Grothendieck: hermit mathematician

September 1, 2024 4:51 AM

'He was in mystic delirium' : was this hermit mathematician a forgotten genius whose ideas could transform AI – or a lonely madman? (Guardian)
posted by jouke (28 comments total)

Previously - a brief sentence or two on how this new link differs from or adds to the previously would nicely finish or round off this post.
posted by eviemath at 5:03 AM on September 1 [1 favorite]

This piece is built on interviews with family, goes much less into his mathematical career.

Imo, It's a portrait of untreated mental illness, probably left to get worse because of grothendieck's genius.
posted by kaibutsu at 5:31 AM on September 1 [2 favorites]

I enjoyed reading this, it's hard reading about the visit to the home that the son is overwhelmed by and only slowly able to clear out, about the family impact of the deeply damaged person costume by heterodox thoughts...

Grothendieck added tools to maths that mathematicians didn't know they needed -- but expected a purity in lived life that messy humans don't achieve.
posted by k3ninho at 5:32 AM on September 1

A Grothendieck topos 𝒯 is a category that admits a geometric embedding. 𝒯 ↪ ← lex PSh ( C ) in a presheaf category.

Discuss.
posted by sammyo at 6:02 AM on September 1 [2 favorites]

I find it impossible to romanticise dying alone after decades of ill health. The AI connection is pretty spurious.
posted by The River Ivel at 6:08 AM on September 1 [2 favorites]

cool post!

i feel like TFA's AI angle (i agree spurious) could have been balanced (by its author) by some mention of stuff like survivre et vivre that grothendieck was involved in earlier in his life. i find it sad that the "genius madman" stuff about his later life and pretty obvious mental illness is better-known than his earlier (and more, like, mainstream and in tune with what plenty of others think and do, still) ideas about ethical, political, social environmental questions inherent in scientific research. and these are still live questions in math on which there is, say, not broad agreement. i've seen grothendieck's later, more personal, struggles and fixations --- things the article connects to pain and trauma inflicted by systematic evils made possible largely by turning scientific/technical creativity toward destructive ends --- get used to dismiss people who think like he did about science's destructive or anti-human potentialities as luddites and kooks. so it's good to remember this person also as someone who seemingly thought seriously about, like, applied morality, as well as just as the person with the admirably implacably patient approach to building mathematical understanding or as the tragic casualty of mental illness.
posted by busted_crayons at 6:15 AM on September 1 [5 favorites]

Pet peeve: characterizing someone like Grothendiek as "forgotten" just because he isn't a topic of lay conversations. Every person with a need to engage with his work knows his name.
posted by ocschwar at 6:27 AM on September 1 [15 favorites]

A Grothendieck topos 𝒯 is a category that admits a geometric embedding. 𝒯 ↪ ← lex PSh ( C ) in a presheaf category.


There's a paper on Arxiv about categorical modeling of finite state machines.

In laymen's terms it means moving most of the safety checks that industrial controller software needs, from post hoc testing and onto the programming language compilers we use.

I'm sloooowly sloggng through it and the constant confrontation with my own limits in grokking higher math is beyond humbling. But if a PDF is going to put me out of a job as a QA engineer, I at least want to read it.
posted by ocschwar at 6:29 AM on September 1 [6 favorites]

Please, I beg you, read Rivka Galchen's New Yorker piece, which takes Grothendieck's life, mind, and work seriously, instead of this take-a-fancy-sounding-math-word-and-staple-"AI"-to-the-end nonsense.
posted by escabeche at 7:08 AM on September 1 [13 favorites]

Don't worry about it, ocschwar, Ada is an expensive toolset to use even if it's obviously a better way to operate as it makes it much easier to prove the design correct, and algebraic proofs of correctness exist but, again, are expensive.
posted by k3ninho at 7:14 AM on September 1 [2 favorites]

Whereof I cannot speak, thereof...
posted by y2karl at 7:36 AM on September 1 [2 favorites]

I bet those flasks contain sunbeams extracted from cucumbers. /flippant joke about truly sad case of mental illness
posted by jabah at 7:36 AM on September 1

I wholeheartedly recommend Benjamín Labatut’s When We Cease to Understand the World, which tells a number of true stories in varyingly fictionalized ways, among them Grothendieck's.
posted by the sobsister at 8:28 AM on September 1 [4 favorites]

> was this hermit mathematician a forgotten genius whose ideas could transform AI – or a lonely madman


What? Grothendieck "became the leading figure in the creation of modern algebraic geometry" to quote Wikipedia.

I'm tempted to flag this article.
posted by constraint at 8:43 AM on September 1 [4 favorites]

brief sentence or two on how this new link differs from or adds

physical geography is juxtaposed with abstract topology: “colossal folds of [wiki:] Mont Ventoux’s southern flank are mottled with April cloud shadow as cyclists skirt the mountain. In the Vaucluse département of Provence, this is the terrain...”

