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As you all probably know, Vladimir I. Arnold passed away yesterday. In the obituaries, I found the following statement (AFP)

In 1974 the Soviet Union opposed Arnold's award of the Fields Medal, the most prestigious recognition in work in mathematics that is often compared to the Nobel Prize, making him one of the most preeminent mathematicians to never receive the prize.

Since he made some key results before 1974, it seems that the award would have been deserved. Knowing that the Soviets sometimes forced Nobel laureates not to accept their prizes, I thought at first that the same happened here - but noticing that Kantorovich received his Nobel prize the next year, and that Fields laureates both in 1970 and 1978 were Russians (Novikov and Margulis, respectively), I cannot understand why did the Soviets oppose it in case of Arnold. Can someone shed some light?

EDIT: I googled the resources online in English before asking this question here and found no answers. But after posting it here, I googled it in Russian, and found the following:

Владимир Игоревич Арнольд был номинирован на медаль Филдса 1974 году. Далее — изложение рассказа самого Арнольда; надеюсь, что помню его правильно. Всё было на мази, Филдсовский комитет рекомендовал присудить Арнольду медаль. Окончательное решение должен был принять высший орган Международного математического союза — его исполнительный комитет. В 1971 — 1974 годах вице-президентом Исполнительного комитета был один из крупнейших советских (да и мировых) математиков академик Лев Семёнович Понтрягин. Накануне своей поездки на заседание исполкома Понтрягин пригласил Арнольда к себе домой на обед и на беседу о его, Арнольда, работах. Как Понтрягин сообщил Арнольду, он получил задание не допустить присуждение тому филдсовской медали. В случае, если исполком с этим не согласится и всё же присудит Арнольду медаль, Понтрягин был уполномочен пригрозить неприездом советской делегации в Ванкувер на очередной Международный конгресс математиков, а то и выходом СССР из Международного математического союза. Но чтобы суждения Понтрягина о работах Арнольда звучали убедительно, он, Понтрягин, по его словам, должен очень хорошо их знать. Поэтому он и пригласил Арнольда, чтобы тот подробно рассказал ему о своих работах. Что Арнольд и сделал. По словам Арнольда, задаваемые ему Понтрягиным вопросы были весьма содержательны, беседа с ним — интересна, а обед — хорош. Не знаю, пришлось ли Понтрягину оглашать свою угрозу, но только филдсовскую медаль Арнольд тогда не получил — и было выдано две медали вместо намечавшихся трёх. К следующему присуждению медалей родившийся в 1937 году Арнольд исчерпал возрастной лимит. В 1995 году Арнольд уже сам стал вице-президентом, и тогда он узнал, что в 1974 году на членов исполкома большое впечатление произвела глубина знакомства Понтрягина с работами Арнольда.

Translation of the text (combination of Google translate and my knowledge of Russian)

Vladimir I. Arnold was nominated for the Fields Medal in 1974. Next - summary of the story of Arnold, I hope I remember it correctly. Everything was going fine, Fields Committee recommended an award to Arnold medal. The final decision was to be taken by the supreme organ of the International Mathematical Union - its executive committee. In 1971 - 1974 the vice-president of the Executive Committee was one of the greatest Soviet (and world) mathematicians, Academician Lev Semenovich Pontryagin. On the eve of his visit to the meeting of the Executive Committee, Pontryagin invited Arnold to his home for lunch and to talk about Arnold's work. As Pontryagin said then, he was ordered not to allow the award of Fields Medal to Arnold. In case the executive committee wouldn't agree and still try to award the medal to Arnold, Pontryagin was authorized to threaten the Soviet delegation's no-show in Vancouver at the next International Congress of Mathematicians, and Soviets leaving the International Mathematical Union. In order for the judgment of Pontryagin about the work of Arnold to be persuasive, Pontryagin, in his own words, had to know the work very well. Therefore, he invited Arnold to tell him in detail about his work, which Arnold did. According to Arnold, the questions Pontryagin asked him were very thorough, the talk with him was interesting, and the meal was good. I do not know whether Pontryagin had read out his threat, but Arnold did not receive the medal - and only two medals were given instead of the intended three. By the next award of medals Arnold (b. 1937) was too old for awarding the Fields Medal. In 1995, Arnold himself became vice-president, and then he heard that in 1974 the depth of Pontryagin's familiarity with Arnold's work made a great impression on the members of the executive committee.

