OpenAI Can't Rule Out Its AI Model Used a Mathematician's Private Data in Navier-Stokes Priority Dispute
NYU mathematician Tristan Buckmaster says OpenAI pressured him over authorship after its AI agents produced a proof resembling an approach he had kept in private Codex sessions.
Overview
OpenAI said this week that it “cannot rule out” that a mathematician’s private research data indirectly helped improve the internal AI model it used to resolve part of a decades-old fluid-dynamics problem, after NYU mathematician Tristan Buckmaster published a written statement alleging the company pressured him over authorship credit in the days before its public announcement.
What We Know
OpenAI announced that an internal AI system, using roughly 10,000 concurrent AI agents, produced a proof related to the Navier-Stokes existence and smoothness problem, according to VentureBeat. The problem is one of seven Millennium Prize Problems set by the Clay Mathematics Institute, each carrying a $1 million prize, according to VentureBeat and TechCrunch. According to VentureBeat, the effort reached a resolution on September 5, roughly 88 hours after the agents began work, with 17 additional hours spent formalizing the proof in the Lean theorem prover.
Across the broader effort, which also tackled related equations, OpenAI’s agents exchanged roughly 4.9 million messages and generated about 300 billion output tokens in total; the Navier-Stokes-specific work alone involved roughly 2.7 million messages and about 130 billion output tokens, according to VentureBeat. At the $50-per-million-output-token rate VentureBeat reported for the model involved, those output tokens alone would cost roughly $6.5 million.
Buckmaster, in his statement, wrote that he and Levent Alpöge, a mathematician at Anthropic, had spent months on “a purely personal collaboration, free of any institutional agreements or official involvement by either of our employers,” using several large language models including OpenAI’s Codex and Anthropic’s Claude. He wrote that the approach he and Alpöge were pursuing — proving blowup using a “smooth force” — built on earlier work by Diego Córdoba and Luis Martínez-Zoroa, adding, “almost nobody else I know of was working on it,” which is why he grew suspicious after learning OpenAI’s model had also produced a proof involving forcing: “When I heard ‘forced,’ it was a bright red flag.”
According to Buckmaster’s statement, on September 3, after hearing rumors that Anthropic had resolved a major open problem, he emailed a mathematician at OpenAI to clarify that his and Alpöge’s work was a personal collaboration and not conducted on behalf of either researcher’s employer. He wrote that on September 6 he spoke twice by phone with OpenAI researcher Sébastien Bubeck, who told him an internal OpenAI model had produced a proof of finite-time blowup for the “forced” Navier-Stokes equations.
Buckmaster wrote that he asked directly “whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project,” and that he “was told the model did not look up user data” but received no answer when he asked again specifically about training. He also wrote that Bubeck “twice asserted that he wanted Levent removed from authorship” of the eventual writeup, citing Alpöge’s employment at Anthropic as a complication. When Buckmaster said he would go public if OpenAI released its result the way it had proposed, he wrote that the reply was “Why would you ruin your career?” and, when he pushed back, “If you don’t want me to be nice, then I don’t have to be nice.” Both lines are also reported by TechCrunch.
In response, OpenAI said in a statement reported by both VentureBeat and TechCrunch: “We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.” OpenAI added that “our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs. unforced).”
OpenAI Chief Research Officer Mark Chen said in a video briefing that “No people or AI systems searched through user data to solve this problem or any specific problem that we were trying,” according to VentureBeat. Bubeck, defending the project publicly, said the effort began “due to viral twitter rumors that Anthropic had resolved 2 Millenium problems” and said, “I never ever asked for Levent to be removed from authorship of his own work,” VentureBeat reported.
What We Don’t Know
Buckmaster was explicit about the limits of his own knowledge, writing in his statement: “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.”
OpenAI has not disclosed the training data or full timeline for the unreleased internal model used in the effort, nor a precise total compute cost for the project beyond the per-output-token rate VentureBeat reported. Buckmaster’s statement also does not name the OpenAI mathematician he first emailed on September 3, identifying Bubeck only as joining the calls that took place three days later — so it is not established from his account whether that initial recipient and Bubeck are the same person.