OpenAI Says It Solved Navier-Stokes, and Mathematicians Are Uneasy

The Verge reported that it spoke with more than a dozen mathematicians, including Tristan Buckmaster, a professor at New York University, and Andreas Thom, both of whom are at the center of recent controversies over OpenAI's work in the field. Even researchers skeptical of the most serious allegations described a discipline shaken by the company's conduct and uncertain what it will do next in its effort to beat its rivals.

According to OpenAI, the company heard that some researchers were making progress on Millennium Prize problems and decided to test whether one of its advanced, unreleased models could make headway. It could. In the course of that work, OpenAI says it learned whom it was racing: Buckmaster and Levent Alpöge, a researcher at Anthropic, one of OpenAI's fiercest competitors. The two were pursuing Navier-Stokes among several lines of research and had not yet completed a proof.

Alpöge has described his work as a "personal collaboration" independent of his employer, but his involvement was a problem for OpenAI. Buckmaster said he contacted the company after learning it had become aware of their progress and was racing toward a solution of its own, and that discussions with OpenAI researcher Sébastien Bubeck grew contentious and, in his view, threatening.

Buckmaster said OpenAI offered him a path forward that excluded Alpöge: practically unlimited compute to finish his own work, and the chance to be the sole author of the company's paper announcing the breakthrough, which would credit OpenAI's tools. "All I had to do was throw Levent under the bus," Buckmaster told The Verge in a phone interview. He said he rejected the offer, which he regarded as a bribe.

He also began questioning whether OpenAI might have benefited from his earlier use of Codex, one of the company's AI tools, which he had been using to attack the problem. OpenAI spokesperson Laurance Fauconnet denied that material from his prompts played any role. "We can say categorically that it is impossible for Dr. Buckmaster's Codex prompts over the last two months to have influenced the system in any way, including training," Fauconnet said in a statement. The company has denied that anyone, or any agent, accessed his specific user data, and in earlier comments acknowledged it could not rule out the possibility that data derived from his use of its products was used to improve the model.

Buckmaster said the denial did not settle the matter. "Given their behavior up until this point, one should take such statements with great skepticism," he said. He decided to make both his mathematics and his account of OpenAI's conduct public, and said his office had been turned into something of a "war room," with colleagues helping scrutinize his work, coordinate outreach and contact lawyers.

Bubeck has rejected Buckmaster's characterization of the conversations, both on social media and in an interview with The New York Times.

The dispute has landed in a field that is not accustomed to this kind of drama. Several mathematicians told The Verge that OpenAI appears less like an enthusiastic newcomer than an impossibly well-resourced interloper, moving into problems they have spent careers on with little apparent regard for long-standing norms or for those left behind. At the center of that unease, they said, is a difference in purpose: mathematicians want to advance the field, while OpenAI wants to win.