Was it just a sign of humility? Or was his idea of ​​‘talent’ a bit different from the general realm? And did Grothendieck regret that he could not solve the last part of the Weil conjecture?


1 Answer 1


Grothendieck's assessment is not related to Deligne's proof of the Weil conjectures, which Grothendieck was not impressed by. As Deligne himself remarked, "since the proof used a trick, he did not care". But Grothendieck does elaborate on Deligne's superior talents in Récoltes et Semailles. His impressions were, apparently, based on their personal interactions in the early years of collaboration, when Deligne showed himself as a 'child prodigy':

"His perennial receptiveness and the ease with which he learned about each thing ("as if he had always known it") acted as a constant source of enchantment... His comments always ran ahead of my own intuitions or restraint, or shed some new light on the reality I was painstakingly trying to grasp through the mist that still surrounded it. As I have said elsewhere, he often has answers to the questions which I was asking, sometimes even on the spot, while other times he would reach the answer in the days or weeks that followed. The role of the listener was reciprocated when he took his turn in sharing the answers which he had found, which he presented as no more than the nature of things, always appearing with perfect naturality, and presented with the same ease which had tantalized me and certain of my elders such as Schwartz and Serre (as well as Cartier).

Ever since we first met, I had felt that his "abilities", as we say, were of a very rare quality, and far exceeded the modest abilities which I myself possessed, even though we were of the same breed when it came to our passion for understanding and our exigency regarding the comprehension of mathematical things. I also sensed, dimly, without yet being able to put my finger on it that this "strength" which I noticed in him (and which I also noticed in myself, although present to a lesser degree) of "seeing" the obvious things which nobody else could see was the faculty of a child as well as the innocence of a child's eyes. He held within him something of a child, much more visibly than other mathematicians whom I have known, and this was surely not an accident."

It should be said that Grothendieck shares these impressions right after characterizing Deligne's later behavior as deeply unethical and unfair, effectively, passing ideas of others as his own:

"In all of these cases and others of lesser scale, I was able to realize that the internal attitude and "method" which allowed Deligne to claim credit for others' ideas with flawless good conscience was that of disdain (one which remains partially tacit, all the while being deftly suggested) towards the "little" which we are about to appropriate - so "little" in fact that there is no need to even speak about it, especially given that we are about to use it right away to do truly powerful things - think Weil conjectures, theory of so-called "perverse" sheaves, ...

After the operation is finished, and the appropriation is complete and accepted by all, there is always time to rectify the situation and to modestly show off that which has been appropriated. The same contribution is treated with offhand disdain while it remains attached to the name of one of those who are to be buried, only to be highlighted once it has been appropriated by himself ($l$-adic cohomology, motives, Mebkhout's yoga) or by a good friend (yoga of derived categories and yoga of duality, appropriated by Verdier under Deligne's active encouragement)."


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