Alexander Grothendieck
41–50 of 57 posts
Re: Alexander Grothendieck
#42Earlier quoted context omitted.
Classic application of abstract math in something sexy at the time. I once saw a paper describing a trading strategy using stochastic calculus. Turns out it boiled down to buying when price went under some indicator variable, selling when above another.
Stochastic calculus is the only available tool for proving things about continuous-time stochastic processes. There aren't any alternatives, save guessing at criteria and backtesting them.
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Re: Alexander Grothendieck
#43Earlier quoted context omitted.
Classic application of abstract math in something sexy at the time. I once saw a paper describing a trading strategy using stochastic calculus. Turns out it boiled down to buying when price went under some indicator variable, selling when above another.
Stochastic calculus is the only available tool for proving things about continuous-time stochastic processes. There aren't any alternatives, save guessing at criteria and backtesting them.
ugh
Re: Alexander Grothendieck
#44‘ 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…
There is nothing esoteric about topos theory, it is a formally defined concept: https://en.wikipedia.org/wiki/Topos Thought it was important to state this, as Grothendieck also wrote rather esoteric texts, Récoltes et Semailles as well as La Clé des Songes, which haven't been translated or even published.
Récoltes et Semailles is translated, e.g. the mathematical stuff:
Re: Alexander Grothendieck
#45Always 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
Re: Alexander Grothendieck
#46Earlier quoted context omitted.
The root cause for his departure from mathematics was his categorical refusal to let the military-industrial complex invest in his research at Bures-sur-Yvette. Source: https://www.jp-petit.org/Nouvelles/Grothendieck.htm - I know the story. He was a man viscerally opposed to militarism. He once said "he'd rather be shot than wear a uniform." One day a letter arrived at IHES in Bures, where the army's scientific servi…
This text is a short story ("nouvelle" in French).
That's correct! The text is presented on the source web page as a story, and it does not claim to be factual.
Alexander Grothendieck was indeed awarded the Crafoord Prize, which he rejected. (It was never worth 40 mil francs as the translation above claims. The original French put it at "40 briques" = 400,000, currency not specified, which is much closer to the more accurate 800K SEK ~ 800K FFr that he would have received. The fact that the full amount, 1,6M SEK, would be split between him and Pierre Deligne, whom Grothendieck had denounced, might have contributed to his decision.) Grothendieck's rejection letter was remarkably lucid and articulate: https://www.fermentmagazine.org/quest88.
Re: Alexander Grothendieck
#47Earlier quoted context omitted.
this paper is not good: it's easy to describe things in a categorical language (which this paper does), but not as easy to draw insights from that framework (which this paper does not do)
It is rarely within reach to draw new insights from applied category theory, in particular because of the Yoneda lemma and the greater familiarity of sets and functions, and also because as algebraic objects categories have very few properties.
Bare categories do not give much insight in pure mathematics either, it's just a common language; interesting things are categories with lots of extra structure like toposes, derived categories, infinity-categories, and so on.
Re: Alexander Grothendieck
#48The 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 app…
> As far as I know, the full weight of topos theory isn’t even needed for algebraic geometry
The original topos theory developed by Grothendieck and his collaborators in the 60s is quite pragmatic and served to define cohomology theories for varieties over finite fields. Later other people, coming from mathematical logic, distilled "elementary" axioms from there and developed another kind of topos theory that is pretty much divorced from algebraic geometry.
Re: Alexander Grothendieck
#49Earlier quoted context omitted.
this paper is not good: it's easy to describe things in a categorical language (which this paper does), but not as easy to draw insights from that framework (which this paper does not do)
Classic application of abstract math in something sexy at the time. I once saw a paper describing a trading strategy using stochastic calculus. Turns out it boiled down to buying when price went under some indicator variable, selling when above another.
Huge difference between stochastic (processes, ODEs, PDEs, etc) and category theory. One makes money every day and the other is only good for writing papers.
Re: Alexander Grothendieck
#50Earlier quoted context omitted.
agree, forgotten genius AND lonely madman, there is no contradiction.. In mathematics, and science, these people are not uncommon.
The root cause for his departure from mathematics was his categorical refusal to let the military-industrial complex invest in his research at Bures-sur-Yvette. Source: https://www.jp-petit.org/Nouvelles/Grothendieck.htm - I know the story. He was a man viscerally opposed to militarism. He once said "he'd rather be shot than wear a uniform." One day a letter arrived at IHES in Bures, where the army's scientific servi…
thank you for the great story
reminds me of another great mathematician
harvard Phd in math
youngest ever professor, UC berkeley
decided to leave it all behind and live innawoods like this man
oh and he also mailed bombs to people involved with tech (this man's equivalent to the military)
and he would have gotten away with it too if it weren't for that meddling sister in law! I guess he wanted to have his cake and eat it too.