Why didn't Vladimir Arnold get the Fields Medal in 1974?

Question

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 в 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:

Vladimir Arnold was nominated for the Fields Medal in 1974. The following is Arnold’s own version of the story; I hope I’m remembering it correctly. The matter seemed settled: the Fields Medal Committee recommended to award a medal to Arnold. The final decision was to be taken by the top administrative body of the International Mathematical Union, the Executive Committee. In 1971–1974 the vice-president of the Executive Committee was one of Soviet Union’s (even world’s) greatest mathematicians, Lev Semenovich Pontryagin (also a member of the Soviet Academy of Sciences). On the eve of his visit to the meeting of the EC, Pontryagin invited Arnold to his home for lunch and to talk about Arnold’s work. Pontryagin told Arnold he was instructed not to allow the Fields Medal to be awarded to him. In case the executive committee wouldn’t agree and would still try to award the medal to Arnold, Pontryagin was authorized to threaten that the Soviet delegation would boycott the next International Congress of Mathematicians in Vancouver, or even that the USSR would leave the IMU. However, in order for Pontryagin’s assertions about Arnold’s work to be convincing, Pontryagin said, he would need to know that work very well. That’s why he invited Arnold in order that he describe his work in detail. Arnold did. According to Arnold, the questions Pontryagin asked him were profound, the talk with him interesting, and the meal good. I do not know if Pontryagin had to make his threat known, but Arnold did not receive the medal—and only two medals were awarded instead of the intended three. By the next time the medals were being awarded, Arnold, born in 1937, was over the age limit. In 1995, Arnold himself became vice-president and learned that in 1974 the depth of Pontryagin’s familiarity with Arnold’s work made a great impression on the members of the EC.

Answer 1

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.

Answer 2

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.

Answer 3

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 (also check it out here for free access).

Answer 4

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.

Answer 5

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.

Answer 6

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").