On the Navier–Stokes Millennium Prize Problem
OpenAI says an internal AI system produced a Lean-formalized proof that smooth 3D Navier-Stokes flow can blow up in finite time.
The note says the proof establishes the Millennium formulation’s “C” and “D” statements by showing a finite-energy singularity under a smooth external force. OpenAI describes the construction as an inward-spiraling vortex whose velocity becomes unbounded while the energy remains finite. The company says roughly 10,000 concurrent agents worked on the Navier-Stokes effort, with Lean verification completed afterward using GPT-6 Astra. OpenAI says it does not intend to claim the Millennium Prize for the result. OpenAI's note
The note says the proof establishes the Millennium formulation’s “C” and “D” statements by showing a finite-energy singularity under a smooth external force. OpenAI describes the construction as an inward-spiraling vortex whose velocity becomes unbounded while the energy remains finite. The company says roughly 10,000 concurrent agents worked on the Navier-Stokes effort, with Lean verification completed afterward using GPT-6 Astra. OpenAI says it does not intend to claim the Millennium Prize for the result. OpenAI's note
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