New York University mathematicians Tristan Buckmaster and Levent Alpöge say they recently used large language models including Claude and Codex to push forward several fluid dynamics problems within a month, with some results already machine-verified in Lean. Before the papers were fully released, their dispute with OpenAI broke into the open.
Contact began after unpublished work reached OpenAI
According to Buckmaster, their unpublished progress reached OpenAI in early September. He said he then contacted the company himself in an effort to avoid the two sides colliding on the same research track.
Three days later, OpenAI researcher Sébastien Bubeck told him that an internal OpenAI model had already written about 100 pages of a Navier-Stokes proof, Buckmaster said. Navier-Stokes is one of the seven Millennium Prize Problems, and the Clay Mathematics Institute has attached a $1 million reward to it.
Questions over timing and possible data use
Buckmaster said he repeatedly asked OpenAI when the work had started. In his account, the company eventually confirmed that the first prompt had been submitted only in the past few days, at a time when OpenAI already knew that he and Alpöge had made progress.
He also said OpenAI was pursuing a route that overlapped closely with their own, a route he described as one that had received little prior attention. Buckmaster added that OpenAI had a team and substantial computing power behind the effort. Drafts of the two mathematicians' work had previously been stored in Codex.
That led him to ask whether those materials had been used for training, but he said he did not receive a clear answer. He also acknowledged that he has no evidence at present that OpenAI used the data.
Authorship dispute pushed the matter public
Buckmaster said later negotiations turned the conflict into a public dispute. In one proposal, he said, OpenAI suggested that he and Alpöge publish their own results first, with OpenAI releasing its Navier-Stokes work the next day.
Another proposal, according to Buckmaster, would have had him write OpenAI's paper without listing Alpöge as an author. He said Bubeck raised removing Alpöge twice and gave as the reason that Alpöge works at Anthropic.
Buckmaster said he refused and warned that if OpenAI published under that arrangement, he would make the full sequence of events public. He said he was then asked, 「Why do you want to destroy your own career?」
Later that day, Bubeck separately contacted Alpöge and said he was unsure whether Buckmaster had been 「fully rational」 at the time, according to Buckmaster's account. Alpöge did not accept the one-on-one exchange.
Buckmaster released his paper early; Bubeck rejects the claims
Buckmaster ultimately published his paper and statement ahead of schedule. He also stressed that he has not seen OpenAI's proof, does not know whether it works, and does not know whether his Codex data was used.
Bubeck later publicly denied the allegations, calling them 「false and inflammatory,」 and said he would respond further.