How much human input did OpenAI's Navier-Stokes proof actually require?

Tristan Buckmaster's public statement describes a dispute over a rumored OpenAI result on the Navier-Stokes blowup problem, timed against his and Levent Alpöge's own LLM-assisted blowup results for porous media, Boussinesq, and Euler. Sebastien Bubeck told Buckmaster that an internal OpenAI model had produced a proof of finite-time blowup for forced Navier-Stokes, and that Levent "had been told by Sebastien 'very little human input' had been used." Buckmaster writes plainly: "This turned out not to be true."

Buckmaster gives the specifics that undercut the "very little human input" framing: as members of the OpenAI team supplied Bubeck with corrections over an internal chat during the call, it emerged that "an entire team had been working on the problem," that the team had first tested the model on easier problems including Euler, that "even the prompt that had been shown to me had been written by prompting Codex," and that the first prompt was sent only "in the past few days, after information about our work had reached OpenAI" — a fact Buckmaster says OpenAI did not answer directly for some time. He also reports pressure that went beyond the mathematics: a proposal to remove Alpöge from authorship because "it was so annoying" that he works at Anthropic, and a reply of "Why would you ruin your career?" when Buckmaster said he would go public.

This sits beside Did GPT-5 really solve previously unsolved math problems? as a second instance of an OpenAI math capability claim needing correction once more of the story came out — but the gap this time is not that a problem was already known to specialists, it is that the degree of human scaffolding behind a model's output was represented as smaller than it was. It also complicates Can opaque machine learning models help prove new mathematics?: Tao's framing assumes validation of a model's output is the open question, whereas Buckmaster's account shows the validation he was denied was of the claim about the process — how much the model was told, tested, and prompted by people — not just the proof itself.

Buckmaster is explicit about the limits of his own claim: "I have not seen OpenAI's proof. I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything. I am stating what I was told, when, and what was proposed to me." The excerpt therefore establishes a credible first-person account of a contested, commercially-pressured framing of human involvement, not a verified fact about what the OpenAI model actually did unaided. The implication the evidence does support is narrower but still real: when a lab's own account of "minimal human input" is the only source for a capability claim, and that account changes once the people who built the result start correcting it on a call, the claim was not fact-checkable from the outside at the time it was first represented.