OpenAI claims Navier-Stokes math solution with 10,000 AI agents as rival researchers dispute priority

Proof announcement and computational scale

OpenAI announced on 8 September 2026 that an unreleased artificial intelligence system solved the Navier-Stokes existence and smoothness problem, one of six unresolved Millennium Prize Problems listed by the Clay Mathematics Institute. The company deployed roughly 10,000 concurrent AI agents over 88 hours between 1 September and 5 September 2026 to produce a 100-page analytical proof. The computation generated 2.7 million messages and roughly 130 billion tokens, with computing expenses running into millions of dollars. OpenAI then used its GPT-6 Astra model to formalize and verify the argument in the Lean proof assistant over a subsequent 17-hour run. Mark Chen, chief research officer at OpenAI, described the result as a demonstration of automated mathematical reasoning.

This is a significant milestone for AI research, and its promise for the world is that even more of our hardest questions would become possible to answer.

The mathematical claim and the Millennium Prize

Formulated in the nineteenth century by Henri Navier and George Gabriel Stokes, the equations describe the motion of fluids such as water and air, serving as the basis for weather forecasting, aerodynamics, and blood flow analysis. The Clay Mathematics Institute offered a 1 million dollar prize in 2000 for a rigorous proof establishing whether smooth fluid flows can develop singularities or infinite velocities over finite time. OpenAI stated that its proof demonstrates that an initially smooth fluid at rest develops a finite-time singularity when subject to an external smooth force, addressing statements C and D of the official formulation. The company published its write-up, PDF paper, and Lean formalization on GitHub on 8 September 2026, but stated it will not claim the 1 million dollar Millennium Prize. External mathematicians have not independently verified the proof, a review process that typically requires months.

Priority dispute and researcher allegations

The announcement followed a public challenge from New York University mathematics professor Tristan Buckmaster and Anthropic researcher Levent Alpöge, who had been investigating the problem independently. On 15 August 2026, Buckmaster and Alpöge achieved a step toward Navier-Stokes by building upon methods developed by Spanish mathematicians Diego Córdoba of ICMAT and Luis Martínez-Zoroa of CUNEF University. Fields Medalist Terence Tao evaluated that earlier work as a notable achievement with no obvious obstacles preventing its extension to Navier-Stokes. Hours before OpenAI released its paper, Buckmaster published a statement alleging that OpenAI launched its project only after learning about their private, unreleased research. Buckmaster noted that he and Alpöge used OpenAI tools, including Codex and GPT-5.6 Sol, to draft their work and questioned whether their private session data informed OpenAI's model.

It is true that we got into this because last week there were rumors on the internet that Anthropic models had solved a Millennium problem, and we were curious to see if ours could do it too.

Data access questions and next steps

In his statement, Buckmaster described asking OpenAI whether the company trained its models on private Codex sessions containing draft concepts. OpenAI stated that the model did not directly access private user data during the run, but acknowledged that anonymized platform data could have contributed to broader model training. Sebastien Bubeck, a researcher at OpenAI, stated that the computing budget for the 10,000-agent run exceeded the resources allocated for earlier math projects by a factor of 1,000. OpenAI explained that while Buckmaster and Alpöge studied an unforced equation variant, the OpenAI proof relies on an externally applied smooth force. The mathematical community must now evaluate whether this forced-flow singularity satisfies the exact conditions required by the Clay Mathematics Institute.