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it does not in any way break the mystique of mathematics for me, though that mystique continues to attach to proofs that are in some way beautiful or elegant, w

by zem 2mo ago

it does not in any way break the mystique of mathematics for me, though that mystique continues to attach to proofs that are in some way beautiful or elegant, whether produced by humans or machines. as for software engineering, I've definitely used claude to help with both complex problems that I could have worked through myself but with greater expenditure of time and effort, and with problems that I would not have been able to do without spending a lot of time learning my way around a whole new domain, but in both cases what I am most keenly aware of is that I am benefitting from some human (or many humans) having solved this problem before.

czgov 2mo ago
I am ABD in mathematics. That was a long time ago. I taught math for many years at a community college. My amateurish but knowledgeable perspective is that these developments shatter the mystique for me. What AI is showing is that mathematics is mostly just pattern searching and AI can do this far better, faster, and with a much wider base than humans can. When I was working on my thesis problem I realized that I worked much less than my fellow students. I was an average student in my program but even for the best students they had to spend a lot of time thinking about stuff. They put in a lot of effort. Is the difference between me and Tao mostly effort and that he has a much better memory of mathematical facts than me?
- gottheUIblues 2mo ago
  This is only the "problem solving" side of mathematics. Completely missing the theory builders who have completely reshaped the world of mathematics (and far beyond). AI is a long way from matching original thinkers of the calibre of Euclid, Al-Khwarizmi, Newton, Leibniz, Euler, Galois, Riemann, Cantor, Hilbert, and Grothendieck. Or Turing, Gödel and Von Neumann?
  - czgov 2mo ago
    According to Tao and Gowers there are AI results that did proofs in clever ways. That’s one way new theories come about.
- zem 2mo ago
  I lean more towards the "proofs from the book" mindset - if there's a really beautiful proof of some theorem out there I would be happy to see it no matter whether it was discovered by a human or a computer, and conversely if a computer has churned through a search space and generated a clunky proof in 100000 lines of lean code that just means that people trying to find a nice proof can do so with the assurance that the theorem is true. note that mathematicians didn't give up on trying to find a better proof of the four colour theorem once a clunky computer assisted proof showed the theorem was true.
  - czgov 2mo ago
    The question is, will universities continue to fund graduate programs to the extent they currently do so that people can find elegant proofs of AI derived theorems? I’m skeptical. A lot of good mathematicians tried to prove or disprove the Jacobian Conjecture and AI did easily. The value added by human mathematicians seems to be low return on the investment.
    - zem 2mo ago
      that is a genuine concern, yeah :( but at least for me it's unrelated to the mystique of mathematics itself.

by zem 2mo ago

czgov 2mo ago

I am ABD in mathematics. That was a long time ago. I taught math for many years at a community college. My amateurish but knowledgeable perspective is that these developments shatter the mystique for me. What AI is showing is that mathematics is mostly just pattern searching and AI can do this far better, faster, and with a much wider base than humans can. When I was working on my thesis problem I realized that I worked much less than my fellow students. I was an average student in my program but even for the best students they had to spend a lot of time thinking about stuff. They put in a lot of effort. Is the difference between me and Tao mostly effort and that he has a much better memory of mathematical facts than me?

gottheUIblues 2mo ago
This is only the "problem solving" side of mathematics. Completely missing the theory builders who have completely reshaped the world of mathematics (and far beyond). AI is a long way from matching original thinkers of the calibre of Euclid, Al-Khwarizmi, Newton, Leibniz, Euler, Galois, Riemann, Cantor, Hilbert, and Grothendieck. Or Turing, Gödel and Von Neumann?
- czgov 2mo ago
  According to Tao and Gowers there are AI results that did proofs in clever ways. That’s one way new theories come about.
zem 2mo ago
I lean more towards the "proofs from the book" mindset - if there's a really beautiful proof of some theorem out there I would be happy to see it no matter whether it was discovered by a human or a computer, and conversely if a computer has churned through a search space and generated a clunky proof in 100000 lines of lean code that just means that people trying to find a nice proof can do so with the assurance that the theorem is true. note that mathematicians didn't give up on trying to find a better proof of the four colour theorem once a clunky computer assisted proof showed the theorem was true.
- czgov 2mo ago
  The question is, will universities continue to fund graduate programs to the extent they currently do so that people can find elegant proofs of AI derived theorems? I’m skeptical. A lot of good mathematicians tried to prove or disprove the Jacobian Conjecture and AI did easily. The value added by human mathematicians seems to be low return on the investment.
  - zem 2mo ago
    that is a genuine concern, yeah :( but at least for me it's unrelated to the mystique of mathematics itself.