A breakthrough that was supposed to cement OpenAI's dominance in AI-driven mathematics has instead exposed the company to its ugliest research controversy yet. Days after announcing that an internal model had cracked a piece of the Navier-Stokes existence and smoothness problem — one of the Clay Mathematics Institute's seven Millennium Prize Problems — OpenAI is facing detailed, on-the-record allegations from an NYU mathematics professor that one of its own scientists pressured and then threatened him during a dispute over credit.
The mathematician, Tristan Buckmaster, says the threat came down to a single line, delivered after he refused to restructure his own paper on OpenAI's terms: if he wouldn't cooperate, the OpenAI researcher wouldn't have to be nice to him. OpenAI disputes the framing of the episode, though the researcher involved has since walked back part of what he said.
How the Dispute Started
Buckmaster had spent months working with Levent Alpöge, a researcher at Anthropic, on a proof related to the forced Euler equations — a close cousin of the Navier-Stokes problem, tied to the same 90-year-old question of whether smooth fluid motion can spin into a singularity in finite time. As part of that work, Buckmaster has said he used AI tools from both OpenAI and Anthropic, and uploaded his drafts to OpenAI's Codex coding assistant throughout the project.
According to Buckmaster's account, rumors about the pair's progress began circulating among AI researchers around September 1. Days later, he says, OpenAI reached out asking for an urgent call. When that call took place on September 6 with Sébastien Bubeck — the OpenAI scientist leading the company's math effort — Buckmaster says he learned that an OpenAI model had independently produced a roughly 100-page proof of finite-time blowup for forced Navier-Stokes, using what he describes as the same unusual line of attack he and Alpöge had quietly settled on months earlier.
The Proposal Buckmaster Says He Was Given
What happened next is the crux of the dispute. Buckmaster says Bubeck laid out two options for how the announcements could proceed. In the first, he and Alpöge would publish their partial result, and OpenAI would announce its fuller solution the following day with an acknowledgment that the two of them were the closest humans to the problem. In the second option, Buckmaster says, he could publish and claim the Millennium Prize himself — but only if his paper stated that OpenAI's model had also solved the problem, and only if he removed Alpöge as a co-author, because OpenAI objected to his affiliation with Anthropic.
Buckmaster says he refused both terms and warned that he would go public if OpenAI proceeded the way it had proposed. It was at that point, he alleges, that the conversation turned confrontational.
The Alleged Threat
"Why would you ruin your career?" — Bubeck, as quoted by Buckmaster
Buckmaster says that when he identified himself as an academic rather than someone who could be pressured that way, Bubeck responded with the line that has since defined the controversy:
"If you don’t want me to be nice, then I don’t have to be nice." — Bubeck, as quoted by Buckmaster
Buckmaster has also said Bubeck separately messaged Alpöge, questioning whether Buckmaster was representing the situation accurately. OpenAI's first public response called the allegations “false and inflammatory.” Bubeck has since acknowledged making the remark about ruining his career, describing it as “ill-chosen” and retracting it, while maintaining that he approached the dispute according to normal academic conventions and expressing disappointment at how the situation had unfolded.
What OpenAI Disputes — and What It Doesn't
OpenAI's substantive defense rests on a narrower claim than the headline suggests: that its model never saw Buckmaster and Alpöge's actual work. In a press briefing, Bubeck said flatly that neither the company's researchers nor its AI agents saw any of the pair's work before it was released publicly. OpenAI has also emphasized that the two results are not the same proof — Buckmaster and Alpöge's work concerns the Euler equations, while OpenAI's concerns the forced Navier-Stokes equations — and the company says it recognizes their priority and has praised their result as a significant achievement in its own right.
That defense, however, doesn't fully address the detail that has kept the story alive: Buckmaster used OpenAI's own Codex product to store and iterate on his drafts throughout the project. Consumer Codex usage is, by OpenAI's own published policies, eligible to be used as training data unless a user has opted out or is on a business tier with different defaults. Buckmaster has said that when he pressed OpenAI on whether his drafts had been used to train the very model that went on to solve a strikingly similar problem via a strikingly similar method, he did not receive a clear answer. That is a different and more specific question than whether a researcher personally read his files, and it remains unresolved in public view, since no outside party has yet compared the two proofs directly.
Why the Timing Makes This Hard to Dismiss
Context is doing a lot of work in how this story is being read. OpenAI has said it began its own push on the problem only after hearing rumors connected to Buckmaster and Alpöge's progress — a sequence the company has not denied. That a rival's rumored progress on a related problem was the trigger for OpenAI's own effort is, by the company's own account, true. What's contested is only whether “hearing a rumor” and “using the underlying work” are the same thing, and Buckmaster's Codex usage is precisely what keeps that line blurry rather than clean.
It's also worth being clear about what remains allegation rather than established fact: the specific quotes attributed to Bubeck come from Buckmaster's own account, and while Bubeck has confirmed and retracted one of them, he has disputed the broader characterization of the exchange as a threat. No recording or transcript of the call has been made public.
The Bottom Line
Whatever the final accounting shows, OpenAI has already lost the cleanest version of its story. A mathematician it needed to co-opt for a smooth announcement instead went public with a detailed, partly corroborated account of pressure tactics, a demand to erase a rival lab's researcher from a paper, and a line — now retracted in part — that reads, in plain English, as a threat. The underlying scientific question of whether OpenAI's model was contaminated by Buckmaster's Codex drafts remains open, and it is the one that actually determines whether this is a story about bad manners in a heated academic dispute, or something considerably more serious about how AI labs treat the unpublished work that passes through their own products. Monday Pulse USA will continue following this story as independent mathematicians review both proofs and as OpenAI faces pressure to clarify exactly what its training pipeline did and did not touch.
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