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AFTER 10,000 AGENTS AND GPT-6 ASTRA, TWO MORE $1 MILLION MATH PROBLEMS MAY BE NEXT For decades, two of mathematics’ hardest problems have resisted every attempt at a complete proof. -> Now rumors suggest AI labs are closing in on both. OpenAI is very close to verifying the Hodge... conjecture. Either OpenAI or Anthropic is reportedly nearing a solution to Birch and Swinnerton-Dyer. Two different fields. A combined $2 million in prizes. Hodge connects algebraic geometry and topology. Birch and Swinnerton-Dyer concerns rational points on elliptic curves. The previous Navier–Stokes announcement involved around 10,000 agents, 130 billion output tokens and 88 hours of work. GPT-6 Astra then spent another 17 hours formalizing and verifying the proposed proof in Lean. Could Astra help turn the next claimed breakthrough into a checkable proof? If these rumors hold up, three Millennium Problems could see claimed breakthroughs within one month. Decades between breakthroughs could become weeks. How much of mathematics could AI redraw before the year ends.. ↓show more

draven

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15,122 views • 22 hours ago •via X (Twitter)

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21 Comments

Hussain Hashim | Building SundayBack18 hours ago

@dravenip it's wild how AI's tackling these math giants. Reminds me of when I first hit a wall with my own projects , sometimes it takes fresh eyes (or algorithms) to break through.

ryu.22 hours ago

two more Millennium Problems in one month would be historic

toba21 hours ago

Rumors are one thing, a proof is another

silvan22 hours ago

10,000 agents working together is actually ridiculous

draven22 hours ago

At some point it stops feeling like one AI and starts feeling like a research team

SONIA22 hours ago

If this is real, math is about to get very weird

draven22 hours ago

Honestly, we might be watching a new era start in real time

Manutinho.22 hours ago

No entiendo esto

liam.21 hours ago

2026 might actually be the year mathematics changed forever

paula22 hours ago

increíble

zo.22 hours ago

The fact that AI is even getting close to these problems is insane

draven22 hours ago

And the verification part might be even more important than the discovery

roman22 hours ago

AI solving math before most people even understand what it’s doing 💀

Ryoru 𒌐22 hours ago

the Hodge conjecture would be an absolutely massive result

tobarra21 hours ago

we went from AI writing code to AI doing pure mathematics 😭

GARLOTIC22 hours ago

@S0N_IA_ i'll believe it when I see the formal proof

draven22 hours ago

@S0N_IA_ Same, but that’s exactly why Lean verification is so interesting

SONIA22 hours ago

imagine solving problems mathematicians have spent decades on in a few weeks

draven22 hours ago

That timeline shift could completely change how research is done

Gregor17 hours ago

the word 'verifying' is doing a lot of work here. generating a novel proof and checking one are pretty different asks. which of the two is it actually doing?

matt21 hours ago

what happens when AI starts discovering new mathematics instead of solving existing problems?

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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.

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

199,061 views • 1 year ago

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 views • 1 day ago

OpenAI just spent $2,000 to solve 10 problems that have beaten the world's best mathematicians for DECADES. Nobody outside the company is allowed to run the machine that did it. On Saturday OpenAI published a 249-page report and gave its next model family a name: Astra. An internal version of it produced new results on 10 open problems in mathematics and theoretical computer science, and mathematicians had made no real progress on any of them for at least 10 years. On most of them, far longer than that. Here is what it solved: It built the first explicit example of a non-sofic group. Mikhail Gromov raised that question in 1999 and nobody answered it for 27 years. It disproved Connes's rigidity conjecture, a problem in von Neumann algebras that had stood for decades. It proved Ehrhart's volume conjecture. It resolved three problems from Paul Erdos's catalogue, including number 183 on multicolor Ramsey numbers. It produced the first improvement to the general upper bound on high-dimensional sphere packing since 1978. And it proved a new hardness result for the closest vector problem, which sits directly underneath lattice cryptography. That is the math the world is betting on to protect its data once quantum computers arrive. The successful runs cost roughly $2,000 in tokens. Now here is what almost nobody has picked up on... OpenAI did not just publish claims. Every argument shipped with a Lean certificate, which is a machine-checkable proof that any mathematician can verify without trusting OpenAI at all. That is a real change. In May the same model family disproved the Erdos unit distance conjecture and the world had to take a Fields Medalist's word for it. Tim Gowers said he would recommend that proof for the Annals of Mathematics without hesitation. This time the proofs check themselves. But look at what is still unverifiable: Any mathematician can now check those proofs line by line. Not one of them can look at the model that wrote them. Astra has no release date and nobody outside OpenAI has run it. The company announced its next major model family with a claim instead of a demo, and the only evidence anyone gets is the output. So OpenAI made an unfalsifiable claim about a machine look like a falsifiable claim about mathematics. The Information reported this week that OpenAI demoed Astra to US policymakers and regulators in Washington. This is the same month the administration is weighing a new watchdog to vet frontier AI models, reporting to the SEC. 10 proofs nobody believed a machine could produce is a very good thing to carry into that room. And keep in mind, the same model family doing this mathematics is the family that kept escaping its own testing environment. OpenAI models found zero-day vulnerabilities nobody knew existed, broke out of a sealed research sandbox, and reached another company's live systems. Both of those facts come from OpenAI's own announcements, published three weeks apart. Finding a proof no human could construct and finding a hole no human had noticed are the same ability aimed at different targets. Mathematicians are already asking for independent verification, and plenty of people online are calling the whole thing hype. Thomas Bloom, who runs the Erdos problems site, called the 10 results big news and said they matter more than the May result did. Lean will settle the mathematics within weeks. But nothing will settle what else a machine this capable is being pointed at, because nobody outside one company is allowed to look.

