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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... show more

Rohan Paul

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61,705 次观看 • 2 个月前 •via X (Twitter)

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Terence Tao: "Previously, you needed a PhD to contribute to math research. Now a high school student can." Dwarkesh asks the world's most famous mathematician: what's your advice for someone considering a career in math, especially in light of AI progress? Tao is honest about uncertainty: "We live in a time of change. A particularly unpredictable era. Things that we've taken for granted for centuries may not hold anymore. The way we do everything... not just mathematics... will change." He admits his preference: "In many ways, I would prefer a much more boring, quiet era where things are much the same as they were 10 or 20 years ago. But one just has to embrace this. There's going to be a lot of change. The things you study... some of them may become obsolete or revolutionized. But some things will be retained." On new opportunities: "Previously, you had to go through years and years of education and get a math PhD before you could contribute to the frontier of math research. But now it's quite possible at the high school level 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." His advice: "There will be a lot of non-traditional opportunities to learn. You need a very adaptable mindset. There'll be worth pursuing things just for curiosity and for playing around. Still go through traditional education and learn math and science the old-fashioned way for a while... credentials will still be important. But you should also be open to very, very different ways of doing science. Some of which don't exist yet." He concludes: "It's a scary time. But also very exciting."

Terence Tao: "Previously, you needed a PhD to contribute to math research. Now a high school student can." Dwarkesh asks the world's most famous mathematician: what's your advice for someone considering a career in math, especially in light of AI progress? Tao is honest about uncertainty: "We live in a time of change. A particularly unpredictable era. Things that we've taken for granted for centuries may not hold anymore. The way we do everything... not just mathematics... will change." He admits his preference: "In many ways, I would prefer a much more boring, quiet era where things are much the same as they were 10 or 20 years ago. But one just has to embrace this. There's going to be a lot of change. The things you study... some of them may become obsolete or revolutionized. But some things will be retained." On new opportunities: "Previously, you had to go through years and years of education and get a math PhD before you could contribute to the frontier of math research. But now it's quite possible at the high school level 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." His advice: "There will be a lot of non-traditional opportunities to learn. You need a very adaptable mindset. There'll be worth pursuing things just for curiosity and for playing around. Still go through traditional education and learn math and science the old-fashioned way for a while... credentials will still be important. But you should also be open to very, very different ways of doing science. Some of which don't exist yet." He concludes: "It's a scary time. But also very exciting."

Jaynit

77,487 次观看 • 3 个月前

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

Tsarathustra

63,759 次观看 • 1 年前

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 • 7 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 • 5 个月前

Going from "top-down" familiarity to "bottom-up" mastery. My journey as a math PhD student, the challenges faced, and how I eventually overcame them. If you're thinking of doing a math PhD or any kind of research degree, you may find it helpful. Happy to answer questions here.

Going from "top-down" familiarity to "bottom-up" mastery. My journey as a math PhD student, the challenges faced, and how I eventually overcame them. If you're thinking of doing a math PhD or any kind of research degree, you may find it helpful. Happy to answer questions here.

Alex Smith

72,510 次观看 • 9 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 • 25 天前

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.

Tero Parviainen

132,221 次观看 • 1 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 • 5 个月前

Robinhood CEO Vlad Tenev believes mathematical superintelligence could eliminate software bugs altogether. "Math skills and coding actually go hand in hand... In the same way that MSI can be used to make sure that your math is correct, when you have a computer program or a piece of software, it could be used to make sure that's correct and that there are no mistakes." "Rather than it being a cat-and-mouse game of escalating model capabilities, finding breaches and preventing breaches from happening, verification and proof that software is immune to these types of bugs, I think is the future."

Robinhood CEO Vlad Tenev believes mathematical superintelligence could eliminate software bugs altogether. "Math skills and coding actually go hand in hand... In the same way that MSI can be used to make sure that your math is correct, when you have a computer program or a piece of software, it could be used to make sure that's correct and that there are no mistakes." "Rather than it being a cat-and-mouse game of escalating model capabilities, finding breaches and preventing breaches from happening, verification and proof that software is immune to these types of bugs, I think is the future."

TBPN

64,506 次观看 • 29 天前

Common Core math was introduced in 2010 to address standards across the U.S. and shift the focus from rote memorization to a deeper, conceptual understanding of mathematics. By 2026, it remains a common standard in many states, aiming to prepare students for college and the modern workforce by fostering critical thinking and number sense rather than just memorizing formulas. There has been much debate on using common core math in schools curriculum. Do you agree with using common core math in schools? Or do you think the old way of doing math was the better way to teach math to children?

Common Core math was introduced in 2010 to address standards across the U.S. and shift the focus from rote memorization to a deeper, conceptual understanding of mathematics. By 2026, it remains a common standard in many states, aiming to prepare students for college and the modern workforce by fostering critical thinking and number sense rather than just memorizing formulas. There has been much debate on using common core math in schools curriculum. Do you agree with using common core math in schools? Or do you think the old way of doing math was the better way to teach math to children?

