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OpenAI solved math Tudor Achim reacts live to OpenAI solving the Navier-Stokes Millennium Prize Problem.

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57,161 просмотров • 4 дней назад •via X (Twitter)

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OpenAI said its new AI agents solved a 90-year-old math problem, known as the Navier-Stokes equations, in under four days. Now, an NYU professor is speaking out, claiming the AI ‘piggy-backed’ off of his research.
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OpenAI said its new AI agents solved a 90-year-old math problem, known as the Navier-Stokes equations, in under four days. Now, an NYU professor is speaking out, claiming the AI ‘piggy-backed’ off of his research.

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Will OpenAI and Anthropic ever crack this one? Behind this beautiful turbulence cascade lies a Millennium Prize Problem: For the 3D Navier-Stokes equations, nobody has proved whether every smooth flow remains smooth forever or whether a singularity can form in finite time.
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Meet Bartosz (Bartosz Naskręcki). A mathematician solving previously unsolvable math problems with GPT-5.6
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The same model solving Navier–Stokes will write the most mediocre copy you’ve ever read.
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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.
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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.

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We partnered with Anthropic OpenAI to host the world's first math hackathon. 40 hours, $2M compute - solve, understand, and present an open problem. Applications are live:
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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.
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The fly is solving Millennium Prize Problems. Just need to RL out the banana factor to crack the last one.
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Greg Brockman says solving a Millennium Prize problem could be just 2-5 years away we’re at AGI level-3; level-4 innovators will be different. Imagine a whole data center focused on curing cancer or solving a Millennium problem: "that level of computational power is something the world has never seen"
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OpenAI President Greg Brockman on solving the Navier-Stokes problem: "If we have models that can solve this kind of problem, what happens from here?" "I think that talking about curing diseases and new medicines we're going to be able to develop, all of that starts to become much more real when you have models that are at this level of assistance and capability." "[This result] is really about the broader insights and methods that can help scientists and mathematicians further accelerate their research."

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Cognition founder and 3x Olympiad gold medalist Scott Wu on the Navier-Stokes solution: "It's actually insane...guys, we just solved Navier-Stokes with AI. That is absurd. And I don't think it's going to stop." "All of this stuff is just going to get done. It's hard to put into words if you're not familiar with the scale of it. But Navier-Stokes is a very fundamental problem about fluid dynamics and such. It's been around forever, basically. And lots of people have sunk lots and lots of time into it." "The fact that this can even just be done in like a week — it's insane."

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Navier–Stokes equation (2D incompressible), solved live numerically on a discrete grid ρ (∂u/∂t + u·∇u) = −∇p + μ Δu + f, ∇·u = 0 The ink (the white stuff on the left) is added so you can see the motion of the fluid.
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Navier–Stokes equation (2D incompressible), solved live numerically on a discrete grid ρ (∂u/∂t + u·∇u) = −∇p + μ Δu + f, ∇·u = 0 The ink (the white stuff on the left) is added so you can see the motion of the fluid.

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