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.<p>I read the linked article and found a few nuggets that I think are of general interest, which I am quoting below:<p>"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)<p>“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)<p>“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)<p>Edit: I just found another quotation about him, not from this article, but too good not to mention here:<p>"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]<p>[1] The Rising Sea: Grothendieck on simplicity and generality <a href="http://www.landsburg.com/grothendieck/mclarty1.pdf" rel="nofollow">http://www.landsburg.com/grothendieck/mclarty1.pdf</a><p>[2] <a href="http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf" rel="nofollow">http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf</a>
by way of
<a href="http://www.quora.com/Why-is-Alexander-Grothendieck-revered-by-mathematicians" rel="nofollow">http://www.quora.com/Why-is-Alexander-Grothendieck-revered-b...</a>