OpenAI says AI solved Navier-Stokes; mathematicians dispute credit

On 8 September 2026 OpenAI published a proposed solution to the Navier-Stokes existence-and-smoothness problem, one of the seven Clay Mathematics Institute Millennium Prize problems. The claim was a blow-up result: that the three-dimensional incompressible equations, with smooth forcing, can develop a singularity in finite time, rather than a proof of global regularity. OpenAI attributed the proof to an unreleased internal model, training since 28 August, run as a swarm of about 10,000 coordinating agents that exchanged roughly 2.7 million messages and 130 billion output tokens over 88 hours, followed by a 17-hour Lean formalization. The company said it would not claim the million-dollar prize.

Within hours the claim was contested. Tristan Buckmaster of New York University and Levent Alpöge of Anthropic said they had reached related results on 15 August, finite-time blow-up for porous media, Boussinesq and three-dimensional Euler, and questioned how OpenAI’s effort, which OpenAI dated to 1 September after hearing a rumor that Millennium problems had fallen, related to their work. Buckmaster said an OpenAI researcher pressured him over credit; OpenAI denied seeing their work and said it could not rule out that de-identified product data had improved its models. Terence Tao warned that racing agent swarms at open problems could strip-mine the field and destroy the ecosystem that produces new mathematical techniques. The Clay Institute had not commented.

The episode became the defining case in the argument over machine-made mathematics: what counts as a solution when a 166-page proof is formalized in hours, who gets credit when humans and models collaborate, and whether the speed of automated discovery endangers the human research culture it draws on.