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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 t
by czgov 1mo 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 1mo agoThis 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 1mo agoAccording to Tao and Gowers there are AI results that did proofs in clever ways. That’s one way new theories come about.
- zem 1mo agoI 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 1mo agoThe 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 1mo agothat is a genuine concern, yeah :( but at least for me it's unrelated to the mystique of mathematics itself.