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I didn't know it! R.I.P. He was one of the most original mathematicians of the 20th century. –  Victor Protsak Jun 5 '10 at 10:25
Here is the original source for Uspenski's article: magazines.russ.ru/novyi_mi/2007/12/us9.html Although this story explains how Arnold was deprived of his medal, it still does not explain why he was deprived of it and who ordered Pontryagin to do what he did. –  Dmitri Pavlov Jun 5 '10 at 10:27
A Fields Medal is a really nice prize, and most of those who receive it are very deserving, but ultimately it has no more fundamental integrity than any other award - Nobels, Pulitzers, Oscars - all are to an extent political and short-sighted, simply because they are awarded by people. The actual reasons have been explained, but an arbitrary oversight/debate/different perspective on the part of the committee is always a plausible explanation. –  DoubleJay Jun 15 '10 at 4:17
I cleaned up the English a bit, but I'm confused by something. The excerpt "Как Понтрягин сообщил Арнольду, он получил задание не допустить присуждение тому филдсовской медали" means Pontryagin said to Arnold that he (Pontryagin) was ordered not to allow Arnold to get the Fields medal. It sounds really weird: first that Pontryagin would lay out his intentions to Arnold and then that Arnold would consider a meeting on those terms to be "interesting"? I left that part of the translation undisturbed for the most part, but I welcome comments from any native speakers on this point. –  KConrad Jun 15 '10 at 5:35
@KConrad: Your translation (in the comment) is correct, and the piece sounds equally weird in Russian. I do not think however that all these details are 100% accurate. Pontryagin in his biography book writes that he was to prevent inviting Arnold to Vancouver, and this sounds more logical to me. –  Sergei Ivanov Jun 15 '10 at 11:45
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6 Answers

up vote 22 down vote accepted

Pontryagin wrote a book "Biography of Lev Semenovich Pontryagin, a mathematician, composed by himself". It is available online at http://www.ega-math.narod.ru/LSP/book.htm, in the original Russian. Google does a fairly good job of translation, although it refuses to translate the individual chapters completely because of their length.

In the book, Pontryagin shares a lot about the inner workings of the IMU Executive Board and his own role in holding the Soviet party line there as its vice president. For example, he recounts his version of how France got the IMU presidency in 1974, so that neither the Soviet Union nor the US would dominate.

The only relevant mention of Arnold that I could find in that book is in chapter 5. He states that in 1974 Arnold was not allowed to leave the country to lecture abroad, and that there was a conflict about this with the Executive Board of the IMU, who insisted that he should. From this, you could extrapolate the reasons for blocking Arnold's Fields medal, if the story is true.

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As a possible counterpoint, Margulis was also barred from attending the IMU by the Soviet authorities, but he was still awarded the Fields Medal. –  bhwang Jun 5 '10 at 18:09
Margulis' medal was in 1978, not 1974. Different times, different rules. –  VA. Jun 5 '10 at 19:11
There is no serious difference between 1978 and 1974. –  Mikhail Bondarko Jun 5 '10 at 22:56
Not that it's important but you know, blocking two Fields medalists is always harder than one. –  VA. Jun 5 '10 at 23:09
Thank you for the link! Pontryagin was a brilliant mathematician and a very dark man. It is fascinating to read about his actions in his own words. Perhaps, he was somewhat ashamed of his position in the Arnold episode, because he is uncharacteristically reticent. –  Victor Protsak Jun 5 '10 at 23:26
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In this interview, Arnol'd says the following:

My personal relation with Pontriagin was rather good. He invited me to his house and to his seminar and showed genuine interest in my work, especially on singularity theory. This was partially due to our common interests in differential topology and control and game theory. The main reason, however, was that he wanted to say something against me at an international meeting. Pontriagin was then the Russian representative in the International Mathematical Union (IMU) and had done a lot to prevent any vote for dissident Russians. (I was blacklisted because I, along with 99 other mathematicians, had signed a letter protesting the imprisonment of a perfectly healthy Soviet mathematician in a psychiatric hospital. This was the standard method of eliminating dissidents.) The IMU had always been very political, and he succeeded.

