The OpenAI Navier-Stokes controversy erupted after the company announced it had solved part of the Navier-Stokes equations, one of the Millennium Problems. According to BBC, OpenAI deployed roughly 10,000 AI agents, and the system worked for 88 hours. However, the announcement is accompanied by a dispute over priority and accusations of plagiarism raised by mathematicians Tristan Buckmaster and Levent Alpöge.
Buckmaster from New York University and Alpöge from Anthropic spent about a year working on a proof of the Euler equations, which are considered a stepping stone to Navier-Stokes. According to BBC, they used OpenAI Codex and Anthropic Claude as assistants. They obtained results on August 15, 2026, and verified them on August 22 using the Lean system. Buckmaster described the AI-generated proof as "AI slop" and wanted to rewrite it.
According to Buckmaster, on September 3, he learned of rumors that Anthropic had solved an important mathematical problem. He therefore wrote to a prominent mathematician at OpenAI. This was followed by conversations with Sébastien Bubeck, who told him that OpenAI had proven the final blowup for forced Navier-Stokes equations. Buckmaster claims this was exactly the direction his team had chosen and that it could not be reached in a few days.
OpenAI Navier-Stokes controversy: Questions over Data and Priority
According to Axios, OpenAI stated that it did not use specific user data to solve the problem but could not rule out that anonymized data from product usage helped improve the models. The company also stated that it has no intention of claiming the million-dollar prize from the Clay Mathematics Institute.
Buckmaster, however, told The Guardian: "I don't know what their model did, or how. I don't know if our data was used. I'm not accusing anyone of anything." At the same time, he questioned whether OpenAI might have used the research direction it learned from their work. OpenAI, in contrast, claims it did not see their work until it was published.
Buckmaster also stated that Bubeck pushed to remove Alpöge from authorship due to his employment at Anthropic and allegedly told him: "Why would you ruin your career?" and "If you don't want me to be nice, I don't have to be." OpenAI CEO Sam Altman, according to Axios, said: "Now that we see their work, the approaches seem different."
The proof still awaits peer review, which could take years. The dispute over priority and data usage thus remains open.