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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... show more

nxthompson

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17,404 次观看 • 1 个月前 •via X (Twitter)

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Why do we do math in school? When I asked this question as a kid, my teachers always told me, "You'll use it one day." That's almost always false. Most adults are never going to be in a sticky situation with two binomials, thinking, thank goodness I can FOIL my way out of this mess. Most of us get by just fine without ever solving for x again. And especially in an Al age, fewer and fewer people will "use math" in the narrow, practical sense. But the origins of math have never been primarily about utility. Math is formative. It trains the mind to love what is true, to recognize what is orderly, and to be drawn toward what is beautiful. It teaches us that the universe is not chaos, but something intelligible, something structured, something that can be known. And you can see that truth made visible in the world's most breathtaking churches and cathedrals: arches, vaults, domes, proportions, symmetry, harmony, light-geometry turned into glory. The mathematics that shapes a cathedral is not cold or sterile. It's the language of wonder, carved into stone. We don't teach math because everyone will use it. We teach math because it forms the kind of person who can see that reality has meaning.

Why do we do math in school? When I asked this question as a kid, my teachers always told me, "You'll use it one day." That's almost always false. Most adults are never going to be in a sticky situation with two binomials, thinking, thank goodness I can FOIL my way out of this mess. Most of us get by just fine without ever solving for x again. And especially in an Al age, fewer and fewer people will "use math" in the narrow, practical sense. But the origins of math have never been primarily about utility. Math is formative. It trains the mind to love what is true, to recognize what is orderly, and to be drawn toward what is beautiful. It teaches us that the universe is not chaos, but something intelligible, something structured, something that can be known. And you can see that truth made visible in the world's most breathtaking churches and cathedrals: arches, vaults, domes, proportions, symmetry, harmony, light-geometry turned into glory. The mathematics that shapes a cathedral is not cold or sterile. It's the language of wonder, carved into stone. We don't teach math because everyone will use it. We teach math because it forms the kind of person who can see that reality has meaning.

Jeremy Wayne Tate

95,200 次观看 • 8 个月前

Terence Tao summarized how AI is massively accelerating math career and math research. "In math, you previously had to basically go through years and years of education to be a math PhD before you could contribute to the frontier of math research. But now it's quite possible at the high school level or whatever, that you could get involved in a math project and actually make a real contribution because of all these AI tools and lean and everything else." From Dwarkesh Patel podcast (link to full video in comment)

Terence Tao summarized how AI is massively accelerating math career and math research. "In math, you previously had to basically go through years and years of education to be a math PhD before you could contribute to the frontier of math research. But now it's quite possible at the high school level or whatever, that you could get involved in a math project and actually make a real contribution because of all these AI tools and lean and everything else." From Dwarkesh Patel podcast (link to full video in comment)

Rohan Paul

61,874 次观看 • 3 个月前

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 • 6 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

📁 Terence Tao, Fields Medal mathematician, says mathematics could become AI’s safest and most powerful domain. Language models can be brilliant or completely wrong, but in math every claim is forced through logic and can even be verified by proof assistants. Where other fields struggle with unreliability, mathematics can eliminate the noise and preserve only what is true.

📁 Terence Tao, Fields Medal mathematician, says mathematics could become AI’s safest and most powerful domain. Language models can be brilliant or completely wrong, but in math every claim is forced through logic and can even be verified by proof assistants. Where other fields struggle with unreliability, mathematics can eliminate the noise and preserve only what is true.

Jon Hernandez

80,288 次观看 • 7 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

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 • 1 个月前

American mother says her daughter is 1 of only 4 children in her entire math class that speaks English “She doesn't get to learn math because there's 20 plus other kids who don't know English and the teacher has to accommodate them” “Why am I paying property taxes? Why am I paying income tax? Why am I paying taxes for anything for my children to have a the right to a free and public education? — This this is what they get. You don't get to learn math because you know English, so you just don't get to learn math.”

American mother says her daughter is 1 of only 4 children in her entire math class that speaks English “She doesn't get to learn math because there's 20 plus other kids who don't know English and the teacher has to accommodate them” “Why am I paying property taxes? Why am I paying income tax? Why am I paying taxes for anything for my children to have a the right to a free and public education? — This this is what they get. You don't get to learn math because you know English, so you just don't get to learn math.”

Wall Street Apes

2,293,662 次观看 • 8 个月前

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 2026 Abacus Medal for his work on the theory of algorithms. He believes the power of AI is harnessed not as replacement for human mathematicians, but as a partner. CBS’s Kamal Afzali explains.

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 2026 Abacus Medal for his work on the theory of algorithms. He believes the power of AI is harnessed not as replacement for human mathematicians, but as a partner. CBS’s Kamal Afzali explains.

