Who is Alexander Grothendieck?

August 17, 2008 5:49 AM

Who is Alexander Grothendieck? [PDF] This lecture is concerned not with Grothendieck's mathematics but with his very unusual life on the fringes of human society. In particular, there is, on the one hand, the question of why at the age of forty-two Grothendieck first of all resigned his professorship at the Institut des Hautes Etudes Scientifiques (IHES); then withdrew from mathematics completely; and finally broke off all connections to his colleagues, students, acquaintances, friends, as well as his own family, to live as a hermit in an unknown place. On the other hand, one would like to know what has occupied this restless and creative spirit since his withdrawal from mathematics.
posted by Wolfdog (31 comments total)

People might want to know that the linked PDF is 11 MB.
posted by jouke at 6:42 AM on August 17, 2008

The most interesting part of the article for me is the inclusion of two photos of Grothendieck I've never seen before, from 1980 and 1988. For years, there have been just a dozen or so extant photos of him, and none after his retreat.
posted by gleuschk at 6:47 AM on August 17, 2008

Much shorter PDF: Grothendieck's letter declaring his refusal of the Crafoord Prize. (576kb)
posted by Smart Dalek at 6:48 AM on August 17, 2008

Here's a companion piece to the linked Notices article (40K PDF), about Grothendieck's 80th birthday coinciding with the 50th anniversary of IHES. Author Allyn Jackson refers to an "open letter" I'd desperately like to read:

Six months to the day before the start of the IHES anniversary celebration, Grothendieck wrote to the institute with a request for books. The IHES sent him the books as quickly as it could. But the exchange of letters between Grothendieck and the IHES administration culminated in his writing a furious “open letter” recounting his view of the exchange, which he took as deeply insulting towards him. He requested that copies of the open letter be sent to all members of the IHES Scientific Council and explicitly states that this letter is public (though he also says he will make no efforts on his own to publicize it). Having seen the open letter, I can say that it conveys an extreme outrage that indicates how difficult it would be to conduct reasonable communication with him.

posted by gleuschk at 6:54 AM on August 17, 2008

From the article: For hundreds of pages Grothendieck describes and discusses the lives and works of a total of eighteen mutants. It becomes clear that he sees a personal connection between these mutants and himself; for example, he occasionally calls himself their heir, or he calls them his elders. We now give the list of these mutants, as he assembled it himself. No doubt their selection is rather arbitrary. A central (and not very original) theme in Grothendieck’s thinking is the spiritual decline of humanity, necessarily followed by an apocalypse and soon thereafter by the “new age”, the age of freedom and self-determination and of life in harmony with one’s own “soul”. The mutants are people who announce and anticipate this new age. This is the criterion by which he selected them.
On this list of mutants like him are Darwin, Riemann, Whitman, Kropotkine, Freud, Steiner, Gandhi, Teilhard de Chardin and Krishnamurti.
posted by jouke at 6:55 AM on August 17, 2008

Fascinating article, Wolfdog, thanks. His early family history is amazing, one-armed Russian anarchist dad and all. I think it's very odd, though, that in an article about Grothendieck's rejection of mathematics, the author dances so delicately around the possibility that the mathematician became mentally ill:

In trying to understand how the “great turning point” happened, one has to take into account Grothendieck’s mental state, which already by then must have been unstable and perhaps sometimes out of control. This would not have been apparent in his interactions with his colleagues and students, even though Cartier hints at it. But in closer interaction, a deep personality disorder is clearly visible. This is not the place to go further into this subject.

Actually, an article about why he disappeared and what he's done since he left mathematics seems the *perfect* place to go further into this subject. The hesitance to even mention the words "mental illness" approaches being bizarre; I mean, the man had visions of angels, wrote thousand-page-long denunciations of his former friends and colleagues, tried to outdo Christ in fasting, came up with a theory of mutants in history that includes himself...surely we can at least drop the coyness in discussing the possibility of mental illness? And how can you mention that your subject wrote a "song" called In Praise of Incest and not explain what that piece was about?

Still, fascinating stuff. Thanks again.
posted by mediareport at 7:21 AM on August 17, 2008 [7 favorites]

Quasi-related linkdump for any who are intrigued:

• Allyn Jackson's excellent two-part biographical article, "Comme Appelé du Néant—As If Summoned from the Void: The Life of Alexandre Grothendieck": Part I (1.25MB PDF), Part II (600KB PDF)
• Colin McLarty's great lecture on Grothendieck's philosophy of doing mathematics ("1. Find a natural world for your problem; 2. Express your problem cohomologically; 3. The cohomology of that world solves your problem, like the bursting of a ripe avocado")
• a short letter about the Riemann-Roch Theorem featuring Devils (anyone feel like translating?)
• a 1987 letter from Grothendieck to Piotr Blass about publishing the prenotes to EGA V ("I am not going even to glance through the manuscript, as I have completely given up mathematics and mathematical involvements.")
• A Mad Day's Work: From Grothendieck to Connes and Kontsevich the evolution of the concepts of space and symmetry (300K PDF)
• The origins of Alexander Grothendieck's `Pursuing Stacks'

posted by gleuschk at 7:27 AM on August 17, 2008 [4 favorites]

