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OpenAI Claims AI-Generated Proof for Navier–Stokes Problem

September 9, 2026 at 21:01 EDT

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OpenAI says an internal AI system has produced a proof for the roughly 90-year-old Navier–Stokes existence and smoothness problem, one of the seven Clay Millennium Prize Problems. The claim is a major test of AI-assisted mathematical discovery, but independent mathematicians have not yet completed a human review of the proof.

SEP 8, 2026 · OPENAI

AI System Claims a Navier–Stokes Breakthrough

OpenAI says an internal multi-agent system produced a proof that a smooth three-dimensional fluid can develop a finite-time singularity. Independent mathematicians are still examining the claim.

What the run involved

10,000

concurrent agents

88h

to reach the result

17h

Lean formalization and verification

130B

output tokens on Navier–Stokes

Search versus formal check

Reported hours, shown with proportional vertical stacks.

88 hours

proof search

17 hours

Lean check

THE CLAIM

A vortex that tightens into a finite-time singularity

OpenAI says the vortex spirals inward and stretches while its speed becomes unbounded, even as the total energy stays finite and the external force remains smooth.

Why it matters

The result could demonstrate that AI systems can contribute to foundational mathematics and coordinate complex proof search.

What remains open

The 166-page proof still needs independent human scrutiny, while the dispute over priority and training data remains unresolved.

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