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Rapidly advancing AI models have sparked breakthroughs in long-standing math problems. From solving problems at the International Math Olympiad to disproving decades-old conjectures - some in the math world are now questioning whether they have a future in the field. But not Professor Shayan Oveis Gharan, who won the... show more

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57,767 次观看 • 1 个月前 •via X (Twitter)

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Feminisce 🥤 的头像

Feminisce 🥤1 个月前

L'avancement rapide des modèles d'IA a suscité des percées dans les problèmes mathématiques de longue date. De la résolution de problèmes à l'Olympiade internationale de mathématiques à la réfuter les conjectures vieilles de plusieurs décennies - certains dans le monde des mathématiques se demandent maintenant s'ils ont un avenir dans le domaine.

Gorefang 的头像

Gorefang1 个月前

Everyone keeps saying that. Ai is a tool, not a replacement. It's just going to elevate those that know how to use it. No. When anyone can ask the AI a math question and the Ai can answer it independently, then no one needs you and the AI can do the job without a handler.

💐The Casual Whistle🎐 的头像

💐The Casual Whistle🎐1 个月前

People acting like AI is about to bench human mathematicians need to relax. Professor Shayan Oveis Gharan just proved partnering with advanced tech is how you actually win championships in this field.

Darkek Metumbo 的头像

Darkek Metumbo1 个月前

Relevant news 👇

Joshua Peters 的头像

Joshua Peters1 个月前

It is definitely emerging as a new branch between mathematics and computer science.

Smitten Kitten 💕🐾😼 的头像

Smitten Kitten 💕🐾😼1 个月前

AI will never be the problem. The problems will chime from nefarious individuals wielding it. Power never corrupts, it simply attracts the corruptible. 🤔🤘🏼

💐The Casual Whistle🎐 的头像

💐The Casual Whistle🎐1 个月前

AI solving complex math problems doesn't spell the end for human researchers. As Shayan Oveis Gharan's work highlights, treating technology as a collaborative partner opens up entirely new horizons for discovery.

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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. That’s problem-solving.” “We have not yet seen models engage in theory building.” “Coming up with powerful new definitions and techniques that create really great breakthroughs that have ripples across the field.”

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. That’s problem-solving.” “We have not yet seen models engage in theory building.” “Coming up with powerful new definitions and techniques that create really great breakthroughs that have ripples across the field.”

MTS

20,952 次观看 • 4 个月前

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?

Epoch AI

178,703 次观看 • 8 个月前

AI has solved 50 Erdős problems in the last year. But on a wider sweep of problems, the models’ success rate is only about 1-2%: labs have just been publishing the wins. This isn’t because AI isn’t useful for mathematicians. Terence Tao thinks the models are currently at the level of a trustworthy coworker. But while they’ve got a strong ability to apply standard math techniques to problems, often more reliably than humans, Terence thinks they currently aren’t great at iterating on partial successes - their understanding of the mathematical object does not advance from session to session. I swear I wasn’t trying to get him to talk about continual learning.

AI has solved 50 Erdős problems in the last year. But on a wider sweep of problems, the models’ success rate is only about 1-2%: labs have just been publishing the wins. This isn’t because AI isn’t useful for mathematicians. Terence Tao thinks the models are currently at the level of a trustworthy coworker. But while they’ve got a strong ability to apply standard math techniques to problems, often more reliably than humans, Terence thinks they currently aren’t great at iterating on partial successes - their understanding of the mathematical object does not advance from session to session. I swear I wasn’t trying to get him to talk about continual learning.

Dwarkesh Patel

146,244 次观看 • 6 个月前

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

64,547 次观看 • 6 个月前

Emad Mostaque takes a jab at mathematicians as well. Says that when AI started solving their hardest problems, their answer was "Math is about the struggle", which is a strange thing to hear from a field that exists to find answers. ---- Full video on "Tom Bilyeu" YouTube channel, (link in comment)

Emad Mostaque takes a jab at mathematicians as well. Says that when AI started solving their hardest problems, their answer was "Math is about the struggle", which is a strange thing to hear from a field that exists to find answers. ---- Full video on "Tom Bilyeu" YouTube channel, (link in comment)