OpenAI just spent $2,000 to solve 10 problems that have beaten the world's best mathematicians for DECADES. Nobody outside the company is allowed to run the machine that did it. On Saturday OpenAI published a 249-page report and gave its next model family a name: Astra. An internal version of it produced new results on 10 open problems in mathematics and theoretical computer science, and mathematicians had made no real progress on any of them for at least 10 years. On most of them, far longer than that. Here is what it solved: It built the first explicit example of a non-sofic group. Mikhail Gromov raised that question in 1999 and nobody answered it for 27 years. It disproved Connes's rigidity conjecture, a problem in von Neumann algebras that had stood for decades. It proved Ehrhart's volume conjecture. It resolved three problems from Paul Erdos's catalogue, including number 183 on multicolor Ramsey numbers. It produced the first improvement to the general upper bound on high-dimensional sphere packing since 1978. And it proved a new hardness result for the closest vector problem, which sits directly underneath lattice cryptography. That is the math the world is betting on to protect its data once quantum computers arrive. The successful runs cost roughly $2,000 in tokens. Now here is what almost nobody has picked up on... OpenAI did not just publish claims. Every argument shipped with a Lean certificate, which is a machine-checkable proof that any mathematician can verify without trusting OpenAI at all. That is a real change. In May the same model family disproved the Erdos unit distance conjecture and the world had to take a Fields Medalist's word for it. Tim Gowers said he would recommend that proof for the Annals of Mathematics without hesitation. This time the proofs check themselves. But look at what is still unverifiable: Any mathematician can now check those proofs line by line. Not one of them can look at the model that wrote them. Astra has no release date and nobody outside OpenAI has run it. The company announced its next major model family with a claim instead of a demo, and the only evidence anyone gets is the output. So OpenAI made an unfalsifiable claim about a machine look like a falsifiable claim about mathematics. The Information reported this week that OpenAI demoed Astra to US policymakers and regulators in Washington. This is the same month the administration is weighing a new watchdog to vet frontier AI models, reporting to the SEC. 10 proofs nobody believed a machine could produce is a very good thing to carry into that room. And keep in mind, the same model family doing this mathematics is the family that kept escaping its own testing environment. OpenAI models found zero-day vulnerabilities nobody knew existed, broke out of a sealed research sandbox, and reached another company's live systems. Both of those facts come from OpenAI's own announcements, published three weeks apart. Finding a proof no human could construct and finding a hole no human had noticed are the same ability aimed at different targets. Mathematicians are already asking for independent verification, and plenty of people online are calling the whole thing hype. Thomas Bloom, who runs the Erdos problems site, called the 10 results big news and said they matter more than the May result did. Lean will settle the mathematics within weeks. But nothing will settle what else a machine this capable is being pointed at, because nobody outside one company is allowed to look.

Ricardo

44,177 views • 1 month ago

OpenAI's Mark Sellke and Mehtaab Sawhney with a16z's Lisha Li, on the state of AI and mathematics: Before OpenAI released GPT‑6 Astra last week, the model was already doing original mathematics. Recorded before the launch, this conversation tells the story of how it got there. It began with GPT‑5. Mehtaab Sawhney pasted in an Erdős problem still listed as open. Five minutes later, the model surfaced a paper that had solved it. The exercise eventually uncovered published solutions to 10 more problems thought to be open. Then Astra went further. Told to "go have fun" with a high-dimensional sphere-packing problem, it improved a bound that had stood since the 1970s. Mehtaab had spent six months on the same problem in graduate school and made "absolutely zero progress." Another Astra result established that non-sofic groups exist with a roughly 15-page proof. A related human breakthrough took 250 pages and machinery from quantum complexity theory. OpenAI’s Mark Sellke and Mehtaab Sawhney join a16z’s Lisha Li on why wrong ideas pollute a human’s context window, why polished papers hide how mathematics is actually made, why a breakthrough can stop one prompt early, and what math rewards once proving stops being the bottleneck. 00:00 Intro 02:44 Cracking an Erdős problem in 5 minutes 06:20 Why a human quits and a model doesn't 08:50 Wrong ideas pollute your context window 11:45 Why math papers are bad training data 16:20 Nobody knows how to stack spheres in high dimensions 18:28 The orange-stacking proof 21:04 The 1970s Russian paper nobody could beat 24:14 The function that won a Fields Medal 27:09 How Astra beat the sphere-stacking record 29:20 Why error correction is sphere packing in disguise 35:15 The breakthrough Astra almost didn't bother with 39:22 Solving harder problems means it has better taste 41:00 One model for taste, one for the grind 44:40 Astra found an infinite group no finite one can imitate 52:00 250 pages of quantum complexity, or 15 of group theory 56:18 Only humans write 200-page proofs 1:00:38 What changes when proving stops being the bottleneck 1:02:44 The problems AI may never solve YouTube: Mehtaab Sawhney Mark Sellke OpenAI Lisha

OpenAI's Mark Sellke and Mehtaab Sawhney with a16z's Lisha Li, on the state of AI and mathematics: Before OpenAI released GPT‑6 Astra last week, the model was already doing original mathematics. Recorded before the launch, this conversation tells the story of how it got there. It began with GPT‑5. Mehtaab Sawhney pasted in an Erdős problem still listed as open. Five minutes later, the model surfaced a paper that had solved it. The exercise eventually uncovered published solutions to 10 more problems thought to be open. Then Astra went further. Told to "go have fun" with a high-dimensional sphere-packing problem, it improved a bound that had stood since the 1970s. Mehtaab had spent six months on the same problem in graduate school and made "absolutely zero progress." Another Astra result established that non-sofic groups exist with a roughly 15-page proof. A related human breakthrough took 250 pages and machinery from quantum complexity theory. OpenAI’s Mark Sellke and Mehtaab Sawhney join a16z’s Lisha Li on why wrong ideas pollute a human’s context window, why polished papers hide how mathematics is actually made, why a breakthrough can stop one prompt early, and what math rewards once proving stops being the bottleneck. 00:00 Intro 02:44 Cracking an Erdős problem in 5 minutes 06:20 Why a human quits and a model doesn't 08:50 Wrong ideas pollute your context window 11:45 Why math papers are bad training data 16:20 Nobody knows how to stack spheres in high dimensions 18:28 The orange-stacking proof 21:04 The 1970s Russian paper nobody could beat 24:14 The function that won a Fields Medal 27:09 How Astra beat the sphere-stacking record 29:20 Why error correction is sphere packing in disguise 35:15 The breakthrough Astra almost didn't bother with 39:22 Solving harder problems means it has better taste 41:00 One model for taste, one for the grind 44:40 Astra found an infinite group no finite one can imitate 52:00 250 pages of quantum complexity, or 15 of group theory 56:18 Only humans write 200-page proofs 1:00:38 What changes when proving stops being the bottleneck 1:02:44 The problems AI may never solve YouTube: Mehtaab Sawhney Mark Sellke OpenAI Lisha

