credited to Archimedes

We have many see-also wikilinks in which the things were named after Archimedes. These links can be beneficial to expand this article. I wonder where can I put them? Dedhert.Jr (talk) 10:58, 15 October 2024 (UTC)

There is an article List of things named after Archimedes and this is given in Template:Archimedes. Some of these need to be taken with a pinch of salt, because they do not have much of a link to Archimedes other than the name given to them.--♦IanMacM♦ ^{(talk to me)} 12:41, 15 October 2024 (UTC)

Semi-protected edit request on 18 November 2024

In Death section, change english translation of his last words from "do not disturb my circles" to "do not turbulate my circles". Latin "turbare" most closely translates to "turbulate", and turbulate is defined as "to turn"...do not turn my circles...Archimedes was a god damn hilarious genius. 166.181.89.139 (talk) 03:09, 18 November 2024 (UTC)

 Not done: please provide reliable sources that support the change you want to be made. Remsense ‥ 论 03:15, 18 November 2024 (UTC)

Specifically, we try not to provide our own translations when published translations already exist, so it would be cogent to provide a source that itself provides this translation for the quote in order to consider changing it. Remsense ‥ 论 03:17, 18 November 2024 (UTC)

"turbulate" is not a word in English, or at any rate is an exceedingly uncommon word not found in English dictionaries. It's not helpful to include obscure words in our English translations, since most readers have no idea what they mean. –jacobolus (t) 06:22, 18 November 2024 (UTC)

MOS:'S

This would seemingly need to be broached across dozens and hundreds of articles, many about figures from the Greco-Roman world, but let's start with one example.

What MOS:'S prescribes is unambiguous, and does not indicate any exceptions that would be applicable here. Attempts to articulate exceptions have not gained any consensus. I think it's pretty important (as far as MOS tedium goes anyway) that our most vital articles adhere to one of our most basic style guidelines, so I'm going to move for that here. It's not acceptable here or elsewhere to have an unsystematic local consensus that directly contradicts established guidelines: if usage in sources were a tenable justification, then the guideline wouldn't even have reason to exist as written. I'm not aware of any objections that would hold water here, but don't want to alienate folks by moving unilaterally. Remsense ‥ 论 21:11, 29 December 2024 (UTC)

(See the 2017 RfC where this consensus was finally established, bringing the MOS into line with most contemporary style guides.) Remsense ‥ 论 21:59, 29 December 2024 (UTC)

This rule (which I disagree with) seems pretty unambiguous. The possessive should be "Archimedes's". Tito Omburo (talk) 22:02, 29 December 2024 (UTC)

There are also these articles whose titles begin with "Archimedes'" (hide redirects). Here it would only make sense to simultaneously bring them into line. Remsense ‥ 论 22:05, 29 December 2024 (UTC)

It is unambiguous because the ‘s indicates there is just one of him. Otherwise it could be referring to a whole family. That reflects increasingly common written usage, with the single ‘ used for single people becoming archaic. MapReader (talk) 05:36, 11 January 2025 (UTC)

This isn't a novel position and I don't mean to beat one of the wiki's distinguished deceased horses, but I mostly just find any argument to be utterly frivolous that prioritizes encoding pronunciation above syntax here—in this of all situations, where said pronunciation information would be maximally variant and minimally useful for readers. Lacking that, there's not really another argument other than one to echo convention, an argument that doesn't bother me nearly as much. Remsense ‥ 论 05:49, 11 January 2025 (UTC)

The MOS discusses ordinary running prose, and discusses official formal names, but doesn't try to address the in-between topic of traditional names for well-defined specific things (relevant here: formulae, theorems, etc.) that use a possessive without an s but aren't official institutional names. I think these still take editor discretion, especially in light of WP:COMMONNAME. You might want to take this to a place with more eyeballs, e.g. WT:WPM. –jacobolus (t) 03:43, 30 December 2024 (UTC)

So, you're saying it would be reasonable to use the possessive sans s in the article titles, but require Archimedes's for every other appearance in the running text of this and those articles? That seems fraught and vaguely bewildering. This clearly seems like a case where we normalize the proper names used as our article titles. Remsense ‥ 论 03:46, 30 December 2024 (UTC)

