Talk:Fields Medal

Source reliability
Following edits discussed above, the main table is now in an improved state (this is the current version), and I'm very pleased that the nature of the "reasons" column is now fully clarified in the text. Unfortunately I think I have to question the reliability of the Albers−Alexanderson−Reid text, which is reproduced on the various subpages on Fields medal website, see e.g. the 1936 awards page. This text (written in 1986/7) is the direct source for all "reasons" in the wiki table for years 1936-1986, except for 1958. A few comments:
 * 1) I think the Fields medal website itself is not a reliable or comprehensive source. It is unclear who has written the website and if they have good judgment. I say this because there are some red flags, such as that its recognition of Vaughan Jones (1990 Fields medalist) is apparently quoted from wikipedia. In 1998 they only name relevant mathematical fields, with no specifics whatsoever. In 2002 they say nothing at all. It seems that the website authors are unable to say anything without the help of the Albers−Alexanderson−Reid text or official commendations/comments with easily-identified quotes.
 * 2) I think the Albers−Alexanderson−Reid text is not a reliable source. Although many entries seem perfectly good, I think there are some troubling ones (all exactly reproduced in the wiki table on Fields medal wiki page):
 * 3) They say Atiyah "proved jointly with Singer the index theorem of elliptic operators on complex manifolds". I suspect they have confused complex vector bundles with complex manifolds, since (as far as I know) the index theorem does not take on a special form for complex manifolds. If they are referring to the generalized Hirzebruch−Riemann−Roch theorem on complex manifolds, proved as a corollary by Atiyah and Singer (as indicated in Henri Cartan's ICM lecture on Atiyah), then it is (at least to my understanding) inappropriate of them to refer to general "elliptic operators" and not to the particular ones of relevance to that case.
 * 4) They say Fefferman "contributed several innovations that revised the study of multidimensional complex analysis by finding correct generalizations of classical (low-dimensional) results". I think this is a misunderstanding of Carleson's ICM lecture. Fefferman's most renowned theorem (with Stein) is the theory of Hardy spaces and their connection with BMO space. The original theory of Hardy spaces does belong to single-variable complex analysis, but the Fefferman−Stein work belongs to multidimensional real analysis, not multidimensional complex analysis. If instead they are describing Fefferman's work on multidimensional complex analysis, then their statement is incorrect, since Fefferman's work there deals with phenomena in higher dimensions which is not present in the single-variable theory; so it is not a generalization of low-dimensional results.
 * 5) They say Donaldson's medal is "especially for showing that there is a differential structure on euclidian four-space which is different from the usual structure". Atiyah's ICM article on Donaldson only refers to this as a striking corollary of the main theorems of Freedman and Donaldson. However, despite Donaldson's paper appearing after Freedman, he does not seem to report this corollary anywhere in his paper. For the proof of this corollary, Robion Kirby's textbook refers to "others" and Freedman and Quinn refer to "many people". (See references in Exotic R4 wikipage.) In both books it is conspicuously not referred to as a theorem of Donaldson's, only that (as Atiyah says) it is a corollary of Donaldson + Freedman (which takes a little bit of work). It would likely be more appropriate to mention Donaldson's actual theorem which is being used here: namely, that he found a strong and striking restriction on the algebraic topology of smooth manifolds in four dimensions. His contribution to Donaldson−Uhlenbeck−Yau theorem is also discussed by Atiyah.
 * 6) They state the Kodaira embedding theorem exactly backwards. I suspect they misunderstood the phrase "One can approach the same question also in opposite direction", from Hermann Weyl's ICM lecture, to be suggesting that a converse statement was about to be discussed.
 * 7) It is strange that they say Douglas "did important work" on the Plateau problem, and not that he resolved it. There is arguably a subtlety about what precisely the "Plateau problem" refers to, but that is a little pedantic. Just as one example, Michael Struwe's standard book Variational Methods refers to "the 1930/31 solution of Plateau’s problem by Douglas and Rado". (Douglas and Rado both resolved it.)
 * 8) It is strange that they say Yau "made contributions" to the Calabi conjecture and the positive mass conjecture, and not that he resolved them.
 * 9) It is strange that they say Thurston "Contributed idea" of hyperbolicity for many manifolds, when in fact this is a highly notable theorem of his. Probably they confused his theorem with his equally famous conjectures.
 * I would appreciate any thoughts on the matter. Gumshoe2 (talk) 07:41, 25 January 2022 (UTC)