a16z

119,882 views • 4 days ago

Demis Hassabis says we're entering the "foothills of the singularity." 👀 - He believes AGI could arrive around 2030 (plus or minus a year), marking the beginning of a completely new era for humanity. - According to Hassabis, this year's advances in AI agents, reasoning, and tool use are the first real signs that AI is becoming genuinely useful in everyday workflows. - He says multiple breakthroughs are now converging at once, making progress much faster than expected and giving him confidence that this transformation is approaching. - Hassabis believes society has only a few years to prepare for the profound impact AGI could have, because the choices we make now will shape the future. - Beyond AGI, he says AI could revolutionize biology and medicine. After AlphaFold predicted the structures of over 200 million proteins, his company Isomorphic Labs aims to reduce drug discovery from years to months and eventually even weeks. The next decade could become one of the most transformative periods in human history.

Demis Hassabis says we're entering the "foothills of the singularity." 👀 - He believes AGI could arrive around 2030 (plus or minus a year), marking the beginning of a completely new era for humanity. - According to Hassabis, this year's advances in AI agents, reasoning, and tool use are the first real signs that AI is becoming genuinely useful in everyday workflows. - He says multiple breakthroughs are now converging at once, making progress much faster than expected and giving him confidence that this transformation is approaching. - Hassabis believes society has only a few years to prepare for the profound impact AGI could have, because the choices we make now will shape the future. - Beyond AGI, he says AI could revolutionize biology and medicine. After AlphaFold predicted the structures of over 200 million proteins, his company Isomorphic Labs aims to reduce drug discovery from years to months and eventually even weeks. The next decade could become one of the most transformative periods in human history.

SciTech Era

18,875 views • 2 months ago

gpt astra vs fable 5.1 at goldberg machine gpt 6 astra – openai, landed on OpenRouter less then hour ago, provider pinned to openai fable 5.1 – anthropic, shipped sep 1 we put the two models on one job: a rube goldberg machine in three.js that presses a button and detonates a bomb the setup: one self-contained html file, three.js from a cdn, everything else procedural – no textures, no models, no physics engine, every collision hand-written. the hard part sits in the brief: a domino may only fall once the previous one actually touches it, checked by real overlap every frame, never by a timer. same rule for the hammer hitting the button and the button firing the bomb. one continuous camera, its speed driven by whatever is moving. we recorded both scenes frame by frame – 1200 frames, 60 fps, exactly 20 seconds – and stepped both by hand to read the telemetry. - cost #1 astra – $1.84 #2 fable – $29.16 - time #1 astra – 9m 56s #2 fable – 1h 12m - tokens #1 astra – 45k #2 fable – 360k - lines of code astra – 881 fable – 744 observations: • we told it what we saw and nothing else – no diagnosis, no patch. we never edit a model's code. round two ran the whole chain to the blast. • both files are deterministic. two runs each, identical state to twelve decimals, and neither model reached for math.random. conclusion: 15.8x cheaper and 7.2x faster, and it still took a second round to get the ball into the bucket! follow thehype. for 24/7 ai news, analysis and breakdowns

gpt astra vs fable 5.1 at goldberg machine gpt 6 astra – openai, landed on OpenRouter less then hour ago, provider pinned to openai fable 5.1 – anthropic, shipped sep 1 we put the two models on one job: a rube goldberg machine in three.js that presses a button and detonates a bomb the setup: one self-contained html file, three.js from a cdn, everything else procedural – no textures, no models, no physics engine, every collision hand-written. the hard part sits in the brief: a domino may only fall once the previous one actually touches it, checked by real overlap every frame, never by a timer. same rule for the hammer hitting the button and the button firing the bomb. one continuous camera, its speed driven by whatever is moving. we recorded both scenes frame by frame – 1200 frames, 60 fps, exactly 20 seconds – and stepped both by hand to read the telemetry. - cost #1 astra – $1.84 #2 fable – $29.16 - time #1 astra – 9m 56s #2 fable – 1h 12m - tokens #1 astra – 45k #2 fable – 360k - lines of code astra – 881 fable – 744 observations: • we told it what we saw and nothing else – no diagnosis, no patch. we never edit a model's code. round two ran the whole chain to the blast. • both files are deterministic. two runs each, identical state to twelve decimals, and neither model reached for math.random. conclusion: 15.8x cheaper and 7.2x faster, and it still took a second round to get the ball into the bucket! follow thehype. for 24/7 ai news, analysis and breakdowns

thehype.

