OpenAI claims Navier-Stokes breakthrough amid accusations from researchers

Before OpenAI's announcement, New York University mathematics professor Tristan Buckmaster and Levent Alpöge, a mathematician employed by Anthropic but working in a personal capacity, had made public their own findings on the same problem. Buckmaster said in a statement that the pair had used both OpenAI's Codex and Anthropic's Claude in the work, and that information about their progress was passed to OpenAI. When they asked OpenAI about this, he said, the company said it already had a full proof. Follow-up questions about when that research began and how much human input was involved produced evasive answers, he said, and an entire team and an 'insane amount of compute' had been deployed.

Buckmaster said the route he and Alpöge had chosen was unusual, and he had asked OpenAI whether its model had been trained on or had access to their Codex sessions, where they had stored their drafts. 'I was told the model did not look up user data. I asked again, about training, and I did not get an answer,' Buckmaster wrote. OpenAI reserves the right to train models on Codex interactions unless users opt out, according to TechCrunch.

OpenAI said in response that no specific user data was accessed in order to solve the problem, while adding that it could not rule out that de-identified data derived from product usage had helped improve its models. Sebastien Bubeck, who leads OpenAI's mathematical research, called Buckmaster's claims 'false and inflammatory.' Bubeck said OpenAI did not see any of Buckmaster and Alpöge's work until it was released publicly. 'One can in hindsight see that our proofs differ significantly and even the precise results proved are different,' he said.

Buckmaster also said Bubeck proposed two ways to handle credit: Buckmaster could publish a partial development and let OpenAI publish its full solution the next day, or he could write a solo paper crediting an OpenAI model and leave Alpöge's name off it. Buckmaster said he refused both options and that Bubeck had asked him to drop Alpöge because Alpöge was affiliated with rival Anthropic. Bubeck denied asking for Alpöge's name to be removed and said he would make a fuller statement soon. Engadget reported that Bubeck specifically refuted that claim.

Buckmaster said Bubeck also warned him against going public, telling him, 'Why would you ruin your career?' and, when he pushed back, 'If you don't want me to be nice, then I don't have to be nice.' OpenAI CEO Sam Altman and Bubeck both posted their versions of events on social media. After OpenAI's statement, Buckmaster wrote on Mastodon that the company was 'openly admitting they used training data from a period after we found our result.' He also wrote that he had not seen OpenAI's proof and did not know whether his team's data was used. 'I am not accusing anyone of anything. I am stating what I was told, when, and what was proposed to me,' he wrote.