No, I'm talking about specific named inventions, etc., with a traditional name, wherever they might be mentioned in an article. For example the name "Archimedes' Screw" is widespread and common, but the variant "Archimedes's Screw" is almost completely unheard of. I'd recommend against using the latter anywhere on Wikipedia, even in light of MOS:'S; it's idiosyncratic, distracting, and gives readers a misleading impression of the common name. –jacobolus (t) 03:52, 30 December 2024 (UTC)

I am too. It would be bewildering for me to read Archimedes' screw but Archimedes's invention within one article. To me, that they are both proper names and composed of discrete functional elements is unavoidable here. Remsense ‥ 论 03:56, 30 December 2024 (UTC)

The latter example can be easily rephrased to avoid the awkward and unconventional "Archimedes's", but the former can't be, since it is treated as a unit. –jacobolus (t) 04:02, 30 December 2024 (UTC)

We don't treat many proper names as units, is my point—we allow ourselves to normalize them. As I said, it is a proper name but one that must agree with the surrounding sentence and article because it's still clearly a grammatical phrase. We would otherwise treat it as such in every other aspect—e.g. we would write Archimedes' screw was not his first invention. Here, we are acknowledging subunits.Remsense ‥ 论 04:05, 30 December 2024 (UTC)

You're going to get some pushback if you start trying to systematically move Achilles' heel → Achilles's heel, Xerxes' pontoon bridges → Xerxes's pontoon bridges, Archimedes' screw → Archimedes's screw, etc. Trying to force strict conformity with the MOS in this case when these spellings are so well entrenched in the existing English language literature seems like a net negative change. If anything it would probably be better to change the MOS, but if that's impossible I'd recommend ignoring this part of it. –jacobolus (t) 07:15, 11 January 2025 (UTC)

And Pythagoras' theorem. Bottom line is that the MOS has gone out on a limb by recommending a type of spelling that reliable sources do not use for ancient Greek names.--♦IanMacM♦ ^{(talk to me)} 08:11, 11 January 2025 (UTC)

It's a limb, but I personally find it rather sturdy. I'm still trying to internalize the other position though—is it mostly just the unfamiliar form plus being clunkier, or is it deeper than that somehow? Anyway, the article title seems to reinforce that the non-astonishing form is, of course, Pythagorean theorem in this particular analog. Remsense ‥ 论 08:49, 11 January 2025 (UTC)

Rather than "unfamiliar", I would say "extremely rare and unusual". In some of these cases the 's version is used like 100–1000x less commonly than the bare apostrophe version, which makes it gratuitously distracting. It reads like a special affectation designed to call special attention to itself, which is jarring to readers and can undermine whatever else the piece of writing is trying to say. One thing some authors do, which might be for the purpose of satisfying an overzealous style guide, is to just drop the apostrophe altogether ("Achilles heel", "Archimedes screw"), since the pronunciation then doesn't change. –jacobolus (t) 09:02, 11 January 2025 (UTC)

This particular case just doesn't hit me that way. It simply appears like it's emphasizing a particular grammatical function I suppose, but I do at least get it by analogy.

I definitely enjoy using base proper names as adjectival forms, so that's another novelty option to root for. Remsense ‥ 论 09:12, 11 January 2025 (UTC)

The possessive is on its way out in English, thanks to texting without punctuation and to non-native English-speaking Europeans who insist on saying "Screw of Archimedes".

Following Jacobolus above and recent examples like Higgs boson, I suggest that we drop the apostrophe in all compound nouns. 173.206.40.108 (talk) 11:44, 7 February 2025 (UTC)

I'll believe it when I actually see it. The instance of Higgs in Higgs boson is not possessive: Higgs does not own the boson, but the boson is merely named for him. Remsense ‥ 论 20:31, 7 February 2025 (UTC)

It could be equally said that Archimedes does not own the screw; it's merely named after its inventor. More examples are Hoover Dam and Einstein field equations. Also compare St. Peter's Basilica (outdated possessive) with Saint Alexander Nevsky Cathedral, Sofia (modern non-possessive). 173.206.40.108 (talk) 19:20, 13 February 2025 (UTC)