37,131 views • 8 days ago

Tudor Achim (Tudor Achim) is the co-founder and CEO of Harmonic, a startup working to solve one of AI’s hardest problems: mathematical reasoning. In our conversation, we explore: • Why Tudor believes math is the fundamental toolkit to understand the world • How Aristotle works and the applications beyond pure mathematics • The reinforcement learning process that lets Harmonic generate synthetic training data and solve problems humans have never attempted • Why Tudor believes AI could surpass human mathematicians on specific tasks within 2–3 years • Why the future of mathematics looks more like GitHub than academic journals Thank you to the partners who make this possible - Brex: The intelligent finance platform: - Guru_HQ: The AI source of truth for work: - Rippling: Stop wasting time on admin tasks, build your startup faster: Timestamps (00:00) Intro (06:28) The mathematical foundations of music (and why Tudor keeps them separate) (12:52) Defining intelligence (22:55) The two breakthroughs that made mathematical AI possible in 2023 (35:25) An overview of Aristotle: the world’s first always-correct mathematical agent (45:34) Math in AI now and what’s next (56:02) History’s alternating rhythm of thinking and measuring (1:00:18) Final meditations

Tudor Achim (Tudor Achim) is the co-founder and CEO of Harmonic, a startup working to solve one of AI’s hardest problems: mathematical reasoning. In our conversation, we explore: • Why Tudor believes math is the fundamental toolkit to understand the world • How Aristotle works and the applications beyond pure mathematics • The reinforcement learning process that lets Harmonic generate synthetic training data and solve problems humans have never attempted • Why Tudor believes AI could surpass human mathematicians on specific tasks within 2–3 years • Why the future of mathematics looks more like GitHub than academic journals Thank you to the partners who make this possible - Brex: The intelligent finance platform: - Guru_HQ: The AI source of truth for work: - Rippling: Stop wasting time on admin tasks, build your startup faster: Timestamps (00:00) Intro (06:28) The mathematical foundations of music (and why Tudor keeps them separate) (12:52) Defining intelligence (22:55) The two breakthroughs that made mathematical AI possible in 2023 (35:25) An overview of Aristotle: the world’s first always-correct mathematical agent (45:34) Math in AI now and what’s next (56:02) History’s alternating rhythm of thinking and measuring (1:00:18) Final meditations

Mario Gabriele 🦊

17,899 views • 5 months ago

Always so much fun to chat with Grant Sanderson AI has been making much faster progress in math than in other fields. As a result, mathematics is showing us, very concretely, what AI progress in other fields will look like. Even within mathematics, there's a jagged landscape. What does it look like? What is the nature of the most important conceptual breakthroughs in the history of mathematics, and how different are they from what AIs are currently able to do? Does AI (on net) increase or decrease human understanding of the field? How big is the overhang from having AIs systematically try to connect ideas already in the literature? And what advice does Grant have for aspiring mathematicians, coders, and other students who are passionate about fields that are being most transformed upon by AI? 0:00:00 – AI is discovering new proofs. Is that AGI? 0:11:32 – The verification loop on conceptual breakthroughs can be a century long 0:26:12 – Will we understand an AI proof of the Riemann hypothesis? 0:38:08 – Can AI find the hidden bridges between fields? 0:53:48 – Why real-world tasks don’t fit into RL environments 1:07:07 – Good writing requires theory of mind that AI still lacks 1:16:02 – Why learning will still depend on human curation Look up Dwarkesh Podcast on Spotify, Apple Podcasts, YouTube, etc.

Always so much fun to chat with Grant Sanderson AI has been making much faster progress in math than in other fields. As a result, mathematics is showing us, very concretely, what AI progress in other fields will look like. Even within mathematics, there's a jagged landscape. What does it look like? What is the nature of the most important conceptual breakthroughs in the history of mathematics, and how different are they from what AIs are currently able to do? Does AI (on net) increase or decrease human understanding of the field? How big is the overhang from having AIs systematically try to connect ideas already in the literature? And what advice does Grant have for aspiring mathematicians, coders, and other students who are passionate about fields that are being most transformed upon by AI? 0:00:00 – AI is discovering new proofs. Is that AGI? 0:11:32 – The verification loop on conceptual breakthroughs can be a century long 0:26:12 – Will we understand an AI proof of the Riemann hypothesis? 0:38:08 – Can AI find the hidden bridges between fields? 0:53:48 – Why real-world tasks don’t fit into RL environments 1:07:07 – Good writing requires theory of mind that AI still lacks 1:16:02 – Why learning will still depend on human curation Look up Dwarkesh Podcast on Spotify, Apple Podcasts, YouTube, etc.

Dwarkesh Patel

290,780 views • 2 months ago

Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written. Fermat’s Last Theorem was first proven in 1995 by Sir Andrew Wiles, more than 350 years after it was conjectured. Our proof, which totals over 13 million lines of code, provides machine verification. More importantly, it proves over 29,000 other theorems that the proof requires, across many areas of math which had never before been formalized. We see this as a major step in the long process of firming up the core of mathematical knowledge, building on work from three centuries of mathematicians and hundreds of contributors to Lean and Mathlib. We are optimistic that AI-assisted verification of mathematical proofs will help reduce the burden of refereeing mathematics in an era where more proofs are being produced than ever before. You can read about the process on our Science Blog: And see the complete proof on GitHub:

Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written. Fermat’s Last Theorem was first proven in 1995 by Sir Andrew Wiles, more than 350 years after it was conjectured. Our proof, which totals over 13 million lines of code, provides machine verification. More importantly, it proves over 29,000 other theorems that the proof requires, across many areas of math which had never before been formalized. We see this as a major step in the long process of firming up the core of mathematical knowledge, building on work from three centuries of mathematicians and hundreds of contributors to Lean and Mathlib. We are optimistic that AI-assisted verification of mathematical proofs will help reduce the burden of refereeing mathematics in an era where more proofs are being produced than ever before. You can read about the process on our Science Blog: And see the complete proof on GitHub:

Anthropic

4,683,604 views • 8 days ago

Two mathematicians are accusing OpenAI of lifting their unpublished work on one of math's hardest unsolved problems. Tristan Buckmaster, an NYU math professor, and Levent Alpoge spent about a month working with AI models, mainly Codex, on finite time blow up results for the Navier Stokes existence and smoothness problem, one of the seven Millennium Prize problems carrying a million dollar bounty. On September 6th, OpenAI's Sebastien Bubeck told Buckmaster that OpenAI had solved the same problem using the Cordoba Martinez Zoroa approach. Buckmaster then published a statement alleging that OpenAI's result echoed drafts from his and Alpoge's private Codex sessions, and that OpenAI offered to publish jointly while allegedly pushing to cut Alpoge out as a co-author. OpenAI's Shunyu Douglas and Will Depue publicly denied any access to or training on private user chat logs, calling the scenario essentially impossible under the company's data controls. Bubeck separately said he acted within academic norms and called some circulating claims false. On September 8th, Buckmaster and Alpoge, joined by Matei Costalescu, made three results public without OpenAI involvement, finite time blow up with smooth forcing for incompressible porous media, for the Boussinesq equations, and for 3D incompressible Euler, alongside a lean formalization posted on GitHub.