 * The proceedings of the ICM are all available online. Every Fields medallist has a short article written about their work in the proceedings, and an expert could summarise these for the table. It would be a shame to lose the style of direct quote for every entry in the table, but as you point out some of them are just wrong. It seems there are no short descriptions to be found in the ICM proceedings however. Tazerenix (talk) 12:53, 25 January 2022 (UTC)
 * Thank you for confirmation of errors. The short descriptions were discussed here in the last couple days, further up the talk page. I've gone through each Proceedings of the ICM, and found that official reasons for the medal were given in 1958, 1998, and every year since 2006 (and only in these years). So those particular entries should not be changed. For the rest, it seems to me that the ICM articles you mention are only superficially related to Fields medal; bureaucratically, they are written for the reason that some so-and-so got Fields medal, but their choice of content is entirely up to the particular writer/lecturer. So I think they are highly appropriate as sources for other wiki pages, whether biography or technical pages or both. But less so for this page. I think it's good for the Fields medal page to be limited to content about the Fields medal. But I will be happy to help with summaries if that's what people want. Gumshoe2 (talk) 14:15, 25 January 2022 (UTC)

I am also suspicious of Deligne's commendation "Gave solution of the three Weil conjectures concerning generalizations of the Riemann hypothesis to finite fields. His work did much to unify algebraic geometry and algebraic number theory". I have very little understanding of the mathematics, but based upon Weil conjecture wikipage and Nicholas Katz's laudatio for Deligne, it seems that there were four Weil conjectures and Deligne proved one of them, with the three others being earlier proved by others in the 1960s. (This also matches what I recall having informally heard from friends who are expert in algebraic geometry.) Is this accurate? Gumshoe2 (talk) 20:28, 3 February 2022 (UTC)

RFC: laudation errors
(The new Fields medals will be announced next week so it would be nice to get this resolved.) This is about the "reasons" column of the main table on the wiki page. Back in January I tried to start some discussion on this talk page, but it didn't go anywhere. Unfortunately requires some explanation, here are a few relevant (hopefully objective) facts: The question is how to (systematically or quasi-systematically) resolve this on the page. There are maybe four possible solutions: Gumshoe2 (talk) 20:18, 30 June 2022 (UTC)
 * 1) at least some of the given laudations on wiki are flatly wrong, which is not surprising since they were written by a few non-expert mathematicians and historians writing a short illustrated history book/pamphlet about the fields medal, and not written by domain experts
 * 2) these laudations are reproduced on the Fields Medal website (potentially giving an appearance of authoritativeness)
 * 3) in the years 1958, 1996, 2006, 2010, 2014, 2018, an official & short citation was announced together with the awarding of the medal, e.g. that Klaus Roth (1958) won "for solving a famous problem of number theory, namely, the determination of the exact exponent in the Thue-Siegel inequality" and that Andrei Okounkov (2006) won "for his contributions bridging probability, representation theory and algebraic geometry"
 * 4) for every single medalist from 1936 to the present, a domain expert has written (for the occasion of the ICM) a short essay about the medalist's work. Sometimes (depending on the individual taste of the expert) this is about a few particular results they find interesting and sometimes it is an overall appraisal of the medalist's entire body of work. In neither case is it indicated that the commentary therein provides "the reason" for the medal to be awarded. The general rule seems to be only that it is a personal celebration of the medalist on the occasion of their fields medal.
 * 5) Some of the awardees (e.g. Hironaka, Freedman) did specific results for which it is (informally, to mathematicians) clear that they won the medal. Some other awardees (e.g. Milnor, Grothendieck, Yau) have an entire body of work, many parts of which could be considered Fields-worthy by various people.
 * 1) Leave the current table as is
 * 2) replace the non-official laudations with short quotes or summaries from the essays about the medalist's work (such as is presently done for the 1990, 1994, 2002 medalists)
 * 3) only give the official citations (from 1958, 1998, 2006, 2010, 2014, 2018) and leave other entries blank
 * 4) (later edit, quoting David Eppstein's suggestion below) replace the non-official laudations with "properly-sourced description of the winner's most significant contributions to mathematics, up to the time of the award, without wording it in a way that implies that those contributions were the specific trigger for the award"


