Second mathematician accuses OpenAI of using unpublished work in AI breakthroughs

OpenAI announced this week that an unreleased AI model, coordinated through a swarm of 10,000 agents, produced a proof showing that the Navier-Stokes equations can "blow up" under certain conditions — a result that, if verified, would represent only the second time one of mathematics' seven Millennium Prize Problems has been solved. The company says it does not plan to claim the million-dollar prize, and the Clay Mathematics Institute still lists the problem as open, since its rules require at least two years of review after publication before any award can be made.theconversation+1

The achievement, however, has been overshadowed by accusations of intellectual theft and ethical violations that have rattled the mathematics community.

The Race to Solve Navier-Stokes

The Navier-Stokes equations describe how fluids like water and air flow, and are foundational to modern science and engineering. The Millennium Prize question asked whether these equations could produce a "singularity" — a scenario in which fluid speeds become infinite, something impossible in nature.scientificamerican+1

OpenAI said it heard rumors on September 1 that researchers at rival company Anthropic were close to solving two Millennium problems. It deployed its latest internal model, which after 88 hours of computation and 17 hours of verification produced the proof. The company said the result was certified using the Lean programming language, which all but guarantees mathematical correctness.theconversation+2

Credit, Ethics, and Corporate Rivalries

The controversy centers on NYU mathematician Tristan Buckmaster and Anthropic employee Levent Alpöge, who had been collaborating in a personal capacity on a related problem. On the night before OpenAI's announcement, Buckmaster posted that the pair had achieved a breakthrough on the Euler equations — widely seen as a stepping stone toward Navier-Stokes.technologyreview+1

In a public statement, Buckmaster alleged that OpenAI contacted him after learning of their progress, then offered to collaborate only if he removed Alpöge's name due to his Anthropic affiliation — a claim OpenAI denies. He also asked whether his and Alpöge's interactions with OpenAI's publicly available models had fed into the company's training data but said he received no clear answer.theverge+3

OpenAI denied accessing any specific user data but acknowledged it "cannot rule out that de-identified data derived from their usage of our products helped improve our models".businessinsider+1

A Chilling Effect on Open Science

German mathematician Andreas Thom has added to the criticism, accusing OpenAI of "dishonesty" after his own questions about whether his ChatGPT interactions contributed to a separate OpenAI result in his field went unanswered to his satisfaction.theverge

Fields Medal winner Terence Tao warned that if AI companies race to scoop researchers based on rumors of promising work, mathematicians may stop sharing progress with the broader community — undermining the principles of open science. As MIT Technology Review reported, the controversy has attracted far more attention than the mathematical breakthrough itself.theconversation+1