Two mathematicians are accusing OpenAI of lifting their unpublished work on one of math's hardest unsolved problems. Tristan Buckmaster, an NYU math professor, and Levent Alpoge spent about a month working with AI models, mainly Codex, on finite time blow up results for the Navier Stokes existence and smoothness problem, one of the seven Millennium Prize problems carrying a million dollar bounty. On September 6th, OpenAI's Sebastien Bubeck told Buckmaster that OpenAI had solved the same problem using the Cordoba Martinez Zoroa approach. Buckmaster then published a statement alleging that OpenAI's result echoed drafts from his and Alpoge's private Codex sessions, and that OpenAI offered to publish jointly while allegedly pushing to cut Alpoge out as a co-author. OpenAI's Shunyu Douglas and Will Depue publicly denied any access to or training on private user chat logs, calling the scenario essentially impossible under the company's data controls. Bubeck separately said he acted within academic norms and called some circulating claims false. On September 8th, Buckmaster and Alpoge, joined by Matei Costalescu, made three results public without OpenAI involvement, finite time blow up with smooth forcing for incompressible porous media, for the Boussinesq equations, and for 3D incompressible Euler, alongside a lean formalization posted on GitHub.

AGTP

61,087 views • 4 days ago

10 GPT-6 ASTRA AGENTS SOLVED A $1,350,000 HEDGE FUND PROBLEM IN 25 HOURS I gave my Money Heist crew one task and took my hands off the keyboard: find a trading pattern that could power a personal mini hedge fund on Robinhood Chain → In 25 hours, they earned back the $120 subscription cost 100 times over The Professor split the research across ten agents. They analyzed 20,000 token launches, matched wallet histories against liquidity and tested trading ideas under different execution conditions. Tokyo gathered evidence. Rio ran the tests. Nairobi compiled the results into an investment memo. Palermo sent back strategies that depended on a perfect entry or one lucky trade. Every objection triggered another round of calculations. By the end of the operation, the crew had $12,000 in capital and a clear understanding of what to research next, how much risk to take and when to avoid trading altogether. Research costs stayed within $120. For hedge funds, investigations like these cost millions of dollars. I set the objective. The agents divided the work, checked the findings and returned one consolidated result. The full architecture of this crew is in my article ↓

10 GPT-6 ASTRA AGENTS SOLVED A $1,350,000 HEDGE FUND PROBLEM IN 25 HOURS I gave my Money Heist crew one task and took my hands off the keyboard: find a trading pattern that could power a personal mini hedge fund on Robinhood Chain → In 25 hours, they earned back the $120 subscription cost 100 times over The Professor split the research across ten agents. They analyzed 20,000 token launches, matched wallet histories against liquidity and tested trading ideas under different execution conditions. Tokyo gathered evidence. Rio ran the tests. Nairobi compiled the results into an investment memo. Palermo sent back strategies that depended on a perfect entry or one lucky trade. Every objection triggered another round of calculations. By the end of the operation, the crew had $12,000 in capital and a clear understanding of what to research next, how much risk to take and when to avoid trading altogether. Research costs stayed within $120. For hedge funds, investigations like these cost millions of dollars. I set the objective. The agents divided the work, checked the findings and returned one consolidated result. The full architecture of this crew is in my article ↓

Logics

16,424 views • 1 day ago

an engineer openai laid off in january open-sourced the exact thing that made gpt-6 astra worth $200 a month, three weeks after they walked him out. call it revenge, call it the most expensive severance package in history. sam altman spent two years telling everyone the magic was locked in the cloud. one bitter ex-employee proved it fits in a github repo, and now the $200 seat is guarding a moat that is already public. here is what he leaked, and it runs local for about $6 instead of $400: -> pull his open repo, load it onto one nvidia card, and you have the part of gpt-6 astra people were actually paying for -> point cursor, cline and every app at localhost, and none of them notice they left openai for a model that never phones home -> route the rare heavy job to a rented gpu by the hour and keep the daily work local for the cost of power -> your $200 chatgpt seat and your $200 claude seat both go dark the same week the repo trended here is the part they will fight me on: openai and anthropic were never selling the model, they were selling the fact that it lived somewhere you could not reach. one guy they underpaid moved it somewhere you can. the $200 was the distance, and he deleted the distance. drop your $400 stack to a $6 local model and run the thing they fired him for sharing. the full build is in the article below, save it before they get the repo taken down.

an engineer openai laid off in january open-sourced the exact thing that made gpt-6 astra worth $200 a month, three weeks after they walked him out. call it revenge, call it the most expensive severance package in history. sam altman spent two years telling everyone the magic was locked in the cloud. one bitter ex-employee proved it fits in a github repo, and now the $200 seat is guarding a moat that is already public. here is what he leaked, and it runs local for about $6 instead of $400: -> pull his open repo, load it onto one nvidia card, and you have the part of gpt-6 astra people were actually paying for -> point cursor, cline and every app at localhost, and none of them notice they left openai for a model that never phones home -> route the rare heavy job to a rented gpu by the hour and keep the daily work local for the cost of power -> your $200 chatgpt seat and your $200 claude seat both go dark the same week the repo trended here is the part they will fight me on: openai and anthropic were never selling the model, they were selling the fact that it lived somewhere you could not reach. one guy they underpaid moved it somewhere you can. the $200 was the distance, and he deleted the distance. drop your $400 stack to a $6 local model and run the thing they fired him for sharing. the full build is in the article below, save it before they get the repo taken down.

