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OpenAI Says AI Agent Swarm Produced a Navier–Stokes Proof

September 9, 2026 at 01:19 EDT

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OpenAI says an internal AI system coordinated roughly 10,000 agents to produce a proof addressing the Navier–Stokes Millennium Prize Problem. The company says the result shows that a smooth three-dimensional fluid can develop a singularity in finite time, and that the work has been formalized in Lean for machine checking.

September 8, 2026 · OpenAI

An AI swarm targets a 90-year math problem

OpenAI says an internal system coordinated roughly 10,000 agents to produce a Navier–Stokes proof, followed by Lean formalization and machine checking.

The operation at a glance

~10,000

agents in the Navier–Stokes group

hours to reach the resolution

hours for Lean verification

130B

output tokens in the effort

Elapsed time, shown to scale

Stacked blocks are proportional to the reported hours.

88 hours

Proof search

17 hours

Lean check

What the claim says

A smooth fluid can break down in finite time

The reported construction uses a spiraling, stretching vortex. Its energy stays finite while the velocity becomes unbounded, matching the breakdown statements in the formal problem.

Why the result remains under review

Publicly checkable work

Analytical write-up shared
Lean formalization shared

Open questions

Specialist scrutiny remains
Credit and data concerns remain

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