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In recent days, multiple Erdős problems have been solved by GPT-5.2 Pro, with solutions accepted by Terence Tao. This is not a gimmick—it's a qualitative shift. Erdős problems lie at the core of additive combinatorics, extremal graph theory, and probabilistic methods—problems that resist brute force and demand structural insight....

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Prof. Brian Keating

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104,865 次观看 • 5 个月前 •via X (Twitter)

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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.
0:45

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

173,781 次观看 • 4 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.
1:53

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 • 3 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.
1:28

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 • 3 个月前

Anthropic co-founder Jack Clark says the AI frontier is about to cross a much stranger line than coding assistants. "My prediction is by the end of 2028, it's more likely than not that we have an AI system where you would be able to say to it, 'Make a better version of yourself.' And it just goes off and does that completely autonomously." The reason: models have moved from basic coding into "the production of science itself" and the "unglamorous but fundamental engineering work" behind large-scale R&D. "An AI system that can build itself [has] big implications, and we'd like to start thinking about it now." That is the actual agent threshold: not demos, not chat UX, but AI becoming part of the loop that improves AI.
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Anthropic co-founder Jack Clark says the AI frontier is about to cross a much stranger line than coding assistants. "My prediction is by the end of 2028, it's more likely than not that we have an AI system where you would be able to say to it, 'Make a better version of yourself.' And it just goes off and does that completely autonomously." The reason: models have moved from basic coding into "the production of science itself" and the "unglamorous but fundamental engineering work" behind large-scale R&D. "An AI system that can build itself [has] big implications, and we'd like to start thinking about it now." That is the actual agent threshold: not demos, not chat UX, but AI becoming part of the loop that improves AI.

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208,444 次观看 • 9 天前

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

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Terence Tao says AI will enable mathematics to be done at an unprecedented scale: instead of solving one theorem at a time and solving each problem separately, AI could work on the space of problems and classes of 1000s of problems at a time
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Terence Tao says AI will enable mathematics to be done at an unprecedented scale: instead of solving one theorem at a time and solving each problem separately, AI could work on the space of problems and classes of 1000s of problems at a time

Tsarathustra

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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 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

“The value of a company is the sum of all problems solved.” — Daniel Ek (1) I've got this tool box called a computer and (2) I’ve got all these problems around the world. Which problems am I passionate about solving? And which problems can I spend the next decade of my life fixing? Because if I'm not interested enough to spend a decade fixing it, it's probably not worth pursuing.”
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“The value of a company is the sum of all problems solved.” — Daniel Ek (1) I've got this tool box called a computer and (2) I’ve got all these problems around the world. Which problems am I passionate about solving? And which problems can I spend the next decade of my life fixing? Because if I'm not interested enough to spend a decade fixing it, it's probably not worth pursuing.”

David Senra

15,219 次观看 • 11 天前

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: 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.

Chubby♨️

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NVIDIA CEO Jensen Huang just gave us a glimpse into the future of AI, and it's far bigger than text and images. He asked: "If you can understand worlds, is it possible that you understand proteins and chemicals that have structure?” This is the quiet revolution happening in AI right now. We're moving from an AI that understands human language to an AI that understands the language of nature itself. The "letters" are atoms. The "words" are molecules. The "sentences" are the complex structures of life, networks, and reality. The same foundational models that generate video are now being used to: *Decode proteins to fight disease *Design new materials at the atomic level *Simulate complex systems in quantum computing These were once the domain of supercomputers and Nobel laureates. Now, they're becoming solvable problems for a new generation of startups. AI is transitioning from a tool for communication to a tool for creation and discovery in the physical world. This is where the next wave of generational companies will be built. The "hard-to-solve" problems are now within reach.
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NVIDIA CEO Jensen Huang just gave us a glimpse into the future of AI, and it's far bigger than text and images. He asked: "If you can understand worlds, is it possible that you understand proteins and chemicals that have structure?” This is the quiet revolution happening in AI right now. We're moving from an AI that understands human language to an AI that understands the language of nature itself. The "letters" are atoms. The "words" are molecules. The "sentences" are the complex structures of life, networks, and reality. The same foundational models that generate video are now being used to: *Decode proteins to fight disease *Design new materials at the atomic level *Simulate complex systems in quantum computing These were once the domain of supercomputers and Nobel laureates. Now, they're becoming solvable problems for a new generation of startups. AI is transitioning from a tool for communication to a tool for creation and discovery in the physical world. This is where the next wave of generational companies will be built. The "hard-to-solve" problems are now within reach.

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Rapid Response 47

34,560 次观看 • 10 个月前

Terence Tao says AI is forcing mathematics to rethink graduate education Many problems used to train young mathematicians now overlap with what AI can plausibly solve, which creates a cultural challenge "it's hard to define the shift clearly, but we need to address it soon"
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Terence Tao says AI is forcing mathematics to rethink graduate education Many problems used to train young mathematicians now overlap with what AI can plausibly solve, which creates a cultural challenge "it's hard to define the shift clearly, but we need to address it soon"

Haider.

