On September 8, OpenAI announced that an unreleased internal model, running roughly 10,000 agents, had produced a proof about the Navier-Stokes equations, the mathematics that describes how air, water and other fluids move. The company said its agents reached the result in about 88 hours and that the argument had been checked in Lean, a proof assistant that verifies every logical step. Then the argument started. The proof has not been reviewed, mathematicians dispute whether it answers the problem as posed, and a lot of the anger is about how OpenAI got there.
What OpenAI says it proved
The Navier-Stokes equations are one of the seven Clay Millennium Prize Problems, each worth $1 million. The question is whether a solution that starts smooth can break down in finite time, producing a singularity. OpenAI's claim concerns the forced equations, where an outside force is applied, and the company says it establishes alternatives (C) and (D) in the official problem statement. Mathematicians dispute whether the result settles the question the field cares about: it establishes alternatives (C) and (D), the forced case, and leaves the unforced case untouched. Clay waits two years after publication before considering an award, so no prize is on the table now.
A rumor started a five-day compute race
OpenAI says its effort began September 1, after the company heard a rumor about work by Buckmaster at NYU and Levent Alpöge, a mathematician at Anthropic. It started with about 100 agents on the simpler unforced Euler equations, got a result after 50 hours, then sent 10,000 agents at Navier-Stokes. Lean verification finished on September 6, and OpenAI offered a concurrent release. Buckmaster describes what followed as a scoop: he and Alpöge posted their own papers roughly 12 hours before OpenAI's announcement. OpenAI has said the run cost millions of dollars; outside estimates run from about $10 million to $15 million at list prices.
Two accounts of one authorship conversation
Buckmaster says Sébastien Bubeck, an OpenAI researcher, twice proposed dropping Alpöge, an Anthropic employee, from a paper. Buckmaster said, "All I had to do was throw Levent under the bus." Bubeck denies asking for Alpöge's removal. His account is that he only remarked it would be simpler if Alpöge were not at Anthropic, during discussions about making Buckmaster lead author on a rewrite of OpenAI's proof. Both versions are on the record and neither has been independently settled.
OpenAI answered the data question twice
Buckmaster had used OpenAI's Codex on the problem. OpenAI first said it could not rule out that de-identified data from researchers' product use had helped improve its models. By September 9 and 10 the position had hardened: spokesperson Laurance Fauconnet said it was "categorically" impossible for Buckmaster's Codex prompts over the previous two months to have influenced the system "in any way, including training." Buckmaster's reply was that such statements deserve skepticism. In Dresden, Andreas Thom published emails asking whether his ChatGPT conversations about non-sofic groups had reached training data; he was told they had not, a response he says covers only direct access during the solve.
Twenty-five Fields medalists call the goals misaligned
On September 11, 25 Fields Medalists including Terence Tao, Maryna Viazovska and Peter Scholze signed a declaration titled "A Severe Misalignment of AI in Mathematics," arguing that treating famous problems as benchmarks harms the science. The day before, OpenAI withdrew its $10,000 share of Caltech's Mathathon sponsorship after an open letter with 771 signatories objected to the contest format. OpenAI research lead Dan Roberts said rapid progress in AI for mathematics is disruptive; Anthropic remains a sponsor. Organizers said they expect little impact.
Why it matters
The mathematics may take years to settle. The consequences mathematicians describe are already visible. Tao warns that a rumor alone can now trigger a compute race that crushes the original project. Buckmaster says nobody wants to share unfinished work anymore, and calls the feud "petty drama between two trillion-dollar companies that are acting like children." Fields Medalist Shing-Tung Yau worries that competing with companies whose resources dwarf academic groups could make researchers more reluctant to pursue ambitious questions.
None of this decides whether OpenAI's proof holds. It does show what changes when a five-day run can outspend a research program, and when the accounts of what happened come from the companies themselves. Credit is no longer only a question for journals. It has become a negotiation between employers.
If a five-day sprint costing an estimated $10 million can decide who gets credit for a theorem, what should a university group share about an unfinished idea, and when?