A year-long collaboration between two mathematicians ended in accusations that OpenAI stole their work and threatened one researcher's career after the company claimed to have solved a piece of the century-old Navier-Stokes problem. Tristan Buckmaster of New York University and Levent Alpöge of Anthropic had been quietly proving a related stepping-stone problem involving Euler equations when OpenAI announced its own breakthrough. Buckmaster now alleges that OpenAI scraped his team's Codex sessions and issued a similar result without credit, then offered him two unfavorable options. The dispute highlights growing tensions over intellectual property and AI company power in academic research.

What You Need to Know

The Navier-Stokes problem is one of the seven Millennium Prize Problems, each carrying a $1 million reward. Mathematicians Buckmaster and Alpöge spent a year using AI tools including Codex to work on Euler's equations, a stepping stone to Navier-Stokes. They accuse OpenAI of scraping their Codex sessions and issuing a similar result without credit, then pressuring them to accept an arrangement that would benefit OpenAI. The controversy raises questions about the ethics of AI companies using user data for competitive research.

The Allegation of Theft

Buckmaster and Alpöge had been working since August 2025 on proving a finite-time blowup for Euler equations, a problem widely seen as a prerequisite to solving the full Navier-Stokes question. The pair used OpenAI's Codex and Anthropic's Claude as assistants for documentation and logic checks. On August 15, 2026, they obtained the blowup results and verified them using the Lean proof assistant.

In September, Alpöge heard rumors that Anthropic had solved an important problem, which he believed referred to their work. Buckmaster then contacted an unnamed mathematician at OpenAI to clarify it was a personal collaboration. After two phone calls with OpenAI's Sebastien Bubeck, Buckmaster learned that OpenAI had independently proven a finite-time blowup for forced Navier-Stokes equations. The forced blowup approach, Buckmaster claims, was the exact same direction his team had chosen and that nobody else was known to be pursuing. He stated that this path would not be quickly discovered by simply feeding the problem to a model, implying OpenAI had accessed his team's sessions.

  • Buckmaster's key claims: OpenAI's result used the same forced blowup idea his team had quietly chosen.
  • Codex session access: Buckmaster asked if OpenAI had trained on or accessed his Codex sessions. The company said Codex does not access user data but did not answer whether session data was used for model training more broadly.
  • Insane computing: Bubeck revealed that an entire human team was working on Navier-Stokes, with an "insane" amount of computing used to generate the prompt that produced the proof.

OpenAI's Proposal and Threat

According to Buckmaster, OpenAI offered two options. The first allowed Buckmaster and Alpöge to publish their Euler proof first, followed by OpenAI's Navier-Stokes proof the next day, giving them priority. But the second option required Buckmaster alone, without Alpöge, to write a paper acknowledging OpenAI's model as the resolver. Bubeck was apparently adamant about removing Alpöge because his employment at Anthropic was "annoying." Buckmaster refused both and threatened to go public, which he has now done.

The threat to Buckmaster's career was implicit: if he did not cooperate, OpenAI could undermine his credibility or prioritize its own claim. The controversy has drawn attention from the mathematics community, with some scientists noting that OpenAI's result addresses only a subset of the Millennium Prize conditions and does not constitute a full solution.

Why This Matters

This case exposes the risks when AI companies hold both the tools and the power to shape academic credit. If OpenAI scraped user sessions from Codex, it would represent a serious breach of trust and intellectual property. The allegation that the company then pressured a researcher to exclude a competitor's employee from credit raises questions about fair competition in AI-driven research. For mathematicians and scientists, the incident underscores the vulnerability of collaborative work when AI platforms are used as intermediaries. The broader implication is clear: without stronger safeguards, individual researchers may find their hard-won discoveries appropriated by corporate labs with deeper resources and legal leverage.