OpenAI claimed a Navier-Stokes Millennium breakthrough before publishing a checkable proof

OpenAI said Tuesday that an internal AI model more powerful than newly released GPT-6 Astra, running alongside about 10,000 concurrent agents, produced a solution to the Navier-Stokes problem, Emma Roth at The Verge writes. Navier-Stokes is the set of equations that describe how fluids move. It is one of seven Millennium Prize Problems, each with a $1 million reward.

The Next Web, summarizing Axios and OpenAI's press call, puts the claim more precisely: the model proved that three-dimensional Navier-Stokes can develop a singularity in finite time, meaning a smooth flow can become infinite in finite time. The effort started around September 1, reached a result in about 88 hours, and cost in the millions of dollars, OpenAI said. As of Tuesday the company had not published the proof.

One day earlier, NYU mathematics professor Tristan Buckmaster and Anthropic researcher Levent Alpöge posted preprints on closely related problems, including finite-time blowup for equations connected to the same fluid-math neighborhood. They published Lean formalisations alongside them. Lean is a proof assistant that machine-checks formal proofs so the files can be verified rather than taken on trust.

Buckmaster says he and Alpöge had been working with OpenAI's Codex and Anthropic's Claude as research notebooks, putting drafts into Codex sessions. After learning OpenAI had heard about their progress, he contacted the company.

He asked whether the model had been trained on or accessed those sessions. He was told the model did not look up user data. He asked again about training and did not get an answer, he writes.

OpenAI said no specific user data was accessed to solve the problem, and that while unlikely it cannot rule out that de-identified data from product use helped improve its models. Sébastien Bubeck of OpenAI said the team did not see Buckmaster and Alpöge's work until public release, and that the proofs and precise results differ. Chief research officer Mark Chen told reporters no people or AI systems searched user data, and that he was disappointed by the allegations.

OpenAI says it does not plan to take the $1 million prize. It frames the result as evidence of how fast its models are advancing.

Buckmaster has also described contested September 6 calls about authorship and career risk, including pressure he says involved excluding Alpöge because he works at Anthropic.

Those are contested claims from one participant about private conversations. OpenAI disputes his characterisation. They are public and material, not established.

Strip the personalities and a structural question remains. Can a researcher use a frontier lab's tools while working on an unpublished result, without racing the lab that sold the tools?

OpenAI's assurances are specific and on the record. From outside they are also hard to verify. That is the same problem the unpublished proof has.

A mathematical claim is not a mathematical result until someone can check it. Publish the file. Then credit narrows to provenance.

Sources: The Verge; The Next Web; Axios.