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Terry Tao: “AI solved the knottiest problems in math”

Prof. Brian Keating

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34,968 次观看 • 5 个月前 •via X (Twitter)

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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.

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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Terence Tao: Will AI solve complex math problems like the Riemann Hypothesis, or is human insight essential? The answer might lie in a collaboration we can't yet imagine, blending AI's power with human ingenuity.

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Terence Tao says AI could help rework mathematics from the ground up, doing math problems at a scale never done before and leading to a new age of discovery

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Terence Tao: AI isn’t hype anymore in Math discovery. Terence Tao is one of the greatest living mathematicians, in his new lecture explains how AI and human professional mathematicians are now complementary. "There has been a really visible increase in capability. It is not pure hype by any means. To me, these advances show there is a complementary way to do mathematics. Humans traditionally work in small groups on hard problems for months, and we will keep doing that. But we can also now set AI to scale: sweep a thousand problems and pick up all the low-hanging fruit. Figure out all the ways to match problems to methods. If there are 20 different techniques, apply them all to 1,000 problems and see which ones can be solved by these methods. This is the capability that is present today." From 'Institute for Pure & Applied Mathematics (IPAM)' YT channel.

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