This subject is not somehow a magical exception to MOS:POSS. Use Archimedes's screw etc. It is one person, Archimedes, not a plural group the individuals within which are each called an Archimede. To the extent we have any related "Give me an exception or else!" yakking going on at some other pages (maybe about Pythagoras, etc.): same answer. The community has already heard all of the "make an exception for ancient figures, or Biblical ones more narrowly, or Greek ones more narrowly, or whatever" arguments, and has rejected them, just has Chicago Manual of Style and various other style guides MoS is roughly based on have come over time to reject them. That some off-site publishers still like to write things like "Archimedes' screw" is irrelevant; their content is not written to our style guide, and our encyclopedia is not written to their style guides. They are different style guides. That's for good reasons. Otherwise we might as well not have any style guide at all but simply enforce whatever style happens to dominate in a particular topic. (Hint: we don't do this also for good reasons, the most obvious being that it would result in utter stylistic chaos from page to page, and would also devolve into editors wasting their time and goodwill on "style warfare" day in and day out, using every manipulation they could to distort the aggregate views of source usage to seem to support their preferred version.)  — SMcCandlish ☏ ¢ 😼  22:44, 17 March 2025 (UTC)

You, personally, have been repeatedly "yakking" about singular possessives for 15+ years across various Wikipedia discussion pages, but there was never any real community consensus about it that I have seen, as regards ancient Greek names in particular, and the prevailing convention (no trailing s) represents the vast, vast majority of practical uses in English, like more than 95%. We might instead say "English speakers have been hearing prescriptivists with made up pet rules yak about them for generations and continue to roundly reject them in favor of traditional conventions." "we might as well not have any style guide at all but simply enforce whatever style happens to dominate in a particular topic" – yes indeed, we can and do adopt that as the general practice at wikipedia for the vast majority of questions of style, and it works very well. The rare exceptions where someone snuck some rule in that isn't supported by general English usage, as in this example (a MOS change supported by yourself and 7 or 8 others at the end of 2017, with no mention of Greek names in the cursory discussion), it tends to just be ignored (as happened in this case), which also works fine. The only real problem is when pedantic rule enforcers come to make a stink about it for no particular reason. –jacobolus (t) 22:53, 17 March 2025 (UTC)

Sicilian coin

Bronze coin of Archimedes

I strongly disagree that my contribution of the Sicilian coin "seems rather misplaced minutiae" as justified for the revert by @Remsense (see diff). Most probably, the Sicilian coin is one the earliest documents of Archimedes' achievements, at least as important as the Fields medal and several stamps in the same section. The portrait on the coin seems to be the oldest depiction of Archimedes, older than Domenico Fetti's painting (1620) in the lead of the article. The coin's picture was first printed as part of Paruta's original work (a collection of Sicilian coins) in 1612 as stated here. In 1697, his work was reprinted with additional comments by Leonardo Agostini. However, it is unclear whether the depicted coin was issued by Marcellus around 210 B.C. (as argued by the German historian Ivo Schneider) or some time later in Sicily (Archimedes' home). Unfortunately, no such coin is available any more for further analysis.

In another talk, @JMF proposed "the possibility to put the Fields Medal at Archimedes#Mathematics and physics instead. Either way Archimedes#Honors and commemorations should have no more than one image." SchmiAlf (talk) 09:26, 22 January 2025 (UTC)

I think this contribution should be restored, and was puzzled by its removal. Tito Omburo (talk) 10:15, 22 January 2025 (UTC)

I think this isn't notable enough without more sourcing discussing it and its relevance.--♦IanMacM♦ ^{(talk to me)} 10:46, 22 January 2025 (UTC)

But what is the relevance of his image on the Field’s medal? A postage stamp? Tito Omburo (talk) 10:58, 22 January 2025 (UTC)

[edit conflict] SchmiAlf really should have relayed the context for my remark. The decision factor here is MOS:IMAGEREL: what part of the text does it illustrate uniquely? To do a reductio ad absurdum, why not replicate each and every postage stamp while you are at it. Coming back to reality, it is a short paragraph and only needs one illustration. So the real question is this: what is that illustration to be? an internationally recognised award or a historic coin for a small island in the Med? IMAGEREL says in summary, images are to illustrate, not to decorate. One image illustrates, two decorate. 𝕁𝕄𝔽 (talk) 10:59, 22 January 2025 (UTC)

and in reply to Tito's reply to IanMacM, the question you should be asking is "what is its relevance to 'Honors and commemorations'"? (in each case). 𝕁𝕄𝔽 (talk) 11:02, 22 January 2025 (UTC)

