OpenAI said in Q3 2026 that it had resolved the Navier-Stokes existence and smoothness problem after running 10,000 AI agents for 88 hours and pushing the work through 130 billion tokens. It then said Astra spent 17 hours on formal verification in Lean.
The claim matters because this was not a single model grinding away at one proof for days on end. Henry Yin said the setup marked a new phase of test-time compute, and OpenAI described a system trained to know when to send messages, when to ask for help and when to change course. In Yin’s words, a lone model could need an extremely long time on a problem this hard, even decades or a century.
That scale is part of why people are reading closely now. The Navier-Stokes existence and smoothness problem is one of the Millennium Prize mathematics problems, so any claimed advance lands well beyond ordinary AI benchmarking. OpenAI said it decided to try the problem in early September after hearing someone had made major progress on an important math problem, and that it moved quickly from the first run to formal checking in Lean once it had a proof.
But the story did not stay inside the clean lane of compute and verification. Tristan Buckmaster, the NYU mathematician OpenAI identified as the person who had made major progress, had a collaborator at Anthropic, and the two had previously given unpublished drafts to Codex for use. OpenAI reached out to Buckmaster proactively and proposed excluding the collaborator from authorship because that person works at Anthropic, then Buckmaster made the entire communication process public online.
OpenAI also said the two sides solved slightly different problems, one with viscosity and one without, and used different proof methods. That distinction is doing a lot of work here: if the equations and methods were genuinely different, the overlap may be narrower than the public dispute suggests; if not, the authorship and access questions stay live. For now, the claim of a breakthrough sits beside an unresolved argument over how much of the path had already been mapped before OpenAI entered the race.
