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Alexander Grothendieck

theguardian.com

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Re: Alexander Grothendieck

#31

Post by catgary »

cc-color wrote: post #20
bubblyworld wrote: post #17

Earlier quoted context omitted.

I was sure this was going to be a case of spraying jargon at investors, but they've actually produced an interesting paper in this direction (in collaboration with some DeepMind people): https://arxiv.org/abs/2402.15332

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)

I was definitely on a group chat of ML/category theory people roasting this paper when it came out, I’m sure I wasn’t the only one.

Re: Alexander Grothendieck

#32

Post by catgary »

gremgoth wrote: post #16
soVeryTired wrote: post #15

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 app…

The folks at Symbolica are also applying topos theory, category theory, etc to AI, backed by serious folks such as Khosla and Wolfram. https://finance.yahoo.com/news/vinod-khosla-betting-former-t...

“A new kind of deep learning.”

Edit: I need to think more before I comment, “A new kind of data science” was right there.

Re: Alexander Grothendieck

#33

Post by FrankWilhoit »

ValentinA23 wrote: post #19
effed3 wrote: post #14

Earlier 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…

The background of this particular case is interesting, but the larger point is that what we call "genius" is a matter of priorities. From some angle, every gifted person appears mad.

Re: Alexander Grothendieck

#34

Post by fjdjshsh »

gremgoth wrote: post #16
soVeryTired wrote: post #15

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 app…

The folks at Symbolica are also applying topos theory, category theory, etc to AI, backed by serious folks such as Khosla and Wolfram. https://finance.yahoo.com/news/vinod-khosla-betting-former-t...

Wolfram is serious about his software, but, to my mind, has been closer to a crackpot scientist than a real researcher the last few decades. Him backing something up diminishes my subjective probability that this is something "serious"

Re: Alexander Grothendieck

#35

Post by karmakurtisaani »

whatshisface wrote: post #27
karmakurtisaani wrote: post #24

Earlier 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.

Yes, for sure useful for the appropriate mathematics. My point is, the trading strategy was a simple heuristic wrapped into overly complicated definitions and proofs. The complicated mathematics added exactly nothing to the application.

Re: Alexander Grothendieck

#36

Post by karmakurtisaani »

webdoodle wrote: post #29
ValentinA23 wrote: post #19

Earlier 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…

Fantastic! In this money driven world, he had the courage to stand up for what he believed in. Also, I seriously doubt he was considered crazy, that was the war time propaganda trying to break him down and make an example of him, so that others wouldn't stand up. It's the same thing we see today with the coercion and censorship that plaques social and old school media.

I feel like it was more like his experiences from WW2 formed a very rigid world view about militaries. Arguing for pacificism is difficult as the Ukraine war rages on.

Re: Alexander Grothendieck

#37

Post by catgary »

karmakurtisaani wrote: post #35
whatshisface wrote: post #27

Earlier quoted context omitted.

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.

Yes, for sure useful for the appropriate mathematics. My point is, the trading strategy was a simple heuristic wrapped into overly complicated definitions and proofs. The complicated mathematics added exactly nothing to the application.

I think the point was they (probably) used the abstract math to prove some desirable properties about the trading strategy?

Re: Alexander Grothendieck

#39

Post by romankolpak »

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.

Re: Alexander Grothendieck

#40

Post by karmakurtisaani »

catgary wrote: post #37
karmakurtisaani wrote: post #35

Earlier quoted context omitted.

Yes, for sure useful for the appropriate mathematics. My point is, the trading strategy was a simple heuristic wrapped into overly complicated definitions and proofs. The complicated mathematics added exactly nothing to the application.

I think the point was they (probably) used the abstract math to prove some desirable properties about the trading strategy?

Yes, it was something like that. But "desirable" here means something very different for mathematicians and traders actually applying the strategy (I.e., they don't care at all, and neither does anyone else working in finance).
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