On Monday, NYU mathematician Tristan Buckmaster published work showing that a simplified Navier–Stokes system could break down — a major advance after nearly a year of collaboration with Anthropic mathematician Levent Alpöge and publicly available AI tools. The full Navier–Stokes existence-and-smoothness question is one of the Clay Mathematics Institute’s seven Millennium Prize Problems, each carrying a $1 million award.¹

Then OpenAI moved. The company says that after hearing rumors on September 1 that two Millennium problems had been solved, it set an unreleased model on the remaining problems. Roughly 10,000 coordinated agents reached a proposed Navier–Stokes proof in about 88 hours, after an effort costing millions of dollars in compute.² CEO Sam Altman called it “one of the most amazing moments” in OpenAI’s history.Sam Altman (sama)³

Buckmaster’s objection is not that OpenAI could not have found a proof, but that its timing and route deserve scrutiny. He says the pair learned that information about their unpublished progress had reached OpenAI, and argues their chosen approach was unusually specific: “It is not the direction one arrives at in a few days by giving a model the problem statement.”⁴ He also raised the possibility that their Codex interactions might have indirectly informed OpenAI’s models.

OpenAI denies its researchers or agents saw the mathematicians’ work before it was public, saying “no specific user data was accessed.” Yet it conceded a narrower uncertainty: it “cannot rule out” that de-identified data from product use helped improve its models.² Altman also rejected allegations that Alpöge was asked to surrender authorship, saying OpenAI initially sought a joint release and that staff acted “with integrity and generosity.”Sam Altman (sama)⁵

The dispute has widened beyond one proof. Critics argue the episode exposes a mismatch between open-ended academic research and companies able to spend millions deploying private models at extraordinary scale. Yann LeCun amplified calls for “alternative points of view” on how OpenAI’s result came about.Yann LeCun (ylecun)⁶ The mathematical claim now awaits outside scrutiny; the trust question is already here.