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.<p>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.
‘ 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.”<p>Never heard of him before, RIP but this reads like the beginning of neal stephenson novel… interesting
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.
This is, in my view, a better article about Grothendieck that's less sensationalist (particularly the guff about AI): <a href="https://planetofstorms.wordpress.com/2021/03/30/the-man-of-the-circular-ruins/" rel="nofollow">https://planetofstorms.wordpress.com/2021/03/30/the-man-of-t...</a>
“ 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.”<p>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.
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.
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].<p>[1] french, <a href="https://www.youtube.com/watch?v=V8BbFTEyvIw" rel="nofollow">https://www.youtube.com/watch?v=V8BbFTEyvIw</a><p>[2] <a href="https://github.com/Lapin0t/grothendieck-cern">https://github.com/Lapin0t/grothendieck-cern</a>