OpenAI claims solution to 90-year-old Navier-Stokes math problem using 10,000 AI agents

Unreleased model and 88-hour computational run

On 8 September 2026, OpenAI announced that an internal artificial intelligence system had solved the Navier-Stokes existence and smoothness problem in 88 hours. The company began training the underlying model on 28 August, describing it as significantly more capable than its recently released GPT-6 Astra. After receiving reports on 1 September that researchers were making progress on Millennium Prize problems, OpenAI deployed roughly 10,000 autonomous agents to target the equations. During the run, the bots exchanged nearly 3 million messages and consumed 130 billion output tokens, an effort estimated at roughly $10 million under standard company pricing. Mark Chen, head of research at OpenAI, stated at a press briefing that computing costs reached millions of dollars.

It is a significant step in AI research. It is the promise that it will become possible to answer other of the most complex questions.

The Navier-Stokes existence and smoothness problem

Formulated by French engineer Henri Navier in 1822 and physicist George Gabriel Stokes in 1845, the equations describe the flow of fluids and gases. They serve as foundational tools for weather forecasting, climate modelling, and aircraft wing design. In 2000, the Clay Mathematics Institute designated the Navier-Stokes existence and smoothness question as one of seven Millennium Prize Problems, offering a $1 million reward for a solution. The core problem asks whether smooth initial fluid motion in three dimensions can break down and develop a singularity in finite time. OpenAI's proof asserts that the equations can develop such singularities, suggesting theoretical conditions under which fluid velocities could become infinite.

Is there some initial fluid configuration where water splashes around and, at some point, all the energy implodes and sends all the water particles off into infinite velocity? Could you set some fluid in motion, watch it flow, and then it blows up?

Allegations of data access and compute race

The announcement coincided with a dispute involving New York University mathematics professor Tristan Buckmaster and Anthropic researcher Levent Alpöge. The pair had published findings on a related problem on 7 September after working with OpenAI's Codex and Anthropic's Claude. Buckmaster stated that after learning OpenAI had heard about their progress, he discovered the company was pursuing a proof along the same mathematical route. He questioned whether OpenAI accessed drafts stored in Codex sessions to inform its research. OpenAI stated that no specific user data was accessed, though it could not rule out that de-identified product usage data contributed to model training.

We did not see any of their work until they released it publicly last night. One can in hindsight see that our proofs differ significantly and even the precise results proved are different.

Verification and academic response

OpenAI mathematical research lead Sebastien Bubeck described the accusations as false and inflammatory, stating that the company followed academic standards. Prior to OpenAI's claim, mathematicians had solved only one of the seven Millennium Prize Problems since their designation in 2000. The Clay Mathematics Institute has not yet verified or accepted OpenAI's proposed solution. Independent mathematicians and peer reviewers must examine the generated proof before any formal acceptance or prize distribution occurs. OpenAI stated that it plans to present further technical details to the scientific community as verification proceeds.