I think that's self-evident. Tito Omburo (talk) 12:00, 22 January 2025 (UTC)

I can see a rather convincing argument that the coin is the first such commemoration. And it is relevant, as SchmiAlf observed elsewhere, that Archimedes lived in Sicily. The case for the Fields Medal seems only that it internationally known. --𝕁𝕄𝔽 (talk) 13:36, 22 January 2025 (UTC)

"One image illustrates, two decorate" – This seems like a made up personal rule, a grossly exaggerated version of the MOS text "Resist the temptation to overwhelm an article with images of marginal value simply because many images are available", and I don't support dogmatically applying it. It's entirely fine to have two images in a section. –jacobolus (t) 15:29, 22 January 2025 (UTC)

No, that's a misrepresentation of what I wrote. Because it is so short and has just one substantive point, a second image in this section is redundant: it illustrates nothing more than does the first [whichever it is] and is therefore decorative. Otherwise let's have all the postage stamps etc etc. If not, why not?

Moving from the particular to the general, yes is entirely fine to have two images in a section if there are two or more substantial points in the section or the section is long enough that the article is not overwhelmed by images from this section spilling into the following section. When that happens, it disrupts the association of images from the text of those sections, that they are there to illustrate. 𝕁𝕄𝔽 (talk) 17:05, 22 January 2025 (UTC)

The first thing being illustrated is an ancient coin, mentioned in one paragraph. The second thing being illustrated is the Fields medal, mentioned in a different paragraph. I can't see how you think these are illustrating the same thing. It would also be fine to add a postage stamp or two here, if there is something to say about them. Images of postage stamps would not be illustrating the same thing. It would also be fine to add one or more drawings or paintings, again if there is something to say about them or if they illustrate some aspect of Archimedes' "Legacy". Images moderately overflowing to the following section are not a real problem unless the following section is also filled with images (though often the best way to deal with overflowing images is to just add more text rather than throwing away the images). –jacobolus (t) 17:09, 22 January 2025 (UTC)

An alternative, if anyone wanted to do the research, could be to greatly expand § Legacy and reorganize it. For example Hypatia § Legacy is quite long with many pictures, arranged chronologically. –jacobolus (t) 17:05, 22 January 2025 (UTC)

As a conclusion from the previous discussions I'm undoing the revert. Following discussions may restrict to the topic of whether the image of the Fields medal in this section is to be kept etc. SchmiAlf (talk) 08:12, 23 January 2025 (UTC)

How old is the coin, and roughly what year was it made? At the moment the caption is way too vague, and as a general rule, images should not be used unless they are discussed in the article text. Simply saying "Bronze coin of Archimedes" isn't enough.--♦IanMacM♦ ^{(talk to me)} 07:41, 24 January 2025 (UTC)

As stated earlier, the coin was first depicted in Paruta's Della Sicilia ... printed in 1612 (see for the index and coin sizes). The depiction itself immediately follows coins of Hiero II of Syracuse and his nephew (or grandson) Hieronimus who were the last kings of Syracuse before it was conquered by the Roman Marcus Claudius Marcellus in 212 B.C. On page 134 Paruta describes the coin as "R D 2", meaning that it was based on "rame" (copper), has a size of "D" (which is about 19 mm) and sequential number "2" in this section "D' Archimede". Sometimes it is also referred to as "bronzo" (bronze) which is a minor difference because copper is the major portion (>80%) anyway.

In addition, Paruta mentions on page 193 that the coin was owned by "Principe di Butera" with some additional information here.

The depiction of the coin was again published by the German historian Ivo Schneider in his research Archimedes, 1979, where he brought up the possible coinage by Marcellus (which, IMHO, is the most plausible interpretation). SchmiAlf (talk) 10:34, 25 January 2025 (UTC)

File:Archimedes_bronze_coin.png is a terrible image compared to the internet archive scan. Ideally this information should be stated a bit more clearly and precisely in the description of File:Archimedes_bronze_coin.png which is currently a bit hard to make sense of. –jacobolus (t) 04:37, 26 January 2025 (UTC)

I uploaded a new version at File:Archimedes bronze coin.jpg, taken from the scan directly; Compare:

–jacobolus (t) 10:56, 26 January 2025 (UTC)