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A curious footnote to the blocking of Arnold's Fields Medal by Pontryagin (if that is what it was) is the comment Arnold made following the award of medals to three French mathematicians (mainly for work in PDE) in 1994:

Unlike the Nobel Prizes, the Fields Medals pass by many of the truly outstanding people, and in particular Russians. To give three medals at once to representatives of the French mathematical school, and all three of them noted for the art of manipulation of inequalities, is hardly a help to the international prestige of French mathematics.

This is part of an article Arnold wrote in the Mathematical Intelligencer in September 1995. It may be read here if you have the appropriate institutional affiliation.

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It seems like many of the comments about being passed by are from Arnold himself. –  Don Stanley Jun 15 '10 at 6:50
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Hard to say. There are strange reasons for certain mathematicians being passed on the Fields Medal. According to the Langlands memorial talk, Harish Chandra was passed over (1958) because a member of the committee felt he was "too much of a Bourbakite". Maybe there were strange political reasons for Arnold being passed over as well.

Personally, it's a mystery why so many brilliant mathematicans like Gromov(!), Manin, Beilinson, etc. have been passed over. Mathematics is such a broad subject, filled with so many really smart people, I would think it would not be hard to find four mathematicians who satisfy the requirements for the medal.

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ICM 1966 in Moscow was the first time that 4 people were awarded the Fields medal. Before, it had always been 2. I don't know how do they determine the number of recipients –  Victor Protsak Jun 5 '10 at 22:52
Question why there were only two recipients in 1974, after two congresses with more recipients appeared in The Mathematical Intelligencer Vol 1 No 3 (1978) [springerlink.com/content/23260u245q251055/] "No reason for the reduction was given, but presumably the anonymous donor who made the additional awards possible in 1966 and 1970 had done so on a one shot basis rather than endowing them in perpetuity". –  Harun Šiljak Jun 6 '10 at 7:12
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In 1974, also, Pierre Deligne had a Fields Medal "withheld", after his proof of the Weil conjectures. That was hypothesised to be prejudice against non-peer reviewed aspects of the proof. I wouldn't read too much into this report about Arnold. I happen to have had a brief conversation with the late Frank Adams about the Deligne case (he was on the committee), and what I picked up there was a merest hint about divisions on the committee that year, when only two medals were given. It seems quite possible that there were several divisive issues that time, and some compromise was made. But I don't think we shall know more than rumours until someone on the committee tells all.

Edit: Now that the source has been posted, I'm not quite sure what to think. The medals went to Bombieri and Mumford. Deligne would have been a third geometer (though Bombieri is also known for analytic number theory). It is plausible that Arnold, at 37, would have been a strong candidate.

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How many of them are still alive??? –  Victor Protsak Jun 5 '10 at 10:28
Robert Langlands, in is excellent article on the life and work of Harish Chandra, talks about how HarishChandra was denied a Fields Medal in 1958. "He was considered for the Fields Medal in 1958, but a forceful member of the selection committee in whose eyes Thom was a Bourbakist was determined not to have two. So HarishChandra, whom he also placed on the Bourbaki camp, was set aside." publications.ias.edu/rpl_works/L12/frs/harish2-ps.pdf –  unramified Jun 5 '10 at 14:21
The "forceful member" was Carl Ludwig Siegel, if the stories I've heard in India are correct. –  Chandan Singh Dalawat Jun 6 '10 at 2:54
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Arnold himself confirmed what you wrote in your question:
V.I.Arnold "Yesterday and long ago", Springer, 2007 (translated from Russian), p. 94:
"...while having dinner he (L.S.Pontryagin) explained to me that he had to go to an international meeting and talk against me..."
So basically what you cited seems to be true, though Arnold did not mention that "...Pontryagin was ordered not to allow the award of Fields Medal to Arnold" (in Russian "had to" not necessary means "was ordered to").

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Does it in English? –  R W Jan 5 at 7:49
@R W Probably the same :) I just expected somebody asking if "had to" has different meaning in Russian. –  TT_ Jan 5 at 14:48
For the sake of completeness, here is the Arnold's list (from the same book) of remarkable mathematicians who also were not awarded: H.Weyl, Whitney, Kolmogorov, Petrovsky, Leray, Pontryagin, Chern, Morse, Zariski, Shannon, Turing. –  TT_ Jan 5 at 18:17
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