NYU mathematician alleges OpenAI used compute advantage to race ahead on Millennium Problem proof

NYU mathematician Tristan Buckmaster posted three proofs two days ago, one containing a preliminary result toward the Navier-Stokes existence and smoothness problem. The real story, Buckmaster says, is what happened behind the scenes.

Buckmaster and Levent Alpöge, a mathematician at Anthropic, had been working quietly on an unusual approach using OpenAI's Codex models and Claude. According to Buckmaster, when information about their progress leaked to OpenAI, the lab allocated an entire team and an extraordinary amount of compute to reach a full proof first.

Their path runs through "smooth force," options c and d in Charles Fefferman's formulation of the problem. According to Buckmaster, almost no other mathematician has pursued this direction, and it is not a route one stumbles onto after a few days of prompting a model. The suspicion arose when OpenAI appeared to adopt exactly the same path in exactly the same time window, after information about the pair's work reached the lab.

Sebastian Bubeck, who leads mathematics research at OpenAI, denies the allegations forcefully, calling them "false and inflammatory." He says he entered the discussion according to academic norms and is disappointed by the escalation. Buckmaster describes a different interaction: when he asked to make the dispute public, Bubeck allegedly replied, "Why would you ruin your career?" and later, "If you don't want me to be nice, I don't have to be nice." Buckmaster also says Bubeck asked him to remove Alpöge's name from the credits as part of a proposed settlement.

A further concern: Buckmaster used Codex extensively to assemble the project. OpenAI reserves the right to use data that passes through the model, raising the possibility that his interaction logs fed directly into the lab's parallel effort. Alpöge, though employed by Anthropic, did not conduct the research on the company's behalf; his institutional affiliation nevertheless appears to have been a friction point for OpenAI.

The Navier-Stokes problem is one of the seven Clay Mathematics Institute Millennium Problems, each carrying a prize of one million dollars. A full solution would significantly advance theoretical understanding of fluid mechanics. The episode exposes a structural tension in the AI-for-mathematics race. When closed models serve as research instruments, who controls the knowledge accumulated through them, and can a resource advantage substitute for open scientific process? Bubeck has promised a more detailed statement soon. In the meantime, the mathematical community is waiting to see whether Buckmaster and Alpöge's proofs survive peer review — and whether OpenAI has anything to show.