Thank you! It's really better quality (analog source in 1612, not digital yet) SchmiAlf (talk) 16:34, 27 January 2025 (UTC)

Oddly enough, I think the addition of the coin is fine as it is, but the previous discussion highlights that the whole legacy section needs a revamp (IMO, there are worse offenders than the coin). Also, do note that this a 17th century description of an allegedly ancient Greek coin that is no longer in existence, and trying to nail a date beyond "after Archimedes' death" is virtually impossible as most ancient coins provided no dates for when they were minted. --Guillermind81 14:30, 26 January 2025 (UTC)

I still think that some explanation of the background history of the coin is necessary in the article text. The image caption explains virtually nothing except that it is a coin with Archimedes on it.--♦IanMacM♦ ^{(talk to me)} 08:12, 26 January 2025 (UTC)

And what about the description in the section? Anything to add? SchmiAlf (talk) 16:35, 27 January 2025 (UTC)

Archimedes and the planetarium

There is some care needed here, because the planetarium does not appear in the known works of Archimedes and was attributed to him many years later by Cicero. The Scientific American source makes this clear. The article should not say that Archimedes built a planetarium when all we have as evidence is Cicero attributing it to him. ♦IanMacM♦ ^{(talk to me)} 08:40, 16 February 2025 (UTC)

Biographical details

I've reverted the accounts of Archimedes' inventions working for the city of Syracuse back to the "biography" section. I believe that having a separate "discoveries and inventions" section for these is misleading, because these accounts from ancient sources are likely apocryphal and not inventions of discoveries that should be attributed to archimedes, and meanwhile there *are* discoveries and inventions that can be attributed to archimedes on the basis of his writings, so we ought to separate fact from fiction more cleanly. Probably more work needs to be done in the biography to make it clear that these stories are largely fiction, but this is often how I see other articles about ancient philosophers and scientists structured; the ancient accounts of their life (with proper caveats about historicity) are included in the "Life" or "Biography" section, but what modern scholars actually believe that the person did is included separately.

Also, as for the ordering, while the current content of the article may not reflect this yet, the reason why the order is "Ship" -> "Wreath" -> "War machines" is that that's the chronological order of the narrative. The ship story is supposed (by ancient authors) to be how Archimedes first made an impression on Hiero II, the wreath is another task that the king asked of him after he had established a reputation, and the war machines were used after the king's death (and lead naturally into the story of Archimedes death when the city fell) Psychastes (talk) 17:23, 30 April 2025 (UTC)

I've also moved the content in the old "mathematics" section to the relevant works in the "writing" section, or to the "legacy" section when it deals with modern assessments of Archimedes' work. Unlike the presentation of the various stories of inventions, I believe the content itself is largely accurate, though I haven't gone through it line-by-line yet, but the implicit claim being made by listing them under a heading about mathematical discoveries that any of these techniques are novel to Archimedes is not; for example, the method of exhaustion is often (erroneously) credited to Archimedes, but it appears in Euclid's elements, which predates Archimedes, so it's impossible for him to have discovered it. Psychastes (talk) 18:55, 30 April 2025 (UTC)

The "implicit" claim argument is subjective, and the article nowhere claims that Archimedes "invented" the method of exhaustion or the infinite series. The closest thing that it asserts is that Archimedes' system to name large numbers is his invention because Archimedes himself claims so in the Sand Reckoner. Guillermind81 (talk) 20:14, 30 April 2025 (UTC)

when the article says While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics followed immediately by a sections titled "Method of exhaustion", "Archimedean property", "Infinite Series" etc. i'm not sure what other conclusions a reader would be expected to come to than that these are Archimedes' contributions? I think at the least, the intro paragraph would benefit from being reworded, and probably the section header "mathematics" too. Psychastes (talk) 20:33, 30 April 2025 (UTC)

I guess that depends what your interpretation for "making contributions" is. I never thought that meant "original contributions" but others might get that impression. I'm Ok with taking that sentence out or reword it. Guillermind81 (talk) 20:40, 30 April 2025 (UTC)

Although ingenious, there's no chronology for any of Archimedes' anecdotes. The story that King Hiero was so impressed by Archimedes that he ordered everyone to believe everything he said appears only in Proclus; neither Vitruvius, Cicero, or Pappus said anything of the sort (thus hardly qualifying for "ancient authors"), there are no clues as to when the wreath problem took place, and no reason to think that it didn't happen earlier (if it happened at all), and the only sure thing is that Archimedes helped with Syracuse defenses when he was in old age because that's what Polybus, as a respectable historian, says. Guillermind81 (talk) 20:11, 30 April 2025 (UTC)

That's a fair point about the chronology being contested, while we may be able to find modern secondary sources arguing for one particular narrative or another, it's certainly flexible, so if you think the wreath story fits better first because it's more famous that's fine.

