OpenAI claims Navier-Stokes solution in 88 hours as rival researchers dispute priority

The Navier-Stokes announcement

On 8 September 2026, OpenAI published a 166-page manuscript detailing a proposed solution to the Navier-Stokes existence and smoothness problem. The equations, originally formulated by French engineer Henri Navier in 1822 and completed by Irish physicist George Gabriel Stokes in 1845, describe three-dimensional fluid motion in water, air, and smoke. The problem represents one of seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000, which offers a 1 million dollar prize for each verified solution. OpenAI reported that its proof demonstrated that Navier-Stokes equations can develop singular behavior in finite time through an inward-spiraling vortex.

The computation was executed by a network of approximately 10,000 autonomous agents powered by an unreleased internal model positioned above GPT-6 Astra. The agent cluster was initiated on 2 September and produced its findings on 5 September after roughly 88 hours of runtime, utilizing code execution, stored web resources, and formal mathematical verification in the Lean language. OpenAI stated that it does not intend to claim the Clay Institute prize money for the result.

Dispute over research priority

The announcement coincided with contestation from academic mathematicians. Tristan Buckmaster, a mathematics professor at New York University, published an open letter twelve hours prior to OpenAI's post, stating that the company moved into the problem only after learning of external progress. Buckmaster had spent a year researching Navier-Stokes and related forced Euler equations in collaboration with Levent Alpöge, a mathematician at rival artificial intelligence firm Anthropic. Spanish mathematician Luis Martínez Zoroa of CUNEF Universidad de Madrid also noted that his foundational handwritten mathematical formulations formed part of the underlying approach.

Buckmaster explained his decision to issue a public statement regarding the sequence of communications between his team and OpenAI.

Because the alternative is to let a series of announcements say something that I know is false.

Dispute over model data and user logs

Buckmaster and Alpöge used OpenAI's Codex system and Anthropic's Claude during their preliminary research. Buckmaster stated that on 3 September he discovered details of their work had reached OpenAI, leading to a telephone discussion on 4 September with OpenAI researcher Sébastien Bubeck. During that call, Buckmaster inquired whether OpenAI's systems had accessed the research team's Codex logs or utilized them for model training.

In his written statement, Buckmaster clarified his stance regarding the model's operation.

I do not know if our data was used. I am not accusing anyone of anything.

Bubeck and OpenAI leadership stated that researchers did not access user files or unpublished work before the release. However, OpenAI stated in its official response that it could not exclude the possibility that interaction data from product usage contributed broadly to foundational model improvements. The company congratulated Buckmaster and Alpöge on their simultaneous work.

Verification and mathematical assessment

The Clay Mathematics Institute has not yet issued a formal comment or validation of the 166-page manuscript. To date, only one Millennium Prize Problem, the Poincaré Conjecture, has been formally recognized as solved, after Russian mathematician Grigori Perelman presented a proof and subsequently declined the 1 million dollar prize in 2010. Independent mathematicians reviewing the 166-page paper noted that full verification through peer review will require extensive technical analysis by specialist committees before any consensus is reached.