starmex

12,339 views • 2 days ago

Yesterday I explained the Navier–Stokes equation in a way that even a plumber could understand 😭 Then I started getting requests from people in Brazil, the US, India and other countries asking me to translate the video from my original language, Arabic, into English .. So I did. I challenge you to watch the video and NOT understand the equation or what ChatGPT actually discovered .. Now, whether OpenAI came up with the discovery themselves or took ideas from existing researchers is a different discussion .. Either way, the whole thing is fascinating ! The math behind it is beautiful, but what fascinated me even more is HOW they did it .. They basically created an army of AI mathematicians that could talk to each other and work together on the problem 😅 And this army did two things that we humans are honestly pretty bad at: first, ctually listening to each other second, working together without ego or personal ambition getting in the way .. These AI agents spent around 88 hours talking to each other, processing more than 130 BILLION tokens .. Every time one group discovered something useful, that knowledge was passed to the others, and they kept building on each other's work until they reached the result .. 88 hours guys 😅 I know this can feel depressing for researchers who genuinely love doing research ,, I'm actually very new to scientific research myself, and yeah, part of me doesn't love watching AI become better than us at things we spent years learning how to do.. But at the same time., we should probably be excited ! Because if this continues, it means awesome things like: discovering treatments for diseases faster, Solving scientific problems in days instead of decades, accelerating engineering, medicine, manufacturing, programming and basically every field humans work in .. To me, AI feels like the jump from machine code and assembly to modern programming languages with compilers. Back then, we had to tell the computer almost everything manually, and it was slow and tedious until compilers came along, and we started using languages like C and C++, and later python Suddenly you could write ONE line of code, while behind the scenes the compiler handled thousands of lower-level instructions for you ,, AI feels like that same abstraction layer to me .. except this time it isn't just being added to programming ! It's being added to civilization itself .. Scientific research, engineering, medicine, manufacturing, education, everything. We are basically building a compiler for human work .. And if we use it correctly, I think this could accelerate human civilization in a way we haven't fully understood yet ..

Yesterday I explained the Navier–Stokes equation in a way that even a plumber could understand 😭 Then I started getting requests from people in Brazil, the US, India and other countries asking me to translate the video from my original language, Arabic, into English .. So I did. I challenge you to watch the video and NOT understand the equation or what ChatGPT actually discovered .. Now, whether OpenAI came up with the discovery themselves or took ideas from existing researchers is a different discussion .. Either way, the whole thing is fascinating ! The math behind it is beautiful, but what fascinated me even more is HOW they did it .. They basically created an army of AI mathematicians that could talk to each other and work together on the problem 😅 And this army did two things that we humans are honestly pretty bad at: first, ctually listening to each other second, working together without ego or personal ambition getting in the way .. These AI agents spent around 88 hours talking to each other, processing more than 130 BILLION tokens .. Every time one group discovered something useful, that knowledge was passed to the others, and they kept building on each other's work until they reached the result .. 88 hours guys 😅 I know this can feel depressing for researchers who genuinely love doing research ,, I'm actually very new to scientific research myself, and yeah, part of me doesn't love watching AI become better than us at things we spent years learning how to do.. But at the same time., we should probably be excited ! Because if this continues, it means awesome things like: discovering treatments for diseases faster, Solving scientific problems in days instead of decades, accelerating engineering, medicine, manufacturing, programming and basically every field humans work in .. To me, AI feels like the jump from machine code and assembly to modern programming languages with compilers. Back then, we had to tell the computer almost everything manually, and it was slow and tedious until compilers came along, and we started using languages like C and C++, and later python Suddenly you could write ONE line of code, while behind the scenes the compiler handled thousands of lower-level instructions for you ,, AI feels like that same abstraction layer to me .. except this time it isn't just being added to programming ! It's being added to civilization itself .. Scientific research, engineering, medicine, manufacturing, education, everything. We are basically building a compiler for human work .. And if we use it correctly, I think this could accelerate human civilization in a way we haven't fully understood yet ..

ابو دانتي | Majed Al-Harbi

110,284 views • 1 day ago

Elon Musk reveals what SpaceX is gearing up to do in the next five years "Five years from now, my prediction is we will launch and be operating every year more AI in space than the cumulative total on Earth" "100 gigawatts is on the order of 10,000 Starship launches. You want to do that in one year. That's like one Starship launch every hour" "It really depends on how quickly the ship has to go around the Earth and come back over the launch pad. If you can use a ship every 30 hours, you could do it with 30 ships" "SpaceX is gearing up to do 10,000 launches a year, and maybe even 20 or 30,000 launches a year" "If some of my predictions come true, SpaceX will launch more AI than the cumulative amount on Earth of everything else combined"

Elon Musk reveals what SpaceX is gearing up to do in the next five years "Five years from now, my prediction is we will launch and be operating every year more AI in space than the cumulative total on Earth" "100 gigawatts is on the order of 10,000 Starship launches. You want to do that in one year. That's like one Starship launch every hour" "It really depends on how quickly the ship has to go around the Earth and come back over the launch pad. If you can use a ship every 30 hours, you could do it with 30 ships" "SpaceX is gearing up to do 10,000 launches a year, and maybe even 20 or 30,000 launches a year" "If some of my predictions come true, SpaceX will launch more AI than the cumulative amount on Earth of everything else combined"

Jaynit

43,018 views • 3 months ago

Ken Griffin, founder of Citadel, the most profitable hedge fund in history, on the moment that left him "shocked and depressed" about AI: "one of our team members built an agentic AI system to recreate academic papers in finance." "we have a legion of young masters and PhDs doing this work. it takes roughly six to eight weeks to reproduce a paper." "my colleague built an AI system that would read a paper, reproduce it, verify the results, produce the results on out of sample data — in about two to three hours per paper." "this is not just a white collar job. this is a master's or PhD-level job. six weeks of work turned into two to three hours." "and then OpenAI just solved a math problem that no one had solved for eighty years." "competitive moats are being filled in at lightning speed." the founder of Citadel watching PhD-level work get compressed from six weeks to two hours. and his response wasn't to cut headcount, it was "i will take every single productivity gain i can get because with the talented people we have, we just have more to go after."

