OpenAI Scoops Navier–Stokes Proof From Team Using Its Own Models

OpenAI used an unreleased internal model to produce a resolution of the Navier–Stokes existence and smoothness problem, one of the seven $1M Millennium Prize Problems. The company launched the effort on September 1st after hearing rumors that Millennium problems had been cracked, and its agents reached a solution roughly 88 hours later, with an additional 17 hours of Lean formalization via GPT-6 Astra. The run was enormous in scale: across all attempted problems the agents exchanged 4.9 million messages and burned about 300 billion output tokens — which at public API rates would run to roughly $15 million.

The achievement is clouded by a dispute over priority. Tristan Buckmaster (NYU) and Levent Alpöge, a mathematician at Anthropic, had spent nearly a year on the same problem, leaning heavily on Claude and OpenAI’s Codex, and reached a breakthrough on August 15th. When rumors of their work reached OpenAI, the company started its own attempt and only afterward contacted the pair to offer a joint announcement — while making clear that Alpöge would be excluded as a co-author because he works for a competitor. OpenAI says no user data was accessed to solve the problem and that the proofs differ substantively, but it conceded it cannot fully rule out that de-identified data from users’ product usage improved its models. Notably, it did not clearly answer whether the model had trained on the pair’s Codex sessions, where they had stored their drafts.

The episode sharpens a growing concern about what “used to improve model performance” actually means in practice. Just as a mere rumor of an unpatched vulnerability can now direct AI agents to go find and exploit it, a rumor that a hard math problem is nearly solved can trigger a multimillion-dollar compute race to publish first. The open question for anyone using these tools is whether their own in-progress work — a security finding, a business strategy, or a partial proof — could end up shaping a later model that helps someone else beat them to the result.