On September 8, 2026, OpenAI announced that an internal model, run as roughly 10,000 coordinating agents over 88 hours, had produced a proof concerning the Navier-Stokes equations -- a 90-year-old open problem in fluid dynamics and one of the seven Millennium Prize problems. The agents produced an analytical proof and a formally verified (Lean) demonstration that Navier-Stokes dynamics can develop a singularity -- a specific vortex solution that spirals inward and stretches indefinitely -- in finite time.[1] Solving Navier-Stokes specifically took roughly 130 billion output tokens and 2.7 million agent messages; across all the problems the same effort tackled, the total ran to roughly 300 billion tokens, an estimated $22.5 million in compute at standard rates.[2]
Tristan Buckmaster, an NYU mathematics professor, had been working the same general territory in collaboration with Levent Alpöge, a mathematician employed by Anthropic, using both Codex and Claude as tools. Buckmaster announced preliminary findings of his own. OpenAI's own account: its effort began September 1, after the company heard a rumor connected to Buckmaster and Alpöge's work, and it completed its result and Lean verification by September 6 -- at which point it reached out to offer a "concurrent release" and credit Buckmaster and Alpöge's priority in a joint announcement.[3] Buckmaster's account of the same week is sharper: he says OpenAI pressured him to drop Alpöge's name from the credit, and that an OpenAI researcher warned him, in his telling, not to "ruin his career" by pushing back.[4] Both accounts agree on the dates. They do not agree on what the dates mean.
There is a real, separate question underneath the credit dispute, and it is about the tool itself, not who said what to whom. Buckmaster had used OpenAI's own Codex extensively while working the problem, and OpenAI's terms reserve the right to train on user interactions. He has said he cannot rule out that his own usage data, even de-identified, informed OpenAI's effort -- and OpenAI itself has said the same: it "cannot rule out" that de-identified data from his usage assisted its models.[4] If that's true even partially, the tool a mathematician used to do his own work became, without his knowledge or consent, part of what let a competitor race him to the finish.
Why does this matter? The mathematical result is real -- a genuinely hard, formally verified proof, produced fast and at real cost. Neither of those facts resolves the other question sitting next to it: whether the company that produced it got there partly by watching, even passively, the work of the people it ended up racing. This outlet has already covered the same research organization's own numbers on what a headline AI achievement actually costs to produce.[5] This is the same pattern at a different altitude -- an achievement and its actual cost, credit, and provenance are three separate questions, and getting the first one right says nothing about the other two.