OpenAI Claims Navier-Stokes Win Amid Plagiarism Row

OpenAI says its AI agents cracked the Navier-Stