OpenAI announced that an internal AI-driven system claimed to have found a solution to the long‑standing Navier–Stokes problem. According to the company, the work was performed by a coordinated agent system comprising roughly ten thousand parallel agents. These agents had access to a cached version of the internet, could execute code, organized into groups, and communicated with one another while working on the problem.
OpenAI says the effort began on September 1 and that a solution emerged about 88 hours later, on Saturday, September 5. The Navier–Stokes problem concerns theoretical questions tied to the partial differential equations describing fluid motion and is one of the seven Millennium Prize Problems announced by the Clay Mathematics Institute in 2000; each problem carries a one‑million‑dollar prize. The Clay Mathematics Institute had not responded to OpenAI’s announcement at the time of reporting.
The announcement quickly prompted a dispute over origin and data use. Tristan Buckmaster, a mathematics professor at New York University, posted a statement on his website saying that he and Levent Alpöge, who works at Anthropic, had previously collaborated on the Navier–Stokes problem. Buckmaster said Alpöge received indications that information about their joint work had reached OpenAI. He added that the solution path presented by OpenAI resembles their approach and argued that this was not the kind of direction one would arrive at in a few days simply by presenting the problem to a model.
Buckmaster also raised the possibility that OpenAI’s models had been trained on data from the two mathematicians’ sessions on the OpenAI Codex platform. He emphasized, however, that he had not seen OpenAI’s proof, does not know the model’s exact behavior, and does not assert with certainty that their data were used.
OpenAI responded that it began working on the problem on September 1 after hearing a rumor, and only later realized the rumor referred to the work of Alpöge and Buckmaster. The company said neither the researchers nor the agents had access to the mathematicians’ work prior to its public release, and that it did not use specific user data in developing the solution. OpenAI did acknowledge that it could not entirely rule out the possibility that anonymized data derived from use of its products contributed to model training.
The dispute touches on ethical and procedural questions about the use of data in training large models and the standards for validating claimed mathematical proofs. Independent review, transparency about methods, and responses from the Clay Mathematics Institute and other experts will be central to assessing whether the claim meets the mathematical community’s standards. Further developments and evaluations by independent mathematicians will be important to watch.
Note: An AI assistant contributed to preparation of the original article; a journalist edited and verified the final content.