> second; previously
posted by HearHere at 8:58 AM on September 1 [1 favorite]

Newton's thinking followed a disturbingly similar trajectory over the course of his life, only some of which can be attributed to his exposures to mercury.

He devoted great effort to decoding 666, the 'number of the Beast' from the Book of Revelations, for example, and has been described by one commentator as "the last of the Magi."
posted by jamjam at 9:22 AM on September 1 [2 favorites]

From what little I've read of Grothendieck, both his politics and his math, I think he would have come up with a deep and sophisticated argument rejecting the simplistic reduction of his life to 'mental illness', a Western category used to atomize individuals. Someone who came up with category theory ("What is the meaning of =") probably had a very different philosophical outlook on human relations, kind of like if you were transported thousands of years back to a feudal society and everyone was still thinking using limited intellectual concepts of the time.
posted by polymodus at 10:08 AM on September 1 [3 favorites]

...Someone who came up with category theory ("What is the meaning of =") probably had a very different philosophical outlook on human relations

hmmm. much as i think that's a useful critique of the "mental illness" label, the authors of category theory and everyone who's contributed to/benefited from that viewpoint since were/are all over the place politically and philosophically so one should probably be careful with trying to match mathematical outlooks to outlooks on human relations (random grim rabbit hole: the queasy history of samuel eilenberg's art collecting).

i don't generally find mathematicians to be any more sophisticated or interesting in their philosophical outlooks than anyone else, although there are many exceptions --- the point being that there are many exceptions in most groups to this general fact about people. my personal experience is that mathematics encourages some habits of thought that might tend to produce certain outlooks outside of mathematics, but that these aren't that special to maths, or aren't systematically that useful outside of maths, and in any case are easily dominated by other factors.

so i'd tend to regard grothendieck's principled and good political and ethical takes as being the product of factors largely independent of his mathematical contributions. and his later disillusionment with institutional science may well reflect an awareness of that disconnect and a sense of betrayal, i dunno.

it's certainly a recurrent bummer to see prominent scientists whom one knows to be capable of great sophistication and depth of thinking in their specialties, and sometimes even capable of great care (lol and sometimes not) in the surrounding communities, embracing terrible evil politics on the basis of embarrassingly shoddy or self-serving reasoning.
posted by busted_crayons at 12:37 PM on September 1 [5 favorites]

From what little I've read of Grothendieck, both his politics and his math, I think he would have come up with a deep and sophisticated argument rejecting the simplistic reduction of his life to 'mental illness',

I would have to agree. Based on the rough outline of his life, I don’t think he was ever “normal” mentally, behaving in ways people seemed to find odd but acceptable. If, in his later life, his behavior became more extreme, it seems to neither have caused him distress or others harm, which is a reasonable benchmark for “illness.”

As for Newton, based on his corpus, he was a speculative theologian and alchemist who dabbled in mathematics and physics.
posted by GenjiandProust at 12:44 PM on September 1 [1 favorite]

As he died in 1982, he most likely never heard of the man but if he had, oh man, would Philip K Dick have gone to town on Grothendieck.
posted by y2karl at 12:50 PM on September 1 [3 favorites]

seems to neither have caused him distress or others harm, which is a reasonable benchmark for “illness.”

Curiously, Grothendieck, per the article, was pretty unhappy with how he was treated by his parents.

'In 1979, he spent a year dwelling intensely on his parents’ letters, a reflection that stripped away any lingering romanticism about them. “The myth of their great love fell flat for Shurik – it was a pure illusion,” says Johanna Grothendieck, who bears her grandmother’s name. “And he was able to decrypt all the traumatic elements of his childhood. He realised he had been quite simply abandoned by his own mother.”'

And he seems to have been at best an absent father, in turn, leaving his son with a real mess to clean up after his passing. So, on his own terms, I don't think 'no harm, no foul' applies here. He failed at human relationships; we are social animals, and failing at relationships so thoroughly does bad things to a person.

Also, I'll posit that once someone starts making specific predictions about the date of the rapture, they've lost the thread... The combinatorics of the second coming are pretty far from the generality of category theory.
posted by kaibutsu at 1:26 PM on September 1 [1 favorite]

hmmm. much as i think that's a useful critique of the "mental illness" label, the authors of category theory and everyone who's contributed to/benefited from that viewpoint since were/are all over the place politically and philosophically so one should probably be careful with trying to match mathematical outlooks to outlooks on human relations .

Yup.

Some counter examples :

Andre Joyal: came up with a notation system for category theory he calls wiring diagrams, which he claims that it make CT accessible to middle schoolers.