Rohan Paul

17,053 次观看 • 6 天前

Peter Thiel just told Silicon Valley it’s automating away its own cognitive moat. Nobody there is paying attention. Thiel: “It is striking to me how bad Silicon Valley is at talking about these sorts of things.” The industry is either arguing over 20% improvements in the next transformer model or jumping straight to simulation theory. They’re missing the massive real-world shift happening right in the middle. Thiel: “My intuition would be it’s going to be quite the opposite, where it seems much worse for the math people than the word people.” For decades, Silicon Valley worshipped quantitative intelligence. Math and coding were the ultimate safety nets. Thiel: “Within three to five years, the AI models will be able to solve all the US Math Olympiad problems.” Once a machine instantly solves the hardest math problems on earth, the economic value of being a human calculator doesn’t just decline. It disappears. And the historical irony is brutal. The societal bias toward math over verbal ability started during the French Revolution. Not because math was more valuable. Because verbal ability ran in aristocratic families, and math was elevated as the great equalizer to break nepotism. A 200-year-old political accident became the foundation of Silicon Valley’s entire hiring philosophy. AI is about to snap it back. The people who built the models that can now outperform them mathematically spent their careers optimizing for the wrong skill. The future belongs to the word people. The engineers didn’t see it coming because they were too busy calculating.

Peter Thiel just told Silicon Valley it’s automating away its own cognitive moat. Nobody there is paying attention. Thiel: “It is striking to me how bad Silicon Valley is at talking about these sorts of things.” The industry is either arguing over 20% improvements in the next transformer model or jumping straight to simulation theory. They’re missing the massive real-world shift happening right in the middle. Thiel: “My intuition would be it’s going to be quite the opposite, where it seems much worse for the math people than the word people.” For decades, Silicon Valley worshipped quantitative intelligence. Math and coding were the ultimate safety nets. Thiel: “Within three to five years, the AI models will be able to solve all the US Math Olympiad problems.” Once a machine instantly solves the hardest math problems on earth, the economic value of being a human calculator doesn’t just decline. It disappears. And the historical irony is brutal. The societal bias toward math over verbal ability started during the French Revolution. Not because math was more valuable. Because verbal ability ran in aristocratic families, and math was elevated as the great equalizer to break nepotism. A 200-year-old political accident became the foundation of Silicon Valley’s entire hiring philosophy. AI is about to snap it back. The people who built the models that can now outperform them mathematically spent their careers optimizing for the wrong skill. The future belongs to the word people. The engineers didn’t see it coming because they were too busy calculating.

Dustin

624,301 次观看 • 7 个月前

If we're going to have AIs that fully automate math, they not only need to solve existing problems. We also need to teach them how to recognize what problem to solve next. Human mathematicians have heuristic models that they use to decide what to work on, like, “There’s something important going on with the randomness of primes - let’s codify some patterns we see into specific conjectures.” But these aren’t currently precise enough for RL.

If we're going to have AIs that fully automate math, they not only need to solve existing problems. We also need to teach them how to recognize what problem to solve next. Human mathematicians have heuristic models that they use to decide what to work on, like, “There’s something important going on with the randomness of primes - let’s codify some patterns we see into specific conjectures.” But these aren’t currently precise enough for RL.

Dwarkesh Patel

54,583 次观看 • 6 个月前

Why is AI suddenly cracking all kinds of previously unsolved problems in math? My guess is that it’s because: A) Math is verifiable so it's easier for models to improve B) Theoretical math highly benefits from chain of thought reasoning C) The answers and breakthroughs can be tested and verified by expert humans. But this leads to another question: what if progress in other fields is moving just as fast and we can't see it?

Why is AI suddenly cracking all kinds of previously unsolved problems in math? My guess is that it’s because: A) Math is verifiable so it's easier for models to improve B) Theoretical math highly benefits from chain of thought reasoning C) The answers and breakthroughs can be tested and verified by expert humans. But this leads to another question: what if progress in other fields is moving just as fast and we can't see it?

nxthompson

17,404 次观看 • 2 个月前

Physicist steve hsu says AI may become superhuman at math long before that translates into cures, better aircraft, or explosive economic growth: "90% of mathematicians, especially the younger ones, realize these models are extremely powerful. Just as they became superhuman in coding, they're becoming superhuman in math." "The Fields Medal work in the last 20 years has had very little impact on physics. Pure math might be decoupled from physics, and theoretical physics might be decoupled from engineering. People say GDP growth is gonna go from 3% to 5% or 10% because of AI. It could happen, but not immediately." "Perelman, who proved the Poincaré conjecture, nothing really useful has come out of that for physics or applied physics, and that was done almost 20 years ago. It's not necessarily the case that a breakthrough in pure math has big real world applications." "Will ASI eventually get us a cure for cancer or more efficient aircraft wings? I think yes, but it'll take longer than most people think. I don't think the FOOM, the fast takeoff, is necessarily gonna happen."

Physicist steve hsu says AI may become superhuman at math long before that translates into cures, better aircraft, or explosive economic growth: "90% of mathematicians, especially the younger ones, realize these models are extremely powerful. Just as they became superhuman in coding, they're becoming superhuman in math." "The Fields Medal work in the last 20 years has had very little impact on physics. Pure math might be decoupled from physics, and theoretical physics might be decoupled from engineering. People say GDP growth is gonna go from 3% to 5% or 10% because of AI. It could happen, but not immediately." "Perelman, who proved the Poincaré conjecture, nothing really useful has come out of that for physics or applied physics, and that was done almost 20 years ago. It's not necessarily the case that a breakthrough in pure math has big real world applications." "Will ASI eventually get us a cure for cancer or more efficient aircraft wings? I think yes, but it'll take longer than most people think. I don't think the FOOM, the fast takeoff, is necessarily gonna happen."

MTS

20,833 次观看 • 1 个月前

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.

Rohan Paul

174,863 次观看 • 8 个月前

Ten days after winning the Fields Medal — math's highest honor — Jacob Tsimerman joins to explain why he's leaving academia temporarily for OpenAI's AI safety team, and why he's grieving even as he does it. The conversation covers why math is one of the first fields being radically reshaped by AI, whether a proof still counts if no one can understand it, what mathematical "understanding" really means, the ethics of elite access to frontier models, his disagreements with the Leiden Declaration, and his advice for young people weighing a career in pure math in an age of rapidly advancing AI. This is an exclusive first podcast with Jacob Tsimerman.

Ten days after winning the Fields Medal — math's highest honor — Jacob Tsimerman joins to explain why he's leaving academia temporarily for OpenAI's AI safety team, and why he's grieving even as he does it. The conversation covers why math is one of the first fields being radically reshaped by AI, whether a proof still counts if no one can understand it, what mathematical "understanding" really means, the ethics of elite access to frontier models, his disagreements with the Leiden Declaration, and his advice for young people weighing a career in pure math in an age of rapidly advancing AI. This is an exclusive first podcast with Jacob Tsimerman.

Curt Jaimungal

50,690 次观看 • 2 个月前

Nigerians are waking up to reality. Lots of Nigerians are now discovering that the Yorubas are indeed the problems of Nigeria. They have been hiding it for a long time but Nigerians have discovered who their problems are currently. I’m glad Nigerians are discovering this now. I have known youbas as the problems of this country for a very long time.

Nigerians are waking up to reality. Lots of Nigerians are now discovering that the Yorubas are indeed the problems of Nigeria. They have been hiding it for a long time but Nigerians have discovered who their problems are currently. I’m glad Nigerians are discovering this now. I have known youbas as the problems of this country for a very long time.

OSE MMUO

59,601 次观看 • 11 个月前

Yann LeCun says AI already outperforms humans at tasks we’re not great at -- like chess, Go, or solving tough math problems that’s how computers have always helped us: by doing what we find hard in the future, smart devices with AI could make everyone feel like they have expert help, like a CEO or professor with a brilliant team

Yann LeCun says AI already outperforms humans at tasks we’re not great at -- like chess, Go, or solving tough math problems that’s how computers have always helped us: by doing what we find hard in the future, smart devices with AI could make everyone feel like they have expert help, like a CEO or professor with a brilliant team

Haider.

26,577 次观看 • 1 年前

Axiom Math founder Carina Hong on why math is the path to general superintelligence: “Math is the sandbox for reality. You very quickly see verifiable rewards because in math, there’s an absolute right or wrong.” “And especially when you have Lean, you can check the proof or solution step by step. You’ll be able to apply reinforcement learning in a much more efficient way.” “We have currently scaled from winning a Putnam perfect score to solving a batch of research problems that professional mathematicians find really challenging. And we also see this transfer to code verification.”

Axiom Math founder Carina Hong on why math is the path to general superintelligence: “Math is the sandbox for reality. You very quickly see verifiable rewards because in math, there’s an absolute right or wrong.” “And especially when you have Lean, you can check the proof or solution step by step. You’ll be able to apply reinforcement learning in a much more efficient way.” “We have currently scaled from winning a Putnam perfect score to solving a batch of research problems that professional mathematicians find really challenging. And we also see this transfer to code verification.”

TBPN

39,589 次观看 • 7 个月前

25 Fields Medalists, including Terrence Tao, just published a joint declaration accusing AI labs of a severe misalignment with mathematics. The letter, posted on Tao's blog and at on September 11th, argues that AI companies are treating math problems as benchmarks to farm for PR wins. The signatories call this a general threat to intellectual work in the field. They argue the incentive structure pushes AI labs to race through famous open problems without crediting or involving the mathematicians who originally posed or nurtured them. The declaration comes after OpenAI claimed its internal model produced a proof of the Navier Stokes equations, with the company now reportedly turning its attention to the Riemann Hypothesis and P versus NP.

