When OpenAI announced on a press call that an internal model had cracked one of mathematics’ hardest open problems, we wrote that nobody had seen the proof.
That is no longer true, and what has now been published narrows the claim in ways the announcement did not.OpenAI has posted a write-up, a PDF paper, and a formalisation of the argument in Lean with a public GitHub repository.
The formalisation is the part that matters most, because a Lean proof can be machine-checked by anyone, which removes the need to take the company’s word for the mathematics. OpenAI says the formalisation and verification took a further 17 hours using GPT-6 Astra.
The result itself is that an initially smooth fluid at rest can develop a singularity in finite time. In OpenAI’s framing, this “resolves the Navier-Stokes Millennium Prize problem by establishing statement ‘C’ (and also ‘D’) in the official Millennium Prize formulation”.
And then, two paragraphs later:
