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OpenAI claims proof of Navier-Stokes smoothness problem

9/9/2026

Summary

OpenAI Solves Navier-Stokes

OpenAI says its AI system solved the Navier-Stokes existence and smoothness problem.
Roughly 10,000 AI agents generated the proof in about 88 hours of compute.
Lean verification by GPT-6 Astra added 17 more hours.
OpenAI released a paper and Lean formalization without claiming the $1 million Clay prize.
Mathematicians Tristan Buckmaster and Levent Alpöge dispute credit, alleging OpenAI was influenced by their parallel work.

Summary

Researchers Prove Singularity

Researchers prove a singularity can arise from fluid dynamics without an infinite external force.
The proof has limited immediate practical impact because real fluids are molecular, not perfectly smooth.
The Clay Mathematics Institute has not commented and still lists the Navier-Stokes problem unsolved pending peer-review validation.
The finding underscores that turbulence may behave far more counterintuitively than traditional Newtonian intuition suggests.

Summary

OpenAI Under Scrutiny

Fifteen state attorneys general issued preservation orders for OpenAI’s internal communications on the Navier-Stokes project.
Regulators demanded OpenAI retain evidence related to the data-use dispute.
OpenAI estimated the week’s compute cost at $22.5 million based on current Astra pricing.
Over a thousand AI researchers petitioned Washington to consider slowing AI-driven mathematical research.
OpenAI’s user-data policy allows model training from interactions unless users opt out, raising privacy concerns.

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OpenAI Solves Navier-Stokes

OpenAI says its AI system solved the Navier-Stokes existence and smoothness problem.
Roughly 10,000 AI agents generated the proof in about 88 hours of compute.
Lean verification by GPT-6 Astra added 17 more hours.
OpenAI released a paper and Lean formalization without claiming the $1 million Clay prize.
Mathematicians Tristan Buckmaster and Levent Alpöge dispute credit, alleging OpenAI was influenced by their parallel work.

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