Ken Griffin, founder of Citadel, the most profitable hedge fund in history, on the moment that left him "shocked and depressed" about AI: "one of our team members built an agentic AI system to recreate academic papers in finance." "we have a legion of young masters and PhDs doing this work. it takes roughly six to eight weeks to reproduce a paper." "my colleague built an AI system that would read a paper, reproduce it, verify the results, produce the results on out of sample data — in about two to three hours per paper." "this is not just a white collar job. this is a master's or PhD-level job. six weeks of work turned into two to three hours." "and then OpenAI just solved a math problem that no one had solved for eighty years." "competitive moats are being filled in at lightning speed." the founder of Citadel watching PhD-level work get compressed from six weeks to two hours. and his response wasn't to cut headcount, it was "i will take every single productivity gain i can get because with the talented people we have, we just have more to go after."

Goshawk Trades

184,255 views • 2 months ago

Chamath says OpenAI and Anthropic could be $5 to $10 trillion companies each if they remain a duopoly "I suspect revenues are going to crank at OpenAI and Anthropic and the open labs for a while. But again, that's not the important thing." "If you're thinking about valuation, the markets will look five to 10 years out to answer that question, they're not going to give you a premium valuation on something that they feel could be fragile in the first two to three years." "Somebody has to answer that question precisely. Because if the answer is that it is a duopoly, then there is no risk to the revenue five to 10 years from now, these things are $5 to $10 trillion companies each." "But if there are harnesses that cut the token consumption, because you stop wasting tokens to get to the same output, then it's a little bit more of a question mark. And I think that'll need to get sorted out."

Chamath says OpenAI and Anthropic could be $5 to $10 trillion companies each if they remain a duopoly "I suspect revenues are going to crank at OpenAI and Anthropic and the open labs for a while. But again, that's not the important thing." "If you're thinking about valuation, the markets will look five to 10 years out to answer that question, they're not going to give you a premium valuation on something that they feel could be fragile in the first two to three years." "Somebody has to answer that question precisely. Because if the answer is that it is a duopoly, then there is no risk to the revenue five to 10 years from now, these things are $5 to $10 trillion companies each." "But if there are harnesses that cut the token consumption, because you stop wasting tokens to get to the same output, then it's a little bit more of a question mark. And I think that'll need to get sorted out."

dnap

275,325 views • 1 month ago

Delete Unreal Engine immediately. The $200 billion gaming industry was permanently destroyed today. OpenAI just officially dropped GPT-6 Astra, and it is generating two completely different interactive 3D AAA games live on screen: 1. Top screen: A hyper-speed sci-fi racer hitting 1,300 km/h with dynamic neon physics and real-time obstacle rendering. 2. Bottom screen: A fully playable FPS shooter with line-of-sight AI bots, weapon recoil, and complex urban geometry. 3. 0 developers involved. 0 lines of C++ code written. 50,000+ 3D assets generated on the fly at 120 FPS. 4. What used to cost Sony and Ubisoft $300,000,000 and 5 years of labor now takes a single text prompt and 2 seconds. 5. In 12 months, 90% of current game studios will either adapt to AI prompt engines or go bankrupt. If you are still ignoring AI in 2026, your skills are officially obsolete. Save this before it gets scrubbed from the internet.

Delete Unreal Engine immediately. The $200 billion gaming industry was permanently destroyed today. OpenAI just officially dropped GPT-6 Astra, and it is generating two completely different interactive 3D AAA games live on screen: 1. Top screen: A hyper-speed sci-fi racer hitting 1,300 km/h with dynamic neon physics and real-time obstacle rendering. 2. Bottom screen: A fully playable FPS shooter with line-of-sight AI bots, weapon recoil, and complex urban geometry. 3. 0 developers involved. 0 lines of C++ code written. 50,000+ 3D assets generated on the fly at 120 FPS. 4. What used to cost Sony and Ubisoft $300,000,000 and 5 years of labor now takes a single text prompt and 2 seconds. 5. In 12 months, 90% of current game studios will either adapt to AI prompt engines or go bankrupt. If you are still ignoring AI in 2026, your skills are officially obsolete. Save this before it gets scrubbed from the internet.

shmidt

83,729 views • 6 days ago

.Dylan Patel forecasts that iPhones could get $250 more expensive for consumers. Smartphone sales could drop from 1.1 billion a year to 500-600 million over the next couple of years, with the low end getting crushed hardest. Around a third of big tech's $600 billion in CapEx this year is going to memory alone. And as AI labs lock up more and more of the world's memory production on long-term contracts at higher margins, there's simply less left for everyone else. The effects are even more extreme than you might think. AI accelerators use HBM, which is made from stacking the DRAM that goes into phones and laptops, but which takes about four times more wafer area per byte. So you have to destroy four bytes of consumer demand for every one byte given to AI. For the first time in decades, consumer computing is going to get incrementally worse year on year, not better. But the price will go up dramatically at the same time.

.Dylan Patel forecasts that iPhones could get $250 more expensive for consumers. Smartphone sales could drop from 1.1 billion a year to 500-600 million over the next couple of years, with the low end getting crushed hardest. Around a third of big tech's $600 billion in CapEx this year is going to memory alone. And as AI labs lock up more and more of the world's memory production on long-term contracts at higher margins, there's simply less left for everyone else. The effects are even more extreme than you might think. AI accelerators use HBM, which is made from stacking the DRAM that goes into phones and laptops, but which takes about four times more wafer area per byte. So you have to destroy four bytes of consumer demand for every one byte given to AI. For the first time in decades, consumer computing is going to get incrementally worse year on year, not better. But the price will go up dramatically at the same time.

