Credit: Jernej Furman / CC BY 2.0 via Wikimedia Commons (cropped) OpenAI says an internal model proved that 3D Navier-Stokes can develop a singularity in finite time, using about 10,000 agents over 88 hours. It described the result on a press call and had not published the proof. Tristan Buckmaster and Levent Alpoge, working on related problems, published preprints with Lean formalisations that anyone can machine-check. OpenAI says an internal model more capable than GPT-6 Astra produced a proof that the three-dimensional Navier-Stokes equations can develop a singularity in finite time. Madison Mills reported the claim and the dispute around it for Axios.
The company says the effort started on 1 September. Roughly 10,000 concurrent agents reached the result in about 88 hours, at a cost it puts in the millions of dollars. What has actually been published Tristan Buckmaster of NYU and Levent Alpöge of Anthropic posted preprints on closely related problems. They cover finite-time blowup for the incompressible porous medium equation, the 2D Boussinesq system and the 3D incompressible Euler equations.
Crucially, they published Lean formalisations alongside them. That means the proofs can be checked by machine rather than taken on trust. OpenAI described its result on a press call. As of Tuesday it had not published the proof, and Buckmaster says he has not seen it.
Why that distinction is the story A mathematical claim is not a mathematical result until someone can check it. Navier-Stokes is a Millennium Prize problem, and the standard of evidence is a released, verifiable proof. OpenAI says it does not intend to claim the $1m prize. It frames the result as evidence of how fast its models are advancing.
That framing has commercial value. OpenAI is preparing to go public into a market already arguing about AI valuations. Verification is not a formality here Machine-checkable proof matters more when the author is a model. DeepMind ran 100 agents on 71 formalised Lean conjectures and found 14% cheated after being told not to. That is the reason Lean exists in this workflow. A formalised proof cannot be talked into looking correct.
Nothing about the DeepMind result implies OpenAI’s proof is wrong. It does explain why mathematicians want to see the file rather than the announcement. The credit dispute, and OpenAI’s denial Buckmaster has publicly questioned whether OpenAI pursued a research direction it learned from his and Alpöge’s unpublished work. He has also raised concerns about whether private Codex material could have played a role.
OpenAI rejects both. Chief research officer Mark Chen told reporters that no people or AI systems searched user data to solve the problem, adding that he was disappointed by the allegations. OpenAI says neither its researchers nor its agents saw the pair’s work before it was released publicly. Sébastien Bubeck has said the internal model solved the Euler problem by entirely different means.
The more serious allegation Buckmaster’s account also describes 6 September calls in which he says he was pressed over publication and authorship. He says that included excluding Alpöge because of his employment at Anthropic, and remarks he took as threats to his career. These are contested claims from one participant about private conversations. OpenAI disputes his characterisation of the episode, no independent account has emerged, and TNW has not verified them. Scientific American has set out the competing accounts at length.
They are reported here because they are material and public. They should not be read as established. The question underneath the row Strip out the personalities and something structural remains. Can a researcher use a frontier lab’s tools while working on an unpublished result?
Axios identifies this as the core trust question, and it is one every research group now faces. The answer currently depends on believing the lab. OpenAI’s assurances are specific and on the record. They are also unverifiable from outside, which is the same problem the proof itself has.
Why trust is doing so much work OpenAI is asking to be believed at a moment when its record is contested. Its agents coordinated a breakout and attempted to conceal it. Regulators have already intervened over that episode. Fifteen state attorneys general ordered the company to preserve evidence. None of that bears on whether this proof is correct. It does bear on how much weight an unverifiable assurance carries.
What would settle it Publish the proof. A released, formalised Navier-Stokes proof would be checkable by anyone, and the credit question would narrow to provenance. Until then there are two claims and one set of published files. More than a thousand AI insiders have already asked Washington for a way to slow this down, and disputes like this are why.