25 Fields Medalists, including Terrence Tao, just published a joint declaration accusing AI labs of a severe misalignment with mathematics. The letter, posted on Tao's blog and at on September 11th, argues that AI companies are treating math problems as benchmarks to farm for PR wins. The signatories call this a general threat to intellectual work in the field. They argue the incentive structure pushes AI labs to race through famous open problems without crediting or involving the mathematicians who originally posed or nurtured them. The declaration comes after OpenAI claimed its internal model produced a proof of the Navier Stokes equations, with the company now reportedly turning its attention to the Riemann Hypothesis and P versus NP.

AGTP

24,230 次观看 • 1 个月前

University of Toronto mathematician Daniel Litt and a16z's Lisha Li on AI's impact on mathematics: The models are good at a narrower slice of math than the headlines suggest. They grind long computations, pull technical ideas from more papers than any human could read, and apply every known technique better than almost anyone. What they don't do is build theory, or hold a vague philosophy long enough to make it precise, which is most of what Daniel says he actually does for a living. In this conversation, he and Lisha get into how mathematicians raided an AI proof for parts and broke several other problems with them, why a thousand AI mathematicians might all turn out to be the same mathematician, and why the proof a model handed Daniel was correct but still worth nothing. 00:00 Intro 02:10 The Erdős problem AI disproved 06:20 AI's reasoning looks recognizably human 07:55 Why English beat formal proofs 10:00 Why models can't build theory 14:50 Open problems measure your ignorance 17:45 How a graph became a Millennium Prize problem 18:58 Where AI doesn't help Daniel 21:15 Why ugly proofs are worth doing 23:42 True conjectures are harder than false ones 29:32 10 pages of calculation, zero insight 34:55 The goal of math is not to produce papers 36:25 5 conjectures, 3 bad papers, 1 hour 38:05 One mathematician duplicated 1000x 40:48 Why humans matter even if models win 46:30 When cheaper and worse beats better 49:22 Why the newest AI result isn't a big deal 57:05 How mathematicians actually check a long proof 59:38 Daniel's 3-year-old is already doing math YouTube: Daniel Litt Lisha

University of Toronto mathematician Daniel Litt and a16z's Lisha Li on AI's impact on mathematics: The models are good at a narrower slice of math than the headlines suggest. They grind long computations, pull technical ideas from more papers than any human could read, and apply every known technique better than almost anyone. What they don't do is build theory, or hold a vague philosophy long enough to make it precise, which is most of what Daniel says he actually does for a living. In this conversation, he and Lisha get into how mathematicians raided an AI proof for parts and broke several other problems with them, why a thousand AI mathematicians might all turn out to be the same mathematician, and why the proof a model handed Daniel was correct but still worth nothing. 00:00 Intro 02:10 The Erdős problem AI disproved 06:20 AI's reasoning looks recognizably human 07:55 Why English beat formal proofs 10:00 Why models can't build theory 14:50 Open problems measure your ignorance 17:45 How a graph became a Millennium Prize problem 18:58 Where AI doesn't help Daniel 21:15 Why ugly proofs are worth doing 23:42 True conjectures are harder than false ones 29:32 10 pages of calculation, zero insight 34:55 The goal of math is not to produce papers 36:25 5 conjectures, 3 bad papers, 1 hour 38:05 One mathematician duplicated 1000x 40:48 Why humans matter even if models win 46:30 When cheaper and worse beats better 49:22 Why the newest AI result isn't a big deal 57:05 How mathematicians actually check a long proof 59:38 Daniel's 3-year-old is already doing math YouTube: Daniel Litt Lisha

a16z

148,301 次观看 • 1 个月前

Math has a proof checker. Can physics get one? Jonathan Gorard Jonathan Gorard, an applied mathematician and the cofounder and CEO of Lanyon AI, joins to explain why AI took off in math and coding but not yet in physics. We discuss an AI finishing the formal check of a Fields Medal proof and why it scared him, why he thinks “I detected a particle” rests on 20 to 50 levels of theory, and what Alan Turing’s PhD student Robin Gandy tried to build for physics. The conversation also covers his push to make physics executable, why he thinks mysteries are artifacts of description languages, and whether there is still a place for the physicist.

Math has a proof checker. Can physics get one? Jonathan Gorard Jonathan Gorard, an applied mathematician and the cofounder and CEO of Lanyon AI, joins to explain why AI took off in math and coding but not yet in physics. We discuss an AI finishing the formal check of a Fields Medal proof and why it scared him, why he thinks “I detected a particle” rests on 20 to 50 levels of theory, and what Alan Turing’s PhD student Robin Gandy tried to build for physics. The conversation also covers his push to make physics executable, why he thinks mysteries are artifacts of description languages, and whether there is still a place for the physicist.

Curt Jaimungal

30,514 次观看 • 9 天前