Bartosz Millevski, Eugenia Cheng, Spivak, Simon Peyton Jones: all of them the opposite of Grothendiek's hermit tendencies. All of them strive to be in this world if not of it.
posted by ocschwar at 2:52 PM on September 1 [2 favorites]

Speaking of Eugenia Chang, her book Is Math Real, presents an extremely humanist look at math, with examples drawn from current politics, personal experience, and more. Math books can be the driest books ever penned, but her book reads as one written by a human being with all their experiences upfront, both good and bad, and the math presented is thus much more relatable in an almost flesh and blood sort of way. She teaches math to artists at the Art Institute of Chicago. I highly recommend this book, even to non mathematically interested people.
posted by njohnson23 at 3:12 PM on September 1 [3 favorites]

To be clear, Grothendieck didn't invent category theory (though he helped make it indispensable to lots of mathematicians who didn't think they had a use for it.)
posted by escabeche at 5:36 PM on September 1 [3 favorites]

I really enjoyed this article as a Sunday morning read. I thought it was an empathetic view through the eyes of his children of their brilliant father who retreated from the world and them. Very moving.

I didn't realise from the article that I've encountered math that is adjacent to his research.
At university in categorical logic and categorical grammar.
And in my work in the category theoretical foundations of functional programming.
posted by jouke at 3:22 AM on September 2 [1 favorite]

Grothendieck’s capacity for abstract thought is legendary: he rarely made use of specific equations to grasp at mathematical truths, instead intuiting the broader conceptual structure around them to make them surrender their solutions all at once. He compared the two approaches to using a hammer to crack a walnut, versus soaking it patiently in water until it opens naturally.

This is truly a wonderful metaphor — but I suspect it became far more than just a metaphor for Grothendieck:

Matthieu leads me into the huge, broken-down barn behind the house. Heaped on the bare-earth floor is a mound of glass flasks encased in wicker baskets: inside them are what remains of the mathematician’s plant infusions, requiring thousands of litres of alcohol. Far removed from conventional mathematics, Grothendieck’s final studies were fixated on the problem of why evil exists in the world. His last recorded writing was a notebook logging the names of the deportees in his father’s convoy in August 1942. Matthieu believes his father’s plant distillations were linked with this attempt to explain the workings of evil: a form of alchemy through which he was attempting to isolate different species’ properties of resilience to adversity and aggression. “It’s hard to understand,” says Matthieu. “All I know is that they weren’t for drinking.”

It is hard to understand, but it looks to me as if Grothendieck thought he could extract metaphysical essences from real plants with real solvents. Perhaps we could generalize to a tentative conclusion that somewhere along the line he lost the ability to distinguish between how the very productive methods he had always used to 'solve' problems differed from the ways reality itself constructs itself.

Once again, maybe not so different from Newton:

Newton's writings suggest that one of the main goals of his alchemy may have been the discovery of the philosopher's stone (a material believed to turn base metals into gold), and perhaps to a lesser extent, the discovery of the highly coveted Elixir of Life.[6] Newton reportedly believed that a Diana's Tree, an alchemical demonstration producing a dendritic "growth" of silver from solution, was evidence that metals "possessed a sort of life."

posted by jamjam at 12:00 PM on September 2

I wholeheartedly recommend Benjamín Labatut’s When We Cease to Understand the World, which tells a number of true stories in varyingly fictionalized ways

I also wholeheartedly recommend this book, which is fantastic, but note that ultimately the book is a work of fiction weaved in with fact and characters that have some basis in history. Many of the elements in the stories are purely invented, including some of the more fantastical ones in the Grothendieck chapter.
posted by gwint at 5:12 PM on September 2

Eugenia Cheng is an example that proves my point, she is an Asian American on record for explaining intersectional theory using category lattices. That video is online.

I also reject the superficial notion that Grothendieck's self abstention was somehow less part of being part of this world than any other academic mathematician who is more conventionally successful and popular. That's the sort of conformist argument neoliberals use to say to marginalize the different. It's also literally false, you see certain mathematicians actually taking the time to read Grothendieck's late writings, for better or worse. How is that not participation from beyond the grave?

I only realized after writing my comment, I also take issue with the very presumption that it is okay to mentally diagnose Grothendieck, or any one else, at all. This is not John Nash whose schizophrenia is considered a documented reality. We do not armchair diagnose mental illness for precisely the reason of stigma and social oppression, and the insight that has been missing in this conversation is that armchair diagnosis fundamentally includes the meta-diagnosis of whether someone has a mental illness. This is certainly not the first time I have seen, in person, an academic who ought to know better saying that their peer left academia because of mental health issues, tsk tsk. Sociopolitically it reifies the atomization of injustice and psychologically it is uncalled for.
posted by polymodus at 11:11 AM on September 7