 * In my opinion choice #1 is unacceptable, given its errors. Choice #2 is ok but I think would be too misleading (given my comments in #4-5 above). I support choice #3, despite the downside that this would create visually unpleasant blank spots and for most medalists offer no information. The aesthetic part of this could be partly remedied by reverting back to an older version of the table such as something like here . (This would also resolve what I think is the very silly surplus of affiliation info in the table.) Gumshoe2 (talk) 20:19, 30 June 2022 (UTC)
 * What about choice #4: provide a properly-sourced description of the winner's most significant contributions to mathematics, up to the time of the award, without wording it in a way that implies that those contributions were the specific trigger for the award? I agree that there is a problem with calling things laudations when they are really backsourced from a popular-mathematics book, but it seems deliberately unhelpful to readers to just provide a long list of names and years without any clue what those people did. This would also allow us to avoid the current WP:QUOTEFARM issues. —David Eppstein (talk) 20:54, 30 June 2022 (UTC)
 * I have added your suggestion to the original post. Although I don't think it is an unacceptable solution like #1, my preference is against it as such info (similar to option #2) is not properly about Fields medal. And in my view it is unnecessary since all such further info is a literal one click away (on the wikibios where I think it is appropriate). I think on this we just have some mutually incompatible perspective on what belongs where, as I think it is perfectly ok to have minimal info on this page. Perhaps it is related to my personal view that Fields is just another award among many, and as such that it's ok to have a minimal/conservative amount of info on this particular page. But, anyway, if other commenters agree with you on this then I'll happily help to make such descriptions. Gumshoe2 (talk) 21:30, 30 June 2022 (UTC)
 * I'm happy to dump the affiliations. But I think the mathematics is more important. If it was important enough to give them a medal, surely it's important enough to give the readers a précis. And having to individually click on each one to find out their research area makes it hard to get a feel for the big picture of what sort of topics tend to get awarded or how that might have shifted. —David Eppstein (talk) 21:33, 30 June 2022 (UTC)
 * How about as a first step put a disputed tag against the problematic entries then they can be worked through putting in better entries. NadVolum (talk) 13:39, 1 July 2022 (UTC)
 * We can't replace them unless we have a clear idea what sort of thing the replacement is supposed to be. A formal laudation, that may only exist in a few cases? A quote pulled from anyone who might have happened to write about the award? Our own reworded description of their accomplishments? This affects even whether an entry should be considered problematic: if we are only including formal laudations, and we have a quote that is not a formal laudation, then it is problematic even if accurate. —David Eppstein (talk) 16:06, 1 July 2022 (UTC)
 * I actually did tag a couple entries as dubious back in January. I would also point out that domain knowledge possessed by wiki editors is (I think) limited enough to not cover all medalists, so that going medalist by medalist might make it very easy to miss some problems. Gumshoe2 (talk) 17:03, 1 July 2022 (UTC)
 * How about:
 * Keep the table structure as it is
 * Change the Reasons heading to Significant achievements
 * Encourage the more mathematically knowledgeable editors to check existing/new entries for accuracy
 * It would seem that the Fields Medal process is somewhat vague or inconsistent about giving specific reasons for the award, so WP is not in a position to be (or claim to be) more precise. Also, putting significant mathematical breakthroughs into 'lay' language is a near-impossible ask, but it is reasonable to offer some explanation (to those with an informed interest in the subject) of why a person has received such an award without requiring click-through to a separate article. -- Verbarson talkedits 10:48, 8 July 2022 (UTC)
 * Of these, choice #4 sounds far and away the best option. Nerd1a4i (talk) 01:22, 25 July 2022 (UTC)
 * Choice #4 sounds good to me. The truth of it is that most readers may get nothing from these descriptions whatever the case: how can we best describe Maryam Mirzakhani's contributions to maths to a non-specialist? Secrets of the Surface tries to answer this question, but it takes a full documentary—and even then it's a very technical answer. But giving editors more leeway to construct their own summaries of the person's contributions, prior to their Fields Medal being given, seems sensible when there are no official laudations. — Bilorv ( talk ) 21:19, 28 July 2022 (UTC)

Affiliation
For consistency, if the nationality is removed because of lack of importance (with which I agree), the subsection "Affiliation" in the "Demographics of recipients" should be removed too. It is just a section for publicity of an institution without any relation to the Fields Medal. The text says "41 are mathematicians who have been affiliated with the IAS as some point in their career". We can see for example that among the 41, we have Martin Hairer which was at IAS from March to April 2014. He received the Fields medal for his work published much before 2014. Cédric Villani is also considered while he was there only during spring 2009...

That section is little relevant to Fields medal and should be kept in the wiki page of the institution. — Preceding unsigned comment added by 102.103.252.48 (talk) 09:19, 5 July 2022 (UTC)
 * I agree, I have removed the promotional section. If that material should go anywhere here (and I think it shouldn't) it should go on the IAS's wikipage. Gumshoe2 (talk) 19:06, 5 July 2022 (UTC)

(Note: did not see above discussion, now moved to the bottom of talk page.) I'm inclined to dispute the removal of the "Affiliation" section. 41 out of 56 is quite a high percentage, more than could be explained simply by chance or as promotional. I would say it was promotional if it was, e.g., 10 out of 56, but this is probably higher than any other institution. It would require care to state it in the right way. Do you think that the affiliation of past winners is noteworthy for the article? 2nd/3rd opinions welcome. Caleb Stanford (talk) 19:38, 5 July 2022 (UTC)
 * IAS is an institution that a very large number of mathematicians visit at some point in their career, because of the special nature of the institute, which is largely based around temporary visitors. It is not analogous to, say, a tally for Harvard or Stanford; it would be if only permanent IAS members were counted. This was also pointed out in a remark earlier today by an IP address on this talk page (improperly added to top of talk page), where it was noted that the tally includes (for instance) mathematicians who were at IAS for a single month. Besides, the only source given is from IAS itself and I do not believe there is any other source showing that anyone else considers the number of IAS affiliations of Fields medalists to be notable. Gumshoe2 (talk) 19:46, 5 July 2022 (UTC)