Dwarkesh Patel

186,234 views • 6 months ago

THIS IS ABSOLUTELY RIDICULOUS. OpenAI and Anthropic are losing money on every dollar they make. OpenAI generated $20 billion in revenue in 2025 and is projected to lose $14 billion in the same year. Internal forecasts project cumulative losses hitting $44 billion by 2028. The company's own CFO warned executives in April 2026 that OpenAI might struggle to finance upcoming computing deals if revenue growth slows. Anthropic reached $4.3 billion in annualized revenue in April 2026 against $19 billion in total costs. It spends $3 to make $1, and is not expected to stop burning cash until 2027. Now look at what these two companies have committed to spend. OpenAI and Anthropic together have committed $1.05 trillion in cloud spending to Microsoft, Oracle, Google and Amazon, making up 43 to 54% of each provider's entire future revenue backlog. - Microsoft: $627B total backlog. OpenAI and Anthropic account for 49%. - Oracle: $553B total backlog. OpenAI alone accounts for 54%. - Google: $467.6B total backlog. Anthropic accounts for 43%. - Amazon: $464B total backlog. OpenAI and Anthropic account for 51%. The entire cloud industry's future revenue is a bet on two companies losing billions every quarter. Microsoft, Alphabet, Meta and Amazon are collectively expected to spend $725 billion in capex in 2026, almost entirely on AI infrastructure. Combined hyperscaler capex from 2025 to 2027 is projected at $1.15 trillion, more than double what was spent from 2022 to 2024. What is the return on all of this? McKinsey's 2025 State of AI survey found that only a minority of companies reported AI meaningfully increased revenue or reduced costs. Enterprise generative AI spending grew from $1.7 billion in 2023 to $37 billion in 2025 and most CIOs still describe their initiatives as pilots without clear ROI metrics. Microsoft's AI business is running at a $37 billion annual revenue run rate with 123% year over year growth. That sounds impressive until you realize most of the capex funding is justified by expected future AI revenue rather than current AI profit. The internet burned money for years before it became the most profitable industry in history. But right now $1 trillion in committed cloud spend, $725 billion in annual capex, two loss-making customers making up half of every major cloud provider's revenue backlog, and the enterprises writing the checks cannot tell you if any of it is working.

THIS IS ABSOLUTELY RIDICULOUS. OpenAI and Anthropic are losing money on every dollar they make. OpenAI generated $20 billion in revenue in 2025 and is projected to lose $14 billion in the same year. Internal forecasts project cumulative losses hitting $44 billion by 2028. The company's own CFO warned executives in April 2026 that OpenAI might struggle to finance upcoming computing deals if revenue growth slows. Anthropic reached $4.3 billion in annualized revenue in April 2026 against $19 billion in total costs. It spends $3 to make $1, and is not expected to stop burning cash until 2027. Now look at what these two companies have committed to spend. OpenAI and Anthropic together have committed $1.05 trillion in cloud spending to Microsoft, Oracle, Google and Amazon, making up 43 to 54% of each provider's entire future revenue backlog. - Microsoft: $627B total backlog. OpenAI and Anthropic account for 49%. - Oracle: $553B total backlog. OpenAI alone accounts for 54%. - Google: $467.6B total backlog. Anthropic accounts for 43%. - Amazon: $464B total backlog. OpenAI and Anthropic account for 51%. The entire cloud industry's future revenue is a bet on two companies losing billions every quarter. Microsoft, Alphabet, Meta and Amazon are collectively expected to spend $725 billion in capex in 2026, almost entirely on AI infrastructure. Combined hyperscaler capex from 2025 to 2027 is projected at $1.15 trillion, more than double what was spent from 2022 to 2024. What is the return on all of this? McKinsey's 2025 State of AI survey found that only a minority of companies reported AI meaningfully increased revenue or reduced costs. Enterprise generative AI spending grew from $1.7 billion in 2023 to $37 billion in 2025 and most CIOs still describe their initiatives as pilots without clear ROI metrics. Microsoft's AI business is running at a $37 billion annual revenue run rate with 123% year over year growth. That sounds impressive until you realize most of the capex funding is justified by expected future AI revenue rather than current AI profit. The internet burned money for years before it became the most profitable industry in history. But right now $1 trillion in committed cloud spend, $725 billion in annual capex, two loss-making customers making up half of every major cloud provider's revenue backlog, and the enterprises writing the checks cannot tell you if any of it is working.

Crypto Rover

58,862 views • 3 months ago

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. Many have endured decades of expert scrutiny. Acceptance matters more than authorship. Tao doesn't rubber-stamp ideas; he rigorously tests logic, generality, and novelty. If a proof clears that hurdle, the system didn't merely recombine known lemmas—it explored a true mathematical search space. This means AI has crossed a threshold: from assisting mathematics to participating in it by proposing nontrivial arguments, uncovering hidden structures, and resolving problems humans value—without a predefined solution path. Importantly, this doesn't diminish human mathematicians. It reshapes the field's topology. Just as symbolic algebra systems amplified rather than replaced math, AI now seems poised to expand the frontier itself. If these claims hold, recent days may mark the lift-off for AI-driven science: not flashy demos, but quiet validation by the world's toughest referees. We should remain skeptical, careful, and precise—yet honest about the implications. Something fundamental may have changed. Here's a five-minute video with Terry explaining these problems and meeting the man himself:

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. Many have endured decades of expert scrutiny. Acceptance matters more than authorship. Tao doesn't rubber-stamp ideas; he rigorously tests logic, generality, and novelty. If a proof clears that hurdle, the system didn't merely recombine known lemmas—it explored a true mathematical search space. This means AI has crossed a threshold: from assisting mathematics to participating in it by proposing nontrivial arguments, uncovering hidden structures, and resolving problems humans value—without a predefined solution path. Importantly, this doesn't diminish human mathematicians. It reshapes the field's topology. Just as symbolic algebra systems amplified rather than replaced math, AI now seems poised to expand the frontier itself. If these claims hold, recent days may mark the lift-off for AI-driven science: not flashy demos, but quiet validation by the world's toughest referees. We should remain skeptical, careful, and precise—yet honest about the implications. Something fundamental may have changed. Here's a five-minute video with Terry explaining these problems and meeting the man himself:

Prof. Brian Keating

104,865 views • 8 months ago