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We can read as a mathunion excerpt that Grothendieck won the Fields medal in 1966

Built on work of Weil and Zariski and effected fundamental advances in algebraic geometry. He introduced the idea of K-theory (the Grothendieck groups and rings). Revolutionized homological algebra in his celebrated "Tohoku paper".

But all of this was already in the proceedings of the congress of 1958.

I would like to know if there are resources to learn why take so much time to give the Fields medal to Grothendieck.

I mean, why he was not awarded the medal in 1962? At that time it was already very clear, that Grothendieck was an outstanding mathematician. He was also not invited to give a talk. Serre would give a talk of his work.

I can imagine the history around, for example, why take some time to give the Nobel prize to Einstein (and why not on relativity!), has a good bibliography or resources here and there... Maybe someone knows something about the case Grothendieck.

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  • $\begingroup$ My guess: Since Fields Medals are awarded to those under age 40, they are typically awarded the last time an individual is eligible. So, for example, in 1962 the recipients were closer to 40 than Grothendieck. $\endgroup$
    – Gerald Edgar
    Commented Mar 9, 2022 at 13:18
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    $\begingroup$ @GeraldEdgar: In 1962, both Fields medallists (Milnor and Hörmander) were 31 years old, Grothendieck was 34. Serre got it in 1954, when he was 28. $\endgroup$
    – markvs
    Commented Mar 10, 2022 at 1:35

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There is a very interesting [resource], let me sum up my conclusions.

The beginnings of the Fields medal were not about honoring the best mathematicians, but "The committees used the medal as a redistributive tool, to give a boost to those who they felt did not already have every advantage but were doing important work nonetheless." This would explain in some aspects, why people like Weil or Hirzebruch did not get the medal.

According to Zariski's letters of the committee of 1958, Grothendieck was already on the list to be awarded the medal, but Schwartz (at the time in the committee) "thought it was better to wait until more of Grothendieck's work had come out (among a few reasons)".

In 1962, Grothendieck was already a high-profile in math, with his institution (founded in 1958) one of the best in the world. And I think that was the reason (as in the case of Weil and Hirzebruch) for not giving him the medal, he would not need more prestige.

In 1966, the medal had acquired the "prestige" of a "Nobel of math" (now the committee would give the prize to the best of mathematicians) and also the limit of age, it was the last chance for Grothendieck to receive the medal. A rather interesting point here, Grothendieck would not go to Moscow for the medal due to political reasons, Smale was also interested in politics.

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  • $\begingroup$ The Schwarz you are mentionning is (Laurent) Schwartz with a "t" in his name $\endgroup$
    – Jean Marie Becker
    Commented Mar 17, 2022 at 22:25

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