From his letter rejecting the Crafoord prize and its cash award:

My salary as a professor, even my pension beginning next October, is sufficient for my own material needs; hence I have no need for money.
posted by three blind mice at 7:27 AM on August 17, 2008

The thought of Grothendieck living as a sheepherder in the french alps makes me happy, just like that island near Canada where the wild horses live.
posted by metastability at 8:48 AM on August 17, 2008 [2 favorites]

All I have to say is: anyone who works that much with sheaves has to be fucking insane.
posted by TypographicalError at 9:48 AM on August 17, 2008 [1 favorite]

surely we can at least drop the coyness in discussing the possibility of mental illness? And how can you mention that your subject wrote a "song" called In Praise of Incest and not explain what that piece was about?

but you see the AMS notices is fundamentally an industry publication, the meat of the newspaper is periodic reports on salaries of mathematicians and the amount of money coming in from the federal government.

a big part of the american mathematics industry is "algebraic geometry" and a great many of the ideas in algebraic geometry and perhaps more importantly it's worldview and problems pass through grothendieck and his collaborators/students.

if you say he is a raving wack-job, what does that say about his ideas?

All I have to say is: anyone who works that much with sheaves has to be fucking insane.

the history of sheaves is interesting. they are largely the child of the french mathematician Jean Leray and were developed while he was in an Austrian prison camp during WWII. The folk-history says he wanted to make sure he worked on something that had no practical application whatsoever. though in the end, sheaves are a fairly natural construction...
posted by geos at 10:14 AM on August 17, 2008

if you say he is a raving wack-job, what does that say about his ideas?

His mathematical ideas? They stand on their own logic, don't they?

And no one's calling him a "raving wack-job;" it just seems obvious that one possible explanation for his behavior late in life is the development of some sort of mental illness. Shying away from that possibility seems silly, even in an industry publication that owes a lot to his thinking. It's as if the author believes mental illness is so stigmatizing it mustn't be discussed in polite company - a strangely archaic view.
posted by mediareport at 10:21 AM on August 17, 2008 [2 favorites]

http://en.wikipedia.org/wiki/Grothendieck
posted by Brian B. at 10:38 AM on August 17, 2008

just seems obvious that one possible explanation for his behavior late in life is the development of some sort of mental illness.

Maybe his patience for other people's stupidity simply ran out. When you are that smart, it must seem as though everyone else is mentally ill.
posted by three blind mice at 10:47 AM on August 17, 2008

though in the end, sheaves are a fairly natural construction...

What? No.

Sheaf theory did not exist until 50 years ago. Hardly any mathematical ideas invented in the 20th century are what I'd call "natural".
posted by TypographicalError at 10:48 AM on August 17, 2008

Maybe his patience for other people's stupidity simply ran out. When you are that smart, it must seem as though everyone else is mentally ill.

Judging from his radical politics (see wiki article) he may have also come to believe that everything he does just ends up helping the wrong side of the fence.
posted by Brian B. at 11:07 AM on August 17, 2008

Funny thing is, I think the 'natural-ness' of the ideas have entirely to do with exposure. I remember when La Grange's theorem didn't seem natural to me; now it's the most natural thing in the world. I don't think I really notcied this phenomenon, though, until cohomology and Poincare duality started seeming 'natural.' Practice with the tools makes them easier to use and more familiar; there's also something to be said just for time and exposure, allowing the notions to sink into the primitive brain. There's also an issue of notation, and our ability to write down what we're trying to do. The really really classical example is division; it was really hard until someone came up with the smart idea of ditching the roman numeral system, and now that we use base 10 and do it every day, it's the most natural thing in the world. (so long as you don't think too hard about it, anyway...)
posted by kaibutsu at 11:07 AM on August 17, 2008

huh. So Grothendieck is a kind of Pynchon-Salinger of math? So interesting to learn about. Thanks for the education Wolfdog. There is a lot that is likable about this man/scientist. Wish I had a brain that understood the math. I love the little I know of math and feel so cut off not being able to understand it, the language of it, only stand at the periphery in awe.

He gave lectures on category theory in the forests surrounding Hanoi while the city was being bombed, to protest against the Vietnam War

wow. Pretty amazing that.

People can be mentally, intellectually, artistically, scientifically brilliant/talented/advanced and also be emotionally, socially, practically, financially unbalanced at the same time. I don't think one necessarily invalidates the other. Sometimes scientists can also be mentally ill, while still being brilliant and innovative, at the same time.

This imbalance is fairly common among genius/advanced thinker types.

Related in the mathematicians struggling with emotional health subject.

