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Comment by Paracompact

2 days ago

Another quote of Grothendieck's that has always stuck with me:

"Since then I’ve had the chance in the world of mathematics that bid me welcome, to meet quite a number of people, both among my 'elders' and among young people in my general age group who were more brilliant, much more ‘gifted’ than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle–while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things I had to learn (so I was assured) things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates almost by sleight of hand, the most forbidding subjects.

"In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still from the perspective or thirty or thirty five years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve done all things, often beautiful things in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have to rediscover in themselves that capability which was their birthright, as it was mine: The capacity to be alone."

(From _Récoltes et Semailles_)

It's only a shame that most aspiring mathematicians with the same disposition as Grothendieck, never do reach the same level of accomplishment and acclaim as Grothendieck, before concluding that they are, in their final opinion, like clumsy, oafish oxen compared to their colleagues.

"To have broken these bounds they would have to rediscover in themselves that capability which was their birthright, as it was mine: The capacity to be alone."

I know someone who believes he has solved all the remaining major math and physics challenges and submitted them for the various awards.

He is alone, too. His schizophrenia has isolated him pretty thoroughly.

  • Grothendieck ended up totally crazy too, unfortunately. Some people might be truthers that his final writings would be made sense of someday, but I don't think that is a responsible hope to carry.

    The idea that Grothendieck both massively succeeded and failed in some sort of countercultural/neurodivergent knife edge is I think the ambiguous but correct morality tale.

    • The most gifted scientists are of one of two flavors, seemingly: Completely lucid and exuberant well into their elderly years, or strange and secluded even in their better years.