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On the Navier–Stokes Millennium Prize Problem

On the Navier–Stokes Millennium Prize Problem

openai.com

September 8, 2026

7 min read

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Summary

On the Navier–Stokes Millennium Prize Problem We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. ...

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