Re: polybius as a respectable historian, I'd recommend checking out WP:CLPRIM which explains quite a lot about what the WP:BESTSOURCES in classics are; we should not be weighing the value of ancient historians ourselves, which is WP:OR, any justification for chronology should come from modern secondary sources written by historians (such as Dijksterhuis). Psychastes (talk) 20:22, 30 April 2025 (UTC)

Modern secondary historians, such as Dijksterhuis, rely on Polybius extensively precisely because he's relatively trustworthy. I wasn't trying to pass judgement on all ancient historians but just commenting on what happens to be the communis opinio. Guillermind81 (talk) 20:46, 30 April 2025 (UTC)

Legacy section

I've added an expansion template to the "Middle Ages" subsection of the Legacy section, as it's the least complete, but I also have concerns about the comprehensiveness of the section as a whole as well.

• For the antiquity section, I think the claim about Archimedes' mathematical work being little read in antiquity is probably not accurate; Pappus of Alexandria, whose Collection was an attempt to sum up all of the canonical mathematics prior to his time, references Archimedes quite a bit, so there are likely reconstructions out there of the five to six centuries between Archimedes and Pappus. I believe Reviel Netz's recent book also has quite a bit of content connecting Archimedes with his immediate successors, e.g. Apollonius of Perga. The part about Eutocius and Isidore is also dubious; while it was previously believed by historians that Isidore supervised Eutocius, Eutocius' lifetime has been revised by modern historians to be earlier, and his teacher was probably Ammonius Hermiae, so his commentaries don't derive from any recompilation done by Isidore. There's also the confusing matter that, despite Eutocius saying he found the work of Archimedes written in Doric Greek (repeated in the article) our extent text in his commentary is not actually *in* Doric.
• For the middle ages, Marshall Clagett's five volume work (actually 10 books!) on Archimedes in the middle ages can probably be used to expand the Latin part beyond a sentence about translation. For the counterpart in Arabic, there may not be a comprehensive work yet on Archimedes in the medieval Islamic world available in English, and certainly nothing like Clagett's work, but we may be able to piece together enough for a paragraph or two from various papers that have been published. We could also say a bit about the manuscript traditions in the Byzantine period, which are probably more relevant to Archimedes than they would be to other historical figures due to the popular interest in the Archimedes Palimpsest, which is one of these three traditions.
• for the renaissance and early modern europe, we've got quite a bit of hagiography from different notable people like da Vinci, which does demonstrate that Archimedes was highly thought of during that time period, but isn't nearly as useful as secondary syntheses about *how* different renaissance mathematicians and scientists were influenced by the publication of the works of Archimedes. in short, we're "telling" much more than we're "showing"
• for modern mathematics, the same "show don't tell" concern applies as with the renaissance, but i think we could probably stand to have a technical discussion about the relation of Archimedes's work to calculus. there's a potential pitfall here though; many mathematicians who might be qualified to write such an article from the analysis perspective may also not have the necessary historical background to correctly separate Archimedes' novel achievements; i believe we need to be wary about anything attributing the method of exhaustion itself to Archimedes, since he didn't invent it, and this is a misconception that is often repeated
• for more contemporary influence, I think a catalogue of all the various attempts to replicate legendary feats of Archimedes in the 20th and 21st century would be interesting and useful, so long as we don't present it in a way that makes it seem like Archimedes definitely did any of it. Much of that content is currently in the article, though it would probably be better to have sources more removed from the people who actually did the experiments.
• I've gathered a number of related sentences into a "cultural influence" section. I'm somewhat wary of the potential for these sorts of "In popular culture" sections to attract WP:FANCRUFT, and would be amenable to removing it entirely, but perhaps it could be structured into paragraphs in a way that doesn't encourage too many uninformed additions.