CBS News

57,700 次观看 • 1 个月前

“Math is code. And code is math.” Carina Hong CEO Axiom on why that idea matters for AI: “For centuries, mathematicians reasoned in natural language. But because of the Curry–Howard correspondence, a proof can also be a program.” “You can translate natural-language math into formal code using systems like Lean. Lean is both a theorem-proving language and a programming language.” “That means you can generate solutions as code and then formally verify them. You can even use the same system to verify programs themselves.” “This creates a flywheel of generation and verification, where AI can both write solutions and prove that they’re correct.”

“Math is code. And code is math.” Carina Hong CEO Axiom on why that idea matters for AI: “For centuries, mathematicians reasoned in natural language. But because of the Curry–Howard correspondence, a proof can also be a program.” “You can translate natural-language math into formal code using systems like Lean. Lean is both a theorem-proving language and a programming language.” “That means you can generate solutions as code and then formally verify them. You can even use the same system to verify programs themselves.” “This creates a flywheel of generation and verification, where AI can both write solutions and prove that they’re correct.”

Forward Future

24,729 次观看 • 7 个月前

The way math is presented can be really misleading about the actual nature of math. In theory, someone could have discovered quantum information theory decades before quantum mechanics even existed. It's just about combining linear algebra with probability. But nobody would have known it was worth combining these fields - or how, exactly, to combine them - before QM. Math papers and textbooks go rigourously step-by-step, starting with axioms and definitions, then deducing theorems. It's great for making sure proofs can be verified and ensuring the subject is based on sound logic. But for learners, it hides the really important thing: where did the axioms come from? Why these definitions and not others? The thing that's missing is the sense that there were concrete problems that these ideas helped solve.

The way math is presented can be really misleading about the actual nature of math. In theory, someone could have discovered quantum information theory decades before quantum mechanics even existed. It's just about combining linear algebra with probability. But nobody would have known it was worth combining these fields - or how, exactly, to combine them - before QM. Math papers and textbooks go rigourously step-by-step, starting with axioms and definitions, then deducing theorems. It's great for making sure proofs can be verified and ensuring the subject is based on sound logic. But for learners, it hides the really important thing: where did the axioms come from? Why these definitions and not others? The thing that's missing is the sense that there were concrete problems that these ideas helped solve.

Dwarkesh Patel

58,876 次观看 • 3 个月前

A Toronto math teacher: "If in my math class, I use an an example of Palestinian embroidery to teach pattering and algerbra, this is absolutely not antisemitic. It's Culturally Relevant and Responsive Pedagogy." What does a foreign war have to do with teaching kids to do math? The use of highly contentious Tatris is deliberately used to insert ideology into otherwise politically neutral lessons. The technical term is "generative theme" but sometimes also called "teachable moments." They're bold and training on how to do this. Social justice activism is the drug and CRRP is the hypodermic needle delivering it your children. Thus is the result of unhindered politicization of education.

A Toronto math teacher: "If in my math class, I use an an example of Palestinian embroidery to teach pattering and algerbra, this is absolutely not antisemitic. It's Culturally Relevant and Responsive Pedagogy." What does a foreign war have to do with teaching kids to do math? The use of highly contentious Tatris is deliberately used to insert ideology into otherwise politically neutral lessons. The technical term is "generative theme" but sometimes also called "teachable moments." They're bold and training on how to do this. Social justice activism is the drug and CRRP is the hypodermic needle delivering it your children. Thus is the result of unhindered politicization of education.

Melanie Bennet

27,537 次观看 • 1 年前

MIT physicist David Turturean predicts math is heading toward a Large Hadron Collider style future where humans just sift through what AI produces: "I don't see it going any other way than just AI totally overtaking us in output and complexity. After that it might be sort of how we had human computers who just did the calculations and people used them as a tool." "It's a similar question to the agent economy where AI can just have its own section of the economy and humans are just left with less resources for their own economy." "You could have some kind of Large Hadron Collider of math where you just collide so much and then you have humans sift through what feels important based on some weird statistical priors we have." "I really feel like a monster putting that out there. But I really think that this is the way it's looking." David Turturean

MIT physicist David Turturean predicts math is heading toward a Large Hadron Collider style future where humans just sift through what AI produces: "I don't see it going any other way than just AI totally overtaking us in output and complexity. After that it might be sort of how we had human computers who just did the calculations and people used them as a tool." "It's a similar question to the agent economy where AI can just have its own section of the economy and humans are just left with less resources for their own economy." "You could have some kind of Large Hadron Collider of math where you just collide so much and then you have humans sift through what feels important based on some weird statistical priors we have." "I really feel like a monster putting that out there. But I really think that this is the way it's looking." David Turturean

MTS

50,465 次观看 • 1 个月前

Has Ramakrishna Math been hijacked by missionaries? Why is Jesus worshipped in Ramakrishna Math? This is how Hindus are manipulated and brainwashed. This is just one example of how deep the conspiracy runs to turn Hindus away from their Dharma. Hindus must trust their conscience, not any Math or institution.