A site dedicated to him with some good photographs and more, Grothendieck Circle. Love this classic counterculture photograph from those days.
posted by nickyskye at 11:34 AM on August 17, 2008 [1 favorite]

Grothendieck Circle? Seems to me that Grothendieck Group would be a bit more fitting.
posted by kaibutsu at 11:48 AM on August 17, 2008

The really really classical example is division; it was really hard until someone came up with the smart idea of ditching the roman numeral system, and now that we use base 10 and do it every day, it's the most natural thing in the world. (so long as you don't think too hard about it, anyway...)

X/V = still equals II no matter how you write the numbers.

Moreover, there is nothing "natural" about base 10. Duodecimal, or base 12, was commonly used in Northern Europe, and particularly Scandinavia for centuries. That's why Germanic languages have a special word for 11 and 12.
posted by three blind mice at 11:58 AM on August 17, 2008

Other scientists have also had regrets about the part their genius played in the world.

Robert Oppenheimer, though ecstatic about the success of the project, quoted a remembered fragment from the Bhagavad Gita. "I am become Death," he said, "the destroyer of worlds." Ken Bainbridge, the test director, told Oppenheimer, "Now we're all sons of bitches."

But it seems like Grothendieck took action on feeling his regret by opting out of the official scientific community.
posted by nickyskye at 12:20 PM on August 17, 2008

X/V = still equals II no matter how you write the numbers.

I think the point is that there is a fairly straightforward division algorithm in base 10. No similarly straightforward algorithm is known for numbers represented in Roman numerals. (If I'm wrong, I'd love to know of one!)

Also, base 10 vs. base 12 is a red herring. When you represent a number in base X (where X is a positive integer), you can generalize the algorithm you learned in grade school for dividing two numbers to that base.

Kaibutsu's point stands: certain representations of the same thing can simplify other things, like computation.
posted by A dead Quaker at 12:41 PM on August 17, 2008 [1 favorite]

I wonder what happened to his family. Did he take them with him when he disappeared? As "cool" as the mad mathematician trope may be, I wonder what life is/was like for his kids. It could have been great to have a bohemian free-thinking dad who went to farm in the south of France, or it could have been crappy to have to deal with a crazy person no matter how genius he is.
posted by bluefly at 2:59 PM on August 17, 2008

Thanks, Quaker, for making explicit the point I failed to explain.
Also, I wasn't saying base 10 was natural, but rather the division algorithm. (Though I guess I could go out on to uber-subjective limb and say that base 10 is natural - because we use it and are familiar with it.)
posted by kaibutsu at 4:19 PM on August 17, 2008

it could have been crappy to have to deal with a crazy person no matter how genius he is.
In a lot of ways, the smarter the crazy person, the crappier it is to have to deal with them.
posted by aeschenkarnos at 4:31 PM on August 17, 2008

Also, I wasn't saying base 10 was natural, but rather the division algorithm.
Similar insights have come from the extensive use of base 2 in computer programming over the last few decades. I wonder how many more could be discovered by people taught from childhood to naturally think in base 2 as well as in base 10.
posted by aeschenkarnos at 4:35 PM on August 17, 2008

I found that academia was particularly cut throat & nasty in France. Not saying he wasn't bonkers, but even crazy people often need some environmental stimulus. I suppose such competitive behavior is normal when people have less money to fight over.

As an aside, French academics often slight the Ecole Normale behind the scenes, saying ENS kids get all the jobs but aren't any better than others. I'm suppose this may hold true if your working in some broad field like number theory. But I gather the real reason the French process favors ENS people is that French PhDs are only 3 years, meaning your not acquiring breadth then either. Btw, a student could always rectify this situation by doing their PhD in the U.S.
posted by jeffburdges at 9:17 PM on August 17, 2008

Mental illness, recall, is defined by the rules of the society in whose context the illness manifests. Paranoia, for example: what could that word mean, in relation to a Jew who spent his childhood in Berlin and Hamburg in the late 1930's?

This man is clearly intelligent, ethical, articulate, polite, thoughtful, inner-directed, and courageous enough to pursue his own definition of success. Furthermore, he has earned the accolades of his peers, not once but on numerous occasions.

God forbid I should ever find myself in a society that considers a man like him mentally ill.
posted by ikkyu2 at 10:37 PM on August 17, 2008

About the lack of mention of mental illness, there was this:

"There can be no doubt that, at least since the
end of the 1980s, his life has been dominated for
long periods by delusions and that he would have
needed urgent medical and psychiatric help."
posted by noether at 1:57 AM on August 18, 2008

David Ruelle, a physicist, writes in The Mathematician's Brain":

Understandably, some people would like to blame Grothendieck’s exclusion entirely on Grothendieck himself: he went crazy and left mathematics.

But this does not fit with the known facts and their chronology. Something shameful has taken place. And the disposal of Grothendieck will remain a disgrace in the history of twentieth-century mathematics.

God keep Alexander Grothendieck.
posted by fold_and_mutilate at 8:49 PM on August 19, 2008

But this does not fit with the known facts and their chronology. Something shameful has taken place. And the disposal of Grothendieck will remain a disgrace in the history of twentieth-century mathematics.

What are the known facts then? What shameful thing has taken place?
posted by Brian B. at 8:59 PM on August 19, 2008