Psychastes (talk) 19:37, 30 April 2025 (UTC)

Thanks for working on the Legacy section, as I agree it has the most need of improvements. My comments are for the first bullet only:

The claim about Archimedes' mathematical work being little read in antiquity was meant in general; there was a dedicated readership, to be sure, and it is thanks to them that Archimedes' mathematics is extant to some degree. But this was a tiny fraction of the readership in Antiquity, and the more popular authors didn't know Archimedes' mathematics in any detail: Cicero, Vitruvius, Ovid, etc. know him mainly as a maker of ingenious devices, mostly connected with mechanics or astronomy; Livy knows him only as the Syracusan defender who single-handedly stopped the Romans, as does the elder Pliny; of the later scholars, only Quintilian and Augustine make references to Archimedes as a "geometer" but it is plainly clear that they have not read Archimedes' mathematical writings but only go by hearsay. Yes, unlike these authors, Pappus and Hero did read Archimedes and extensively quote him--but these were mathematicians (in the sense of working in ancient "mathemata") writing for other mathematicians, not for "general" readership. The truth is that Archimedes' standing in the popular imagination in antiquity was not that different from today's, the sole genius inventor of wonderful devices that almost miraculously beat the Romans (e.g., Indiana Jones and the Dial of Destiny). Perhaps we should add a qualifier "little read by the general readership in antiquity" or something less awkward; nonetheless, the claim is solid.-- Guillermind81 (talk) 21:49, 30 April 2025 (UTC)

Ahhhhh okay, yeah, that makes sense; i was thinking in the context of mathematicians rather than a general audience. I agree, probably a bit of clarification about "general readership" or something like that would help. Psychastes (talk) 01:12, 1 May 2025 (UTC)

Writings section

I believe the writings section should be expanded, as analysis of these works by WP:SCHOLARSHIP in the history of mathematics will provide accurate characterization of what Archimedes actually did, as opposed to the popular legends about him that tend to circulate uncritically. Each of these works has their own article, which ought to have a more in-depth treatment of the work itself, but we could probably pull some information back into this article. I believe that some more in-depth coverage of the content of On the Sphere and Cylinder, On Spirals, On Conoids and Spheroids, and The Method of Mechanical Theorems would probably add a lot of information about Archimedes' work that hasn't been covered in the article so far, though in the case of the first three, there's not much on those spinout articles to begin with. On the Sphere and Cylinder and On Spirals can probably be improved with Netz's books on those works, but I'm currently unaware of any WP:SCHOLARSHIP on Conoids and Spheroids more recent than Heath, and it would probably be best to avoid his work while possible.

Comparatively, Measurement of a Circle, The Sand Reckoner, and Ostomachion are short works and probably what we have now is close to enough as far as depth of coverage. Quadrature of the Parabola meanwhile has the mathematical derivation but not the mechanical one, which would probably tie in nicely with more through coverage of The Method of Mechanical Theorems. I'm also skeptical about the value of organizing the works chronologically; I believe Netz argues for a different ordering than Knorr, and there are likely divergences of opinion beyond this, though a discussion of relative chronology might still be valuable even if it doesn't determine the ordering of the article. But also it may be more coherent to have the mechanical works (On the Equilibrium of Planes, The Method of Mechanical Theorems, On Floating Bodies) treated together, possibly with Quadrature of the Parabola acting as a transition from mathematical to mechanical. Psychastes (talk) 20:12, 30 April 2025 (UTC)

This is all good but the bigger question is whether there should be a separate "Mathematics" section highlighting Archimedes' mathematical techniques (not necessarily that he invented them but their use), or whether the "Writing" section and the "Mathematics" section should be merged into what would amount to a very long one. Expanding on each writing is also doable but I'm weary of just repeating what is in the longer articles for no good reason other than length; I believe these should be short summaries and the reader can click on the appropriate links if it wants to know more.

Quadrature of the Parabola does have the mechanical derivation under "Structure of the Text" rather than in its own section. There's even a picture that goes with it.

Ordering is open to interpretation but the list needs to be ordered somehow; chronologically, although tentative, makes the more sense IMO, and Sato & Knorr's ordering has some evidence to back it up, though a "thematic" ordering like yours is not an unreasonable one. Guillermind81 (talk) 20:35, 30 April 2025 (UTC)