OpenAI published an AI-generated proof for the Navier-Stokes problem on September 8, 2026, one of seven Millennium Problems, each with a prize of one million US dollars, from the Clay Mathematics Institute. Around ten thousand agents from an unpublished internal model worked on the solution in 88 hours. At the same time, a mathematician from New York University accuses OpenAI of having used its unpublished preliminary work.
Ten thousand agents develop the proof in four days
According to OpenAI, around ten thousand autonomous agents from an internal, yet unpublished model were deployed. The agents reached the solution on Saturday, September 5, after 88 hours of computation time. The subsequent formalization with the proof assistant Lean required the model GPT-6 Astra an additional 17 hours. In August, OpenAI had reported that an internal Astra version had solved ten long-standing unsolved math problems. The new, stronger model is said by OpenAI to go significantly beyond that. In total, the systems exchanged nearly 4.9 million messages and generated around 300 billion output tokens. Of these, 2.7 million messages and about 130 billion tokens were attributed to the Navier-Stokes problem. There are varying estimates regarding the computational costs. An industry observer estimates public prices for GPT-6 Astra at around 15 million dollars. Buckmaster himself cites 22.5 million dollars. An OpenAI researcher speaks generally of several million dollars – independently unverified. The formal verification by Lean gives professionals confidence in the technical correctness of the proof, but does not replace a complete review by the mathematical community.
Mathematician accuses OpenAI of accessing private preliminary work
The dispute began when NYU mathematician Tristan Buckmaster, along with Anthropic researcher Levent Alpöge, published their own Lean-verified proofs on related questions on the same Tuesday. This occurred just hours before OpenAI’s complete Navier-Stokes proof. Both had previously used both OpenAI’s Codex and Anthropic’s Claude for their private preliminary work. Anthropic itself had reported in early September that dozens of Claude agents had formalized Fermat’s Last Theorem in Lean. In a public statement on his NYU page, Buckmaster writes that rumors about this unpublished work had reached OpenAI as early as September 1. Shortly thereafter, the company launched its own campaign with the same unusual solution approach. According to Buckmaster, an OpenAI employee offered him a mention as co-author – on the condition that Alpöge be removed from the author list due to his employment at Anthropic. Additionally, Buckmaster doubts OpenAI’s original account that the model found the solution with almost no human intervention. OpenAI researcher Sébastien Bubeck dismisses the accusations on platform X as false and inflammatory. Neither the researchers nor the agents had seen the private work of the two mathematicians before its publication, Bubeck explains. He also offers to disclose all prompts and documents used.
Clay Institute officially recognizes proofs only after years
Should the proof be confirmed, it would be only the second solved Millennium Problem after the Poincaré Conjecture. Russian mathematician Grigori Perelman solved this in 2002 but declined the award and prize money. Five of the seven problems, including the Riemann Hypothesis and the P versus NP question, remain unsolved. The Clay Mathematics Institute officially recognizes a proof only when it appears in a recognized scientific publication. Additionally, it must stand unchallenged for at least two years there and gain acceptance in the scientific community. A decision on OpenAI’s proof is still pending, and there has been no statement from the institute itself so far. Princeton mathematician Charles Fefferman expressed, according to Quanta Magazine, his pleasure that the problem appears to be solved, without commenting on the authorship issue. On the betting platform Manifold Markets, participants currently assess the probability that OpenAI will actually receive the prize money at only ten percent. This indicates significant skepticism in the community even before the actual peer review has begun.
It will now be crucial whether the scientific community confirms the proof in the coming months. It also remains open how the Clay Mathematics Institute will handle the unresolved authorship issue should a review take place. The incident also shows how quickly AI systems are now working in parallel on the same open research questions. How little the rules for priority and attribution are clarified is only now becoming visible – in a research field that has so far been designed around human timelines.
