where does he rate now, legacy wise, among mathematicians
I’m not sure what the point is of all of your threads about ranking mathematicians and their contributions, but to answer your question: Grothendieck was undeniably a great mathematician whose seminal work in algebraic geometry and related areas is remarkable not only for the results themselves, but his reorganization of the subject (and quite a few other areas) in terms of category theory and similar abstractions. As for his rating: We usually wait a week or two before convening to decide his ranking, but the rumors are that he’ll be somewhere between 48th and 51st.
When I was in graduate school in 1959, one of the professors claimed he was the greatest mathematician alive. This was even before he had really begun reorganizing algebraic geometry. In truth he had but there was only one relevant publication at that time (the famous “Tohoku” paper). He had reorganized the study of topological vector spaces, the area also called “soft analysis”, which is what the professor worked in. I feel certain that his work on algebraic geometry, mostly published in the 1960s totally revolutionized the field. Then around 1969 he abruptly quit doing mathematics. He had realized that his position at the Institut de Hautes Etudes Scientifiques was funded by the military and he quit. He then became involved with a cult-like group called “Survivre” (Survive!) that was concerned with the future. He also got a job with the University of Montpellier and–I gather–became the financial support of the group. I had a private conversation with him for about an hour in the summer of 1971, but I could not get a clear statement of what he was doing. Then he retired, bought a farm in some secret place, and disappeared from public view. I never met him again.
At the time, you would have gotten general agreement that he was the #1. Since then, a couple other names have come up, but lower than #3 or #4 is not plausible.
Later he wrote an intemperate memoir, claiming, among other things, that all his best ideas had been stolen by students and colleagues and declaring that he didn’t want any publications of his ever translated or reprinted. A French group hoping to prepare his collected works then disbanded. My online journal was trying to reprint the Tohoku paper or maybe translate it, but he would not give permission. Finally, my wife and I translated it and posted it privately (and it has been downloaded hundreds of times) despite his express wishes. My attitude is that once published it is owned by mankind. That was the original purpose of the copyright laws.
One of the lesser-known Millennium Prizes is for the person who comes up with an algorithm for rating mathematicians. For a while there, Ed Witten seemed to have a lock on it until someone noticed that his formula stacked the deck in favor of himself.
It’s “Alexander”, not “Alexandre”.
Did anyone else laugh when they saw dude’s last name, and as they moused over link to find out who dude was, misread “mathematician” as “masturbator?”
Me too!
He ranks among the deadest, at least for certain values of death.
Also amongst the *least *dead of dead mathematicians for certain values of death. Both at once!!!1!
Math is weird that way.
Le headline on the article in Le Monde: http://www.lemonde.fr/disparitions/article/2014/11/14/le-mathematicien-alexandre-grothendieck-est-mort_4523482_3382.html makes no bones about it: Alexandre Grothendieck, le plus grand mathématicien du XXe siècle, est mort (Alexandre Grothendieck, the greatest 20th century mathematician is dead).
Maybe they meant “the largest mathematician.” Just on the name alone, I’m picturing a big guy.
Hmm, I wouldn’t say he was the greatest mathematician of the 20th century, but he would definitely be on the short-list. (I don’t have anyone in particular in mind for the title of the greatest; that’s an odd thing to even contemplate naming.) He’s also something like the equivalent of Mike Tyson for mathematicians: someone about whom there’s no story crazy enough to immediately dismiss.
Indeed, he is maximally dead.
“greatest” is always tough to assign, but I think you would have a hard time finding someone more influential without going back before World War II.
Here is a link to an English translation of a long essay by Pierre Cartier who makes a pretty good case (although that was not his purpose): A Country Known Only by Name | Pierre Cartier | Inference. I was astonished by how much of his work is unpublished. Thousands and thousands of pages. And if, despite instructions to the contrary, the hoard is eventually opened, material for a dozen PhDs. A truly amazing person with his own unique vision of mathematics.
The man seems to have had heterodox religious views.
Without providing detail, the New York Times tells us that “he studied Buddhism and mysticism,” and that “he gradually withdrew from society and, according to his biographer, began devoting himself obsessively to writing what he called his ‘meditations’.”
His English-language Wikipedia page mentions a manuscript, La Clef des Songes, in which “he explains how considering the source of dreams led him to conclude that God exists,” and a letter, written in 1990, in which “he described his encounters with a deity and announced that a ‘New Age’ would commence on 14 October 1996.” Following a footnote, I came across this .pdf, which provides further detail:
Another .pdf provides an English-summary of La Clef des Songes. Aged 16, he first “became aware of the existence of God as an obvious fact.” Later on, in 1957, he felt a “strong call to find himself.” Only in 1976 did he took up meditation, followed by “self-discovery via dreams.” This finally led a personal encounter with “the Dreamer,” which he identifies as God.
I imagine there’s even more of the sort among his Nachlass in Montpellier.
I don’t know— how about Serre, or even Thurston? It is hard to come up with an example of someone who revised a subject as thoroughly as Grothendieck did with algebraic geometry.