 * Oh, I see, not sure how I missed that. I've moved it now to the bottom and merged the two sections. OK. Is there anything else useful that could go under Demographics? Perhaps a comparison of permanent affiliation, not including temporary visits? Especially if there are references discussing that. Else, do you have a better suggestion for where the discussion of gender should be placed? Caleb Stanford (talk) 20:02, 5 July 2022 (UTC)
 * Affiliation comparison should not be added if it is original research, which I think it would likely inevitably have to be.
 * In my opinion, until the gender sentence is expanded appropriately, it should be moved into the Landmarks section (where it already appears in part). But I think others such as David Eppstein strongly believe that it should remain as a standalone section. On the other hand, some of the landmarks section is clearly demographical in nature and could probably be moved to a demographics section. Gumshoe2 (talk) 20:18, 5 July 2022 (UTC)
 * Mirzakhani clearly belongs in landmarks as the first woman medalist. I am less convinced that Viazovska does, so now after she has won the choice of separately discussing women winners seems stronger. There is a small but consistent group of usually-anonymous editors who think that any recognition of diversity is inappropriate in mathematics and should be removed altogether; my opposition is more to them than to any fixed choice of how we organize that material. But I am also a little irritated that whenever you think there is disagreement about some position you pick on me as your imaginary straw-opponent, and put opinions in my mouth that might be less nuanced than my actual opinions, as you recently did at WT:WPM re 177 (number) and now again here. Argue based on content, not based on ad hominems about who might agree or disagree with you. —David Eppstein (talk) 08:34, 6 July 2022 (UTC)
 * I really do apologize since that is not my goal at all. For instance in this message I consciously chose to frame it as only what I think you believe, and I thought the purpose was clearly just to indicate that I have only one opinion among many (and to be honest I have no idea how it could be interpreted as ad hominem, of all things). In future I'll be more conscious to just refer to opinion of generic "other people" when appropriate, as would have been in this case. Gumshoe2 (talk) 16:04, 6 July 2022 (UTC)

IAS
List of Fields medalists affiliated with the Institute for Advanced Study was merged into this article on 7 July 2022. The consensus seems to be to redirect the list to this article in order to preserve the attribution history. But adding the contents of the list to this article was not done. We probably need to discuss whether to add the contents of the list to this article. -- SilverMatsu (talk) 00:19, 16 July 2022 (UTC)

Age of medalists
Since the age of medalists is occasionally a topic of interest, e.g. Jean-Pierre Serre, the 1954 Congress medalist is the youngest at 27, is there any interest in adding a column to the medalist table, age at 1 January of congress year (which is one of the qualifications) ?

I calculated the ages to address a citation needed comment, so I have that info currently available. Turtlens (talk) 20:09, 30 August 2022 (UTC)


 * In my opinion it would be a bad addition, needless information. I've also removed the new sentence about Peter Scholze's age relative to Simon Donaldson's, which seems like original research and is of dubious notability. I've restored the citation needed tag for Serre, since it is necessary to have a reference to establish notability; it is not enough to calculate everyone's ages yourself. Gumshoe2 (talk) 18:14, 10 September 2022 (UTC)
 * I found a source for Serre being youngest. Additional calculations such as that should only be added if sourced. —David Eppstein (talk) 19:22, 10 September 2022 (UTC)

Back story
What was the source of the money? In 1924 the International Congress of Mathematicians came to Toronto. The event was extended by a cross-country train trip to Vancouver and ferry to Victoria. Among the attendees was Ludwik Silberstein and family. The massive volumes to preserve the mathematicians' work dwarfs the volumes published for other ICM meetings. Evidently the conference ran a surplus and Fields held the sum until he discharged it in his will to establish the Medals.

What made the 1924 meeting so grand? Silberstein issued his second edition of The Theory of Relativity in 1924 to compete with Eddington's Mathematical Theory of Relativity. Both books explicated general relativity which had gained adherents after the 1919 Solar Eclipse Expeditions supported the new cosmology of Einstein. Silberstein's 1914 edition, on special relativity, had used biquaternions to elucidate the transformation geometry of the "flat cosmology" of Minkowski space. Southern Ontario had been home to Alexander Macfarlane (Chatham, Ontario) who had presided over an international, special interest group concerned with hypercomplex numbers. Thus the 1924 ICM was a portal out of abstraction into the physical cosmos with its temporal dimension accommodated. Rgdboer (talk) 01:17, 25 February 2023 (UTC)