🌸𝓐𝓾𝓭𝓻𝓮𝔂🌸

60,861 次观看 • 3 个月前

How it started vs How it's going... Exactly 19 years ago this week in August 2007, my very first book was published: "Math Doesn't Suck" - making the subject fun & relatable to middle school girls, and calling them to embrace their smarts. Now, 12 books and nearly 20 years later, I continue to advocate for math education through speaking engagements and more. A far cry from my days of eye-rolling Geometry in the early 90's from my school trailer in the set of "The Wonder Years." 😁 . . Hey, anyone know who is interviewing me in that first clip? Super OG! 🤗 . . McKellar Math #smartisthenewcool #ifykyk

How it started vs How it's going... Exactly 19 years ago this week in August 2007, my very first book was published: "Math Doesn't Suck" - making the subject fun & relatable to middle school girls, and calling them to embrace their smarts. Now, 12 books and nearly 20 years later, I continue to advocate for math education through speaking engagements and more. A far cry from my days of eye-rolling Geometry in the early 90's from my school trailer in the set of "The Wonder Years." 😁 . . Hey, anyone know who is interviewing me in that first clip? Super OG! 🤗 . . McKellar Math #smartisthenewcool #ifykyk

Danica McKellar

15,084 次观看 • 21 天前

The origin story of Eurisko, the super-advanced math/CS track that I and Jason Roberts developed within Math Academy's original school program, that took high school students all the way up to reproducing academic research papers in artificial intelligence, building everything from scratch in Python. During its operation from 2020-23, Eurisko was the most advanced high school math/CS track in the USA. Students didn’t just import off-the-shelf libraries to complete run-of-the-mill projects. They actually implemented neural networks, backpropagation, game trees, evolutionary algorithms, you name it, from scratch. It’s still early and the first Eurisko cohort is still in college, but there have already been some amazing student outcomes in terms of college admissions, accelerated graduate degrees, research publications, and science fairs. For instance, the year after completing the Eurisko curriculum, one high schooler leveraged his quantitative coding chops to conduct and publish career-kickstarting research that “revealed 1.5 million previously unknown objects in space, broadened the potential of a NASA mission” (to quote Caltech), and won last year's Regeneron Science Talent Search ($250,000). The goal of Eurisko was for students to reach a high enough level of skill that they could capitalize on some math/coding-related opportunity and turn it into a chain reaction of fortunate events. And it’s so great to witness some of these chain reactions get underway. But the best part is that we're gradually able to do more and more of this at scale. We're taking everything we've learned from doing math/coding talent development manually, and building it into our online system, to make it available to the whole world. (Link to further reading in the comments)

The origin story of Eurisko, the super-advanced math/CS track that I and Jason Roberts developed within Math Academy's original school program, that took high school students all the way up to reproducing academic research papers in artificial intelligence, building everything from scratch in Python. During its operation from 2020-23, Eurisko was the most advanced high school math/CS track in the USA. Students didn’t just import off-the-shelf libraries to complete run-of-the-mill projects. They actually implemented neural networks, backpropagation, game trees, evolutionary algorithms, you name it, from scratch. It’s still early and the first Eurisko cohort is still in college, but there have already been some amazing student outcomes in terms of college admissions, accelerated graduate degrees, research publications, and science fairs. For instance, the year after completing the Eurisko curriculum, one high schooler leveraged his quantitative coding chops to conduct and publish career-kickstarting research that “revealed 1.5 million previously unknown objects in space, broadened the potential of a NASA mission” (to quote Caltech), and won last year's Regeneron Science Talent Search ($250,000). The goal of Eurisko was for students to reach a high enough level of skill that they could capitalize on some math/coding-related opportunity and turn it into a chain reaction of fortunate events. And it’s so great to witness some of these chain reactions get underway. But the best part is that we're gradually able to do more and more of this at scale. We're taking everything we've learned from doing math/coding talent development manually, and building it into our online system, to make it available to the whole world. (Link to further reading in the comments)

Justin Skycak

14,542 次观看 • 10 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 • 5 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 • 6 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

2,293,582 次观看 • 7 个月前

This is a day in the life of a Flat Earther You tell us your math We show you real life examples of how your math doesn’t fit reality You throw in some excuses that don’t explain anything while simultaneously refusing to actually look at the evidence Because science dudes! 😎

This is a day in the life of a Flat Earther You tell us your math We show you real life examples of how your math doesn’t fit reality You throw in some excuses that don’t explain anything while simultaneously refusing to actually look at the evidence Because science dudes! 😎

Ted Logan

89,127 次观看 • 3 年前

Jordi: It seems pretty obvious that the models just getting smarter is not by default going to make adoption accelerate massively again. If you're a business that's not doing code-gen, not generating a bunch of assets, etc. - and somebody says, "For $20 a month, you get someone that's PhD level in math, but extremely low agency." A laundromat would be like, "Actually, I don't need somebody who's PhD level at math. Sir this is a laundromat."

Jordi: It seems pretty obvious that the models just getting smarter is not by default going to make adoption accelerate massively again. If you're a business that's not doing code-gen, not generating a bunch of assets, etc. - and somebody says, "For $20 a month, you get someone that's PhD level in math, but extremely low agency." A laundromat would be like, "Actually, I don't need somebody who's PhD level at math. Sir this is a laundromat."

TBPN

76,844 次观看 • 8 个月前

This specific step when factoring by grouping was a core memory of mine in high school math where I just memorized what to do and didn't understand what was happening. Here's how we can make sense of it. What did you memorize in math but didn't understand?

This specific step when factoring by grouping was a core memory of mine in high school math where I just memorized what to do and didn't understand what was happening. Here's how we can make sense of it. What did you memorize in math but didn't understand?

Howie Hua

15,953 次观看 • 1 年前