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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 • 8 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.

Dwarkesh Patel

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Terence Tao, UCLA math professor and Fields Medalist, says AI is still terrible at genuinely hard problems but unbeatable at breadth:

Terence Tao, UCLA math professor and Fields Medalist, says AI is still terrible at genuinely hard problems but unbeatable at breadth:

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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.

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

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 says evolution hasn't given us a "math center" in the brain, so different people repurpose different areas of the brain to solve math problems. Which leads to different styles of learning and communication.

Terence Tao says evolution hasn't given us a "math center" in the brain, so different people repurpose different areas of the brain to solve math problems. Which leads to different styles of learning and communication.

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Can an AI trained in English solve math problems in other languages without extra training?

Can an AI trained in English solve math problems in other languages without extra training?

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How does math research change when the cost of trying your first dumb idea goes to zero? Daniel Litt joins Greg Burnham and Anson Ho to discuss what today’s models can and can’t do in math, and how far they are from doing high-quality research. 0:00:00 What's the hardest math problem AI can solve today? 00:16:08 How helpful are today’s AI models for math research? 00:23:36 Junk papers, LLM-generated proofs, and the refereeing crisis 00:27:21 AI enables searching through problems at scale 00:33:49 When will AI be good enough to publish in top math journals? 00:42:15 What are the returns to intelligence? 00:59:50 Will AI solve Millennium problems? 01:11:54 Is math full of low-hanging fruit? 01:18:47 How Daniel has adapted his professional life to AI progress 01:25:28 What do AI math benchmarks actually measure? 01:33:05 Designing the Open Problems benchmark 01:56:35 Do mathematicians believe heuristic arguments about conjectures? 02:01:24 What if FrontierMath: Open Problems gets solved? 02:06:53 Is AI on the cusp of accelerating math progress?

How does math research change when the cost of trying your first dumb idea goes to zero? Daniel Litt joins Greg Burnham and Anson Ho to discuss what today’s models can and can’t do in math, and how far they are from doing high-quality research. 0:00:00 What's the hardest math problem AI can solve today? 00:16:08 How helpful are today’s AI models for math research? 00:23:36 Junk papers, LLM-generated proofs, and the refereeing crisis 00:27:21 AI enables searching through problems at scale 00:33:49 When will AI be good enough to publish in top math journals? 00:42:15 What are the returns to intelligence? 00:59:50 Will AI solve Millennium problems? 01:11:54 Is math full of low-hanging fruit? 01:18:47 How Daniel has adapted his professional life to AI progress 01:25:28 What do AI math benchmarks actually measure? 01:33:05 Designing the Open Problems benchmark 01:56:35 Do mathematicians believe heuristic arguments about conjectures? 02:01:24 What if FrontierMath: Open Problems gets solved? 02:06:53 Is AI on the cusp of accelerating math progress?

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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.

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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The box solved all his problems

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Terence Tao predicts the end of math gatekeeping with AI. AI proof assistants are smashing the technical barriers that keep amateurs out. By automating verification, AI empowers anyone to contribute rigorous pro-level Math. The Ivory Tower is falling

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PROBLEMS? SOLVED!

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Terence Tao: AI is creating a “traffic jam” in math If AI generates more proofs than humans can verify, science needs new infrastructure. SAIR competitions build that infrastructure by surfacing high-quality results, so the best work is not lost in a flood of AI-generated math.

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Terence Tao says AI can flood you with new mathematical ideas, but maybe 1 in 100 is actually good, and it can't tell the difference Where math is verifiable, you either solved it, or you didn't — AI is already useful "it might occasionally hit gold, then move right past it and give you 99 things that are rubbish"

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This guy placed himself in Titanic and solved all the Titanic problems 😭

This guy placed himself in Titanic and solved all the Titanic problems 😭

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