August 31st, 2024

Alexander Grothendieck: a forgotten genius– or a lonely madman?

Alexander Grothendieck, a revolutionary mathematician, withdrew from academia in 1970, lived in isolation, produced extensive writings, and his ideas are now being explored for applications in artificial intelligence.

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Alexander Grothendieck: a forgotten genius– or a lonely madman?

Alexander Grothendieck, a renowned mathematician, lived a life marked by brilliance and isolation. Born in 1928, he fled Nazi Germany and later transformed mathematics by unifying various disciplines through innovative concepts. His work, which introduced a new understanding of space, earned him a place among the greats of postwar mathematics. However, in 1970, Grothendieck abruptly left his prestigious position at the Institut des Hautes Études Scientifiques, disillusioned by its funding sources. He retreated into seclusion, living in a dilapidated home in the French Pyrenees, where he became increasingly disconnected from reality. His later years were characterized by a prolific output of writings, totaling around 70,000 pages, which some view as the ramblings of a madman, while others believe they may hold profound insights. His son, Matthieu, reflects on the burdens of his father's legacy, suggesting that Grothendieck's genius was intertwined with personal trauma and existential inquiries, particularly regarding the nature of evil. Despite his withdrawal from the mathematical community, Grothendieck's ideas are experiencing renewed interest, with potential applications in artificial intelligence being explored by companies like Huawei. The future of his extensive writings remains uncertain as they are set to be archived for scholarly research.

- Alexander Grothendieck revolutionized mathematics but withdrew from the field in 1970.

- He lived in isolation for decades, producing a vast amount of esoteric writings.

- His concepts are now being considered for applications in artificial intelligence.

- Grothendieck's legacy is complicated by personal trauma and existential questions.

- His son is navigating the implications of his father's extensive and complex body of work.

Link Icon 10 comments
By @soVeryTired - 5 months
The AI angle is weird, and a red herring. I’ll happily give 100 to 1 odds that something as abstract as topos theory isn’t useful to machine learning. As far as I know, the full weight of topos theory isn’t even needed for algebraic geometry.

The story of Grothendieck is a tragedy about a generational genius, not unlike Godel’s story. It’s deep and far reaching enough to stand on its own without AI hype making it appear more relevant.

By @Jevon23 - 5 months
Nothing forgotten about him. His work is foundational to modern algebraic geometry and there’s no mathematician who doesn’t know who he is.
By @AIorNot - 5 months
‘ And there is growing academic and corporate attention to how Grothendieckian concepts could be practically applied for technological ends. Chinese telecoms giant Huawei believes his esoteric concept of the topos could be key to building the next generation of AI, and has hired Fields medal-winner Laurent Lafforgue to explore this subject. But Grothendieck’s motivations were not worldly ones, as his former colleague Pierre Cartier understood. “Even in his mathematical milieu, he wasn’t quite a member of the family,” writes Cartier. “He pursued a kind of monologue, or rather a dialogue with mathematics and God, which to him were one and the same.”

Never heard of him before, RIP but this reads like the beginning of neal stephenson novel… interesting

By @FrankWilhoit - 5 months
Suppose he were both. Then do we need to distinguish between them? If so, would it be possible to make that distinction? If not, can we afford to need to make it? This applies to all incomprehensibly gifted persons.
By @frereubu - 5 months
This is, in my view, a better article about Grothendieck that's less sensationalist (particularly the guff about AI): https://planetofstorms.wordpress.com/2021/03/30/the-man-of-t...
By @ballooney - 5 months
I shall choose to remember him in his prime.
By @enlightenedfool - 5 months
“ 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.”

Something that caught my attention recalling Arthur Schopenhauer’s philosophy on the need for conceptual or apriori knowledge based proofs than empirical or derived in math.

By @romankolpak - 5 months
The stories of geniuses suffering from depression and other mental illnesses sure make remarkably interesting reads. It’s a pity he didn’t get psychiatric help, this could have been a boring story of an aging scientist taking care of his plants.
By @lapinot - 5 months
Always infuriating to see that people always focus on the his pre-70s (hardcore math) or post-80s period (borderline mysticism ramp up). In the 70s he was most politically active and _definitely_ not delirious in any sense of the word and in fact according to Leila Schneps this is one of the few periods of his life he described as happy, the "sunday of his life" [1]. I translated the '72 CERN talk, its baffling how relevant it is, to this day [2].

[1] french, https://www.youtube.com/watch?v=V8BbFTEyvIw

[2] https://github.com/Lapin0t/grothendieck-cern