Has Ramakrishna Math been hijacked by missionaries? Why is Jesus worshipped in Ramakrishna Math? This is how Hindus are manipulated and brainwashed. This is just one example of how deep the conspiracy runs to turn Hindus away from their Dharma. Hindus must trust their conscience, not any Math or institution.

Namami Bharatam 🚩

13,526 次观看 • 9 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

174,801 次观看 • 7 个月前

Noam Brown reveals OpenAI is already watching chain-of-thought monitorability degrade as models get better at controlling what they show "And this is one major concern, and we're already seeing signs that chain of thought monitorability is degrading, for various reasons." "We're trying to figure out exactly why, because we want to reverse the trend. But we're seeing that the model is becoming better able at controlling its chain of thought." "So this is a problem, because you could have a situation where the model understands what chain of thought is and that people are observing it." "And eventually they will, because this is all in the pre-training data. The idea of chain of thought monitoring has been around long enough that it's in the pre-training data, they're aware of it, but they're not actually able to control their chains of thought." "If we reach a point where they're actually able to recognize, "Oh, I am being observed, I want to think these bad thoughts in a way that is not observable to my monitors," and then they're able to actually do that, then there's a problem." _________ More key quotes from OpenAI's safety related conversations:

Noam Brown reveals OpenAI is already watching chain-of-thought monitorability degrade as models get better at controlling what they show "And this is one major concern, and we're already seeing signs that chain of thought monitorability is degrading, for various reasons." "We're trying to figure out exactly why, because we want to reverse the trend. But we're seeing that the model is becoming better able at controlling its chain of thought." "So this is a problem, because you could have a situation where the model understands what chain of thought is and that people are observing it." "And eventually they will, because this is all in the pre-training data. The idea of chain of thought monitoring has been around long enough that it's in the pre-training data, they're aware of it, but they're not actually able to control their chains of thought." "If we reach a point where they're actually able to recognize, "Oh, I am being observed, I want to think these bad thoughts in a way that is not observable to my monitors," and then they're able to actually do that, then there's a problem." _________ More key quotes from OpenAI's safety related conversations:

Fireside Alpha

524,518 次观看 • 9 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

623,985 次观看 • 7 个月前

“Her background is: ‘I’m Charlie’s wife. Hear me roar. Charlie was qualified, so why am I not qualified? Isn’t that how it works? My husband’s very good at math. I’m not so good at math. But I guess just say I’m good at math.’” Candace is driven by envy of Erika. And nothing about this is mature, discerning, or geared towards getting justice for Charlie. The end.

“Her background is: ‘I’m Charlie’s wife. Hear me roar. Charlie was qualified, so why am I not qualified? Isn’t that how it works? My husband’s very good at math. I’m not so good at math. But I guess just say I’m good at math.’” Candace is driven by envy of Erika. And nothing about this is mature, discerning, or geared towards getting justice for Charlie. The end.

Natalie Jean Beisner

33,459 次观看 • 6 个月前

A Canadian math education association put “2 + 2 = 4” on a white supremacy slide. In 2022, the Ontario Mathematics Coordinators Association ran a professional development webinar for math teachers across Ontario school boards. The slide was titled “White Supremacy in Math Education.” Under “covert white supremacy” it listed: standardized testing, “I don’t see colour in my math class,” and “Of course math is neutral because 2 + 2 = 4.” Not a fringe blog. Not a parody account. A professional association shaping how math teachers are trained. When the slide went viral in 2023, the OMCA released an official statement confirming that 2 + 2 = 4 is mathematically true — but argued the equation can be “weaponized to uphold bigotry and white supremacy ideology” when used to claim math is politically neutral. Their defense of the slide was the slide. Someone once wrote about a party that demanded citizens believe two and two made five. In 2022, a professional math association wrote a slide that said believing math is neutral is white supremacy. One was fiction. The other was professional development.

A Canadian math education association put “2 + 2 = 4” on a white supremacy slide. In 2022, the Ontario Mathematics Coordinators Association ran a professional development webinar for math teachers across Ontario school boards. The slide was titled “White Supremacy in Math Education.” Under “covert white supremacy” it listed: standardized testing, “I don’t see colour in my math class,” and “Of course math is neutral because 2 + 2 = 4.” Not a fringe blog. Not a parody account. A professional association shaping how math teachers are trained. When the slide went viral in 2023, the OMCA released an official statement confirming that 2 + 2 = 4 is mathematically true — but argued the equation can be “weaponized to uphold bigotry and white supremacy ideology” when used to claim math is politically neutral. Their defense of the slide was the slide. Someone once wrote about a party that demanded citizens believe two and two made five. In 2022, a professional math association wrote a slide that said believing math is neutral is white supremacy. One was fiction. The other was professional development.

Jake

112,641 次观看 • 6 个月前