Based on these remarks alone, it seems hard to imagine how I could be anything like Grothendeick. But when I read Grothendieck’s own description of himself, it’s hauntingly familiar. He writes:
“I’ve had the chance...to meet quite a number of people, both among my “elders” and among young people in my general age group, who were much 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 a arduous track, like a dumb ox faced with an amorphous mountain of things that 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.”
When I mentioned this to professor at a top math department who had taken a class with Grothendieck, he scoffed and said that he didn’t believe it, apparently thinking that Grothendieck was putting on airs in the above quotation – engaging in a sort of bragging, along the lines of “I’m so awesome that even though I’m not smart I was still one of the greatest mathematicians ever.” It is hard to reconcile Grothendieck’s self-description with how his colleagues describe him. But I was stunned by the professor’s willingness to dismiss the remarks of somebody so great out of hand.
Third alternative: Perhaps Grothendieck felt slow to understand puzzles because he had unrealistic expectations of himself. Perhaps he felt his thinking was sluggish because he had higher standards set for himself. Perhaps he felt the problems were extremely difficult because he was working with problems others barely recognized the existence of.
Knowing very little about mathematics and nothing about Grothendieck, this possibility is what I find most plausible.
The phenomenon that you allude to (great researchers setting a high standard for themselves and feeling inadequate relative to it even while doing extremely good work by most people’s standards) is a real one, but in the above passage Grothendieck is in part (explicitly) comparing himself with other people who he knows.
A version of your comment that takes this into account is that he may have been comparing his speed with that of the greatest mathematicians in the world (e.g. his close correspondent Jean-Pierre Serre, who I believe to be the youngest Fields medalist in history).
That’s a fair reply and I see value in it, but I also suspect Grothendieck was comparing himself to specialists while he pursued an unusually broad understanding of in-depth mathematics.
Third alternative: Perhaps Grothendieck felt slow to understand puzzles because he had unrealistic expectations of himself. Perhaps he felt his thinking was sluggish because he had higher standards set for himself. Perhaps he felt the problems were extremely difficult because he was working with problems others barely recognized the existence of.
Knowing very little about mathematics and nothing about Grothendieck, this possibility is what I find most plausible.
The phenomenon that you allude to (great researchers setting a high standard for themselves and feeling inadequate relative to it even while doing extremely good work by most people’s standards) is a real one, but in the above passage Grothendieck is in part (explicitly) comparing himself with other people who he knows.
A version of your comment that takes this into account is that he may have been comparing his speed with that of the greatest mathematicians in the world (e.g. his close correspondent Jean-Pierre Serre, who I believe to be the youngest Fields medalist in history).
That’s a fair reply and I see value in it, but I also suspect Grothendieck was comparing himself to specialists while he pursued an unusually broad understanding of in-depth mathematics.