NYU mathematics professor Tristan Buckmaster has publicly accused OpenAI of academic misconduct in a high-stakes race to solve the Navier-Stokes existence and smoothness problem — one of the seven Clay Mathematics Institute Millennium Prize problems, each carrying a $1 million bounty.
Buckmaster announced three proofs on Tuesday, including a preliminary finding on the Navier-Stokes problem, made in collaboration with Anthropic mathematician Levent Alpöge. The pair used both OpenAI's Codex and Anthropic's Claude models in their research. However, the announcement was accompanied by an unusual public statement detailing a dispute with OpenAI.
According to Buckmaster, while he and Alpöge were finalizing their results, they learned that information about their progress had been passed to OpenAI. When they contacted OpenAI, the company claimed it had already achieved a full proof of the central problem. However, when asked when OpenAI had begun its research and how much human input was involved, the answers became evasive.
"It emerged that an entire team had been working on the problem," Buckmaster said, "and that an insane amount of compute had been used... Eventually, it was agreed that [the first prompt] had been sent in the past few days, after information about our work had reached OpenAI."
The dispute centers on the unusual research route both parties took — through a smooth force approach that Buckmaster says almost nobody else was pursuing. "It is not the direction one arrives at in a few days by giving a model the problem statement," he wrote.
Sebastian Bubeck, who leads OpenAI's mathematical research, called the claims "false and inflammatory" and said he had followed academic norms. Bubeck also allegedly asked Buckmaster to remove Alpöge's credit as part of a proposed compromise, and when Buckmaster pushed to make the dispute public, Bubeck replied: "Why would you ruin your career?"
Adding another layer of concern, Buckmaster raised the possibility that because he used Codex extensively, information from his work could have been used to train OpenAI's models — potentially allowing the company's AI to regurgitate his research when faced with a similar problem. OpenAI reserves the right to train models on Codex interactions, though users can opt out.
The incident is likely to reignite debate about AI's role in mathematical research and the specific incentives facing companies like OpenAI, which have enormous computing resources and direct access to researchers' working data through their own tools.
