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We asked Elliot Glazer how people should evaluate future AI math breakthroughs. “The buzz phrase you’re gonna be seeing a lot is the difference between problem-solving and theory building.” “You solved the problem using a bunch of techniques, advanced techniques, but very much previously techniques in the human literature....

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Terence Tao thinks AI is already very good at using existing, well-understood math techniques to solve problems. An important question is how many open problems in math could be solved this way, without developing any new ideas. An extreme case of a proof like this is the four-color theorem, which was proved by checking a thousand examples one-by-one. If there are lots of problems that are vulnerable to just mechanically applying existing techniques, AI could start to produce new math results incredibly rapidly. But these proofs might not help advance our civilization’s knowledge the way math has in the past.

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