Pet peeve: AI community defaulted to von Neumann as being the ultimate smart human and therefore the basis of all ASI/human intelligence comparison when the mathematician Alexander Grothendieck exists somehow.
Von Neumann arguably had the highest processor-type “horsepower” we know of plus his breadth of intellectual achievements is unparalleled. But imo Grothendieck is a better comparison point for ASI as his intelligence, while being strangely similar to LLMs in some dimensions, arguably more closely resembles what alien-like intelligence would be: - solving “impossible” problem through meta-language and abstractions. - able to think deeply on his own (re-discovered measure theory alone when he was a teenager, re-discovered Poincaré results when undergrad, apparently solved multiple PhD theses in parallel in less than a year) - almost solely built algebraic geometry (which in turn provided the blueprint for category theory) a domain which scares a part of the mathematics community to this day. - not your typical child prodigy— famously bad at computations: “take a prime number. 57 for instance.”
Even from the AI alignment perspective, Grothendieck is fascinating. Unaligned with “society” incentives and rewards yet having strong moral preferences, in the sense of choosing to work for a public university when he probably could have earned a higher wage elsewhere, holding hardcore communist beliefs, refusing the Fields medal in protest of Soviet Union and on top of that chosing to be stateless. Disappeared the moment he understood that despite all of that his discoveries were still fueling the industrial-military complex.
I agree Grothendieck is fascinating but I mostly just see him as interesting in different ways than von Neumann. von Neumann is often focused on because his subjects are areas that are relevant to either LessWrong’s focuses or (for the cloning posts) that the subjects he was skilled at and polymath capabilities would help with alignment.
Yes, they seem to represent two completely different types of extreme intelligence which is very interesting. I also agree that vN’s ideas are more relevant for the community.
I mean, one of them’s math built bombs and computers & directly influenced pretty much every part of applied math today, and the other one’s math built math. Not saying he wasn’t smart, but no question are bombs & computers more flashy.
Yes. Grothendieck is undoubtedly less innovative and curious all across the board.
But I should have mentioned they are not of the same generation. vN helps build the atom bomb while G grows up in a concentration camp.
vN went along a scientific golden age. I’d argue it was probably harder to have the same impact on Science in the 1960s.
I also model G as having disdain for applying mathematical ideas to “impure” subjects. Maybe because of the Manhattan project itself as well as the escalation of the Cold War.
This would be consistent with a whole school of french mathematicians deifying pure math, N. Bourbaki in general, and being generally skeptical of the potential of pure math on the improvement of society, Roger Godement being the stereotype.
My point was that Grothendieck’s mind is interesting to dissect for someone interested in a general theory of intelligence and AI alignment (and that the von Neumann metaphor becomes kinda tiring)
Pet peeve: AI community defaulted to von Neumann as being the ultimate smart human and therefore the basis of all ASI/human intelligence comparison when the mathematician Alexander Grothendieck exists somehow.
Von Neumann arguably had the highest processor-type “horsepower” we know of plus his breadth of intellectual achievements is unparalleled.
But imo Grothendieck is a better comparison point for ASI as his intelligence, while being strangely similar to LLMs in some dimensions, arguably more closely resembles what alien-like intelligence would be:
- solving “impossible” problem through meta-language and abstractions.
- able to think deeply on his own (re-discovered measure theory alone when he was a teenager, re-discovered Poincaré results when undergrad, apparently solved multiple PhD theses in parallel in less than a year)
- almost solely built algebraic geometry (which in turn provided the blueprint for category theory) a domain which scares a part of the mathematics community to this day.
- not your typical child prodigy—
famously bad at computations: “take a prime number. 57 for instance.”
Even from the AI alignment perspective, Grothendieck is fascinating.
Unaligned with “society” incentives and rewards yet having strong moral preferences, in the sense of choosing to work for a public university when he probably could have earned a higher wage elsewhere, holding hardcore communist beliefs, refusing the Fields medal in protest of Soviet Union and on top of that chosing to be stateless.
Disappeared the moment he understood that despite all of that his discoveries were still fueling the industrial-military complex.
Personally, I’d pick Feynman, but yeah, I agree that von Neumann seems an odd choice.
To me Feynman seems to fall quite on the von Neumann side of the spectrum.
I agree Grothendieck is fascinating but I mostly just see him as interesting in different ways than von Neumann. von Neumann is often focused on because his subjects are areas that are relevant to either LessWrong’s focuses or (for the cloning posts) that the subjects he was skilled at and polymath capabilities would help with alignment.
Yes, they seem to represent two completely different types of extreme intelligence which is very interesting. I also agree that vN’s ideas are more relevant for the community.
I mean, one of them’s math built bombs and computers & directly influenced pretty much every part of applied math today, and the other one’s math built math. Not saying he wasn’t smart, but no question are bombs & computers more flashy.
Yes. Grothendieck is undoubtedly less innovative and curious all across the board.
But I should have mentioned they are not of the same generation. vN helps build the atom bomb while G grows up in a concentration camp.
vN went along a scientific golden age. I’d argue it was probably harder to have the same impact on Science in the 1960s.
I also model G as having disdain for applying mathematical ideas to “impure” subjects. Maybe because of the Manhattan project itself as well as the escalation of the Cold War.
This would be consistent with a whole school of french mathematicians deifying pure math, N. Bourbaki in general, and being generally skeptical of the potential of pure math on the improvement of society, Roger Godement being the stereotype.
My point was that Grothendieck’s mind is interesting to dissect for someone interested in a general theory of intelligence and AI alignment (and that the von Neumann metaphor becomes kinda tiring)