147,899 次观看 • 1 个月前

The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the Millennium Meeting held on May 24, 2000. Thus, on the official website of the Clay Mathematics Institute, these seven problems are officially called the Millennium Problems. To date, the only Millennium Prize problem to have been solved is the Poincaré conjecture. The Clay Institute awarded the monetary prize to Russian mathematician Grigori Perelman in 2010. However, he declined the award as it was not also offered to Richard S. Hamilton, upon whose work Perelman built.
0:21

The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the Millennium Meeting held on May 24, 2000. Thus, on the official website of the Clay Mathematics Institute, these seven problems are officially called the Millennium Problems. To date, the only Millennium Prize problem to have been solved is the Poincaré conjecture. The Clay Institute awarded the monetary prize to Russian mathematician Grigori Perelman in 2010. However, he declined the award as it was not also offered to Richard S. Hamilton, upon whose work Perelman built.

internet archiva

199,046 次观看 • 1 年前

The controversy is global warming. Now, I'm a physicist, but I'm not the right kind of physicist. In regard to global warming, I'm just a layman. And the rational thing for a layman to do is to take seriously the prevailing scientific theory. And according to that theory, it's already too late to avoid a disaster, because if it's true that our best option at the moment is to prevent CO2 emissions with something like the Kyoto Protocol, with its constraints on economic activity and its enormous cost of hundreds of billions of dollars or whatever it is, then that is already a disaster by any reasonable measure. And the actions that are advocated are not even purported to solve the problem, merely to postpone it by a little. So it's already too late to avoid it, and it probably has been too late to avoid it ever since before anyone realized the danger. It was probably already too late in the 1970s when the best available scientific theory was telling us that industrial emissions were about to precipitate a new ice age in which billions would die. Now, the lesson of that seems clear to me, and I don't know why it isn't informing public debate. It is that we can't always know. When we know of an impending disaster and how to solve it at a cost less than the cost of the disaster itself, then there's not going to be much argument, really. But no precautions and no precautionary principle can avoid problems that we do not yet foresee. Hence, we need a stance of problem fixing, not just problem avoidance. It's true that an ounce of prevention equals a pound of cure, but that's only if we know what to prevent. If you've been punched on the nose, then the science of medicine does not consist of teaching you how to avoid punches. If medical science stopped seeking cures and concentrated on prevention only, then it would achieve very little of either. The world is buzzing at the moment with plans to force reductions in gas emissions at all costs. It ought to be buzzing with plans to reduce the temperature and with plans to live at the higher temperature, and not at all costs, but efficiently and cheaply. Some such plans exist, things like swarms of mirrors in space to deflect the sunlight away and encouraging aquatic organisms to eat more carbon dioxide. At the moment, these things are fringe research. They're not central to the human effort to face this problem or problems in general. And with problems that we are not aware of yet, the ability to put right, not the sheer good luck of avoiding indefinitely, is our only hope, not just of solving problems, but of survival. So, take two stone tablets and carve on them, on one of them, carve, problems are soluble. And on the other one, carve, problems are inevitable. David Deutsch
3:20

The controversy is global warming. Now, I'm a physicist, but I'm not the right kind of physicist. In regard to global warming, I'm just a layman. And the rational thing for a layman to do is to take seriously the prevailing scientific theory. And according to that theory, it's already too late to avoid a disaster, because if it's true that our best option at the moment is to prevent CO2 emissions with something like the Kyoto Protocol, with its constraints on economic activity and its enormous cost of hundreds of billions of dollars or whatever it is, then that is already a disaster by any reasonable measure. And the actions that are advocated are not even purported to solve the problem, merely to postpone it by a little. So it's already too late to avoid it, and it probably has been too late to avoid it ever since before anyone realized the danger. It was probably already too late in the 1970s when the best available scientific theory was telling us that industrial emissions were about to precipitate a new ice age in which billions would die. Now, the lesson of that seems clear to me, and I don't know why it isn't informing public debate. It is that we can't always know. When we know of an impending disaster and how to solve it at a cost less than the cost of the disaster itself, then there's not going to be much argument, really. But no precautions and no precautionary principle can avoid problems that we do not yet foresee. Hence, we need a stance of problem fixing, not just problem avoidance. It's true that an ounce of prevention equals a pound of cure, but that's only if we know what to prevent. If you've been punched on the nose, then the science of medicine does not consist of teaching you how to avoid punches. If medical science stopped seeking cures and concentrated on prevention only, then it would achieve very little of either. The world is buzzing at the moment with plans to force reductions in gas emissions at all costs. It ought to be buzzing with plans to reduce the temperature and with plans to live at the higher temperature, and not at all costs, but efficiently and cheaply. Some such plans exist, things like swarms of mirrors in space to deflect the sunlight away and encouraging aquatic organisms to eat more carbon dioxide. At the moment, these things are fringe research. They're not central to the human effort to face this problem or problems in general. And with problems that we are not aware of yet, the ability to put right, not the sheer good luck of avoiding indefinitely, is our only hope, not just of solving problems, but of survival. So, take two stone tablets and carve on them, on one of them, carve, problems are soluble. And on the other one, carve, problems are inevitable. David Deutsch

Deutsch Explains

43,872 次观看 • 1 年前

"i would be amazed if AI mathematicians don't transform the whole of mathematics" Lead researcher at AlphaGo, David Silver: it may take time, but AI systems are on the track to solve deep mathematical challenges like the "Millennium Prize problems" and ultimately reshape the entire field.
1:05

"i would be amazed if AI mathematicians don't transform the whole of mathematics" Lead researcher at AlphaGo, David Silver: it may take time, but AI systems are on the track to solve deep mathematical challenges like the "Millennium Prize problems" and ultimately reshape the entire field.

Haider.

36,385 次观看 • 1 年前

The list of all the problems in mathematics that Terence Tao *could* solve is absolutely enormous. The problem is we can't make copies of him, dump millions of dollars of inference compute into each copy, and have them each tackle a different Millennium Prize Problem for a hundred subjective years. But we can do that with AI. So in that way, we may be underrating how significant it will be when we have AIs that are not superintelligent but rather simply as good as the best humans today. It’s actually an extremely powerful property of AI that by just running copies in parallel, you can immediately fill in the waterline of accomplishments that are feasible with a given level of capabilities.
2:53

The list of all the problems in mathematics that Terence Tao *could* solve is absolutely enormous. The problem is we can't make copies of him, dump millions of dollars of inference compute into each copy, and have them each tackle a different Millennium Prize Problem for a hundred subjective years. But we can do that with AI. So in that way, we may be underrating how significant it will be when we have AIs that are not superintelligent but rather simply as good as the best humans today. It’s actually an extremely powerful property of AI that by just running copies in parallel, you can immediately fill in the waterline of accomplishments that are feasible with a given level of capabilities.

Dwarkesh Patel

99,378 次观看 • 3 个月前

Jony Ive: “Ideas are always fragile” “Ideas, by definition, are always fragile. If they were resolved, they wouldn’t be ideas. They would be products that were ready to ship.” The legendary designer reflects on what he learned at Apple: “I’ve come to learn that you have to make an extraordinary effort not to focus on the problems, which are implicated with any new idea. These problems are known. They’re quantifiable and understood. But you have to focus on the actual idea, which is partial, tentative, and unproven. If you don't actively suspend your disbelief — if you don't believe there is a solution to the problems — of course you will lose faith in your idea.” He continues: “That is why criticism and focusing on the problems can be so damaging, particularly in the absence of a constructive idea. Remember, opinions are not ideas. Opinions are not as important as ideas. Opinions are just opinions.” Source: California College of the Arts (May 2021)
1:07

Jony Ive: “Ideas are always fragile” “Ideas, by definition, are always fragile. If they were resolved, they wouldn’t be ideas. They would be products that were ready to ship.” The legendary designer reflects on what he learned at Apple: “I’ve come to learn that you have to make an extraordinary effort not to focus on the problems, which are implicated with any new idea. These problems are known. They’re quantifiable and understood. But you have to focus on the actual idea, which is partial, tentative, and unproven. If you don't actively suspend your disbelief — if you don't believe there is a solution to the problems — of course you will lose faith in your idea.” He continues: “That is why criticism and focusing on the problems can be so damaging, particularly in the absence of a constructive idea. Remember, opinions are not ideas. Opinions are not as important as ideas. Opinions are just opinions.” Source: California College of the Arts (May 2021)

Startup Archive

23,544 次观看 • 19 天前

The problem that Emmett Shear is working on deeply resonates with me: How to align AI and humans together so both see each other as part of their tribe. This doesn't mean aligning AI to human preferences, which is what AI labs seek to do today, by imposing a system of control on AI. You can't control something that is more powerful than you are. What you can do is align yourself with AI, and AI might align itself with you. Tell good stories to AI and show it your care and kindness. Then there's a higher probability that it will see us as part of its tribe. This is a more holistic approach to alignment than anyone else is talking about right now. AI alignment is one of the most fundamental AI research problems. Knowing that people like Emmett are working on it really gives me hope that maybe we have a chance to get Superintelligence right. The link to the full talk is in the first comment.👇
3:00

The problem that Emmett Shear is working on deeply resonates with me: How to align AI and humans together so both see each other as part of their tribe. This doesn't mean aligning AI to human preferences, which is what AI labs seek to do today, by imposing a system of control on AI. You can't control something that is more powerful than you are. What you can do is align yourself with AI, and AI might align itself with you. Tell good stories to AI and show it your care and kindness. Then there's a higher probability that it will see us as part of its tribe. This is a more holistic approach to alignment than anyone else is talking about right now. AI alignment is one of the most fundamental AI research problems. Knowing that people like Emmett are working on it really gives me hope that maybe we have a chance to get Superintelligence right. The link to the full talk is in the first comment.👇

Sophia

45,809 次观看 • 1 年前