On the Navier–Stokes Millennium Prize Problem
We’re sharing an AI-generated solution to the Navier–Stokes Millennium Prize Problem, including a writeup and a formal proof in Lean.
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The announcement yesterday by OpenAI of a solution to the Millennium Prize Navier-Stokes problem has been causing a great deal of discussion among mathematicians. There’s a lot to be said abo…
OpenAI has recently claimed to have a counterexample https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf to global in time existence of classical smooth solutions to the incompressible Navier-Stokes equations in $\mathbb{R}^3$ . The incompressible Navier-Stokes…
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OpenAI~\cite{OpenAIManuscript} has recently announced a proof of finite time singularity formation for the 3D Navier-Stokes equations, in the presence of a $C^\infty$-smooth body force. The construction in~\cite{OpenAIManuscript} has a few key features, among which we single out: (i) the angular…
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Autoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes equations. In this process, an AI system translates the text from a natural language (NL) into a formal language such as…
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Relevance of the work of Alpöge and Buckmaster to Navier-Stokes?mathoverflow.netLuciaSep 8, 2026
I saw recently a post on Mathstodon by Tristan Buckmaster detailing progress on blow-up for some PDE's related to Navier-Stokes: see https://mastodon.social/@tristanbuckmaster/117233413705701198 which links to the documents https://cims.nyu.edu/~tristanb/statement.pdf…