Reminiscences of Grothendieck and His School (2010) [pdf](ams.org)
ams.org
Reminiscences of Grothendieck and His School (2010) [pdf]
http://www.ams.org/notices/201009/rtx100901106p.pdf
2 comments
It is a weird mode of thought we have, comparing humans on a one-dimensional scale and thus effectively devaluing them into numbers. What does that say about us? It may be useful to see such an expedient in articles on businessmen and their money, I suppose. But when one encounters it in publications on someone's contributions to knowledge and culture, it is out of place.
Arguing about whether Serre was a better mathematician than Grothendieck is a bit like arguing whether Thelonious Monk was a better musician than Duke Ellington...
I've been interested in Grothendieck's thought process in general since I read that thing about opening a nut by submersing it in water for a long time [1]. I'm talking about his general thought process, since I have nowhere near the mathematical maturity to understand any of what he actually did.
I read the linked article and found a few nuggets that I think are of general interest, which I am quoting below:
"To him no statement was ever the best one. He could always find something better, more general or more flexible. Working on a problem, he said he had to sleep with it for some time. He liked mechanisms that had oil in them. For this you had to do scales, exercises (like a pianist), consider special cases, functoriality. At the end you obtained a formalism amenable to dévissage." (p 1113)
“That was one principle of Grothendieck: every assertion should be justified, either by a reference or by a proof. Even a “trivial” one. He hated such phrases as “It’s easy to see,” “It’s easily checked.” When he was writing EGA, you see, he was in unknown territory. Though he had a clear general picture, it was easy to go astray. That’s partly why he wanted a justification for everything. He also wanted Dieudonné to be able to understand!” (p 1115)
“Grothendieck was not thrifty. He thought that some complements, even if they were not immediately useful, could prove important later and therefore should not be removed. He wanted to see all the facets of a theory.” (p. 1115)
Edit: I just found another quotation about him, not from this article, but too good not to mention here:
"What interested him were problems that seemed to point to larger, hidden structures. “He would aim at finding and creating the home which was the problem’s natural habitat,” Deligne noted. “That was the part that interested him, more than solving the problem.”" [2]
[1] The Rising Sea: Grothendieck on simplicity and generality http://www.landsburg.com/grothendieck/mclarty1.pdf
[2] http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf by way of http://www.quora.com/Why-is-Alexander-Grothendieck-revered-b...
I read the linked article and found a few nuggets that I think are of general interest, which I am quoting below:
"To him no statement was ever the best one. He could always find something better, more general or more flexible. Working on a problem, he said he had to sleep with it for some time. He liked mechanisms that had oil in them. For this you had to do scales, exercises (like a pianist), consider special cases, functoriality. At the end you obtained a formalism amenable to dévissage." (p 1113)
“That was one principle of Grothendieck: every assertion should be justified, either by a reference or by a proof. Even a “trivial” one. He hated such phrases as “It’s easy to see,” “It’s easily checked.” When he was writing EGA, you see, he was in unknown territory. Though he had a clear general picture, it was easy to go astray. That’s partly why he wanted a justification for everything. He also wanted Dieudonné to be able to understand!” (p 1115)
“Grothendieck was not thrifty. He thought that some complements, even if they were not immediately useful, could prove important later and therefore should not be removed. He wanted to see all the facets of a theory.” (p. 1115)
Edit: I just found another quotation about him, not from this article, but too good not to mention here:
"What interested him were problems that seemed to point to larger, hidden structures. “He would aim at finding and creating the home which was the problem’s natural habitat,” Deligne noted. “That was the part that interested him, more than solving the problem.”" [2]
[1] The Rising Sea: Grothendieck on simplicity and generality http://www.landsburg.com/grothendieck/mclarty1.pdf
[2] http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf by way of http://www.quora.com/Why-is-Alexander-Grothendieck-revered-b...
This sentence from Illusie says a lot: "The person who at the time could repair anything that went wrong was Deligne. ".
Also, this nod to Knuth is worth mentioning:
"Nowadays you have such efficient TEX systems, manuscripts look very nice. In Grothendieck’s time the presentation was not so beautiful, maybe, but Dieudonné-Grothendieck’s manuscripts were still fantastic."
The amount of time spent formatting papers at the time should have been better spent.
Also, Serre placing Weil higher than Grothendieck is interesting to read. I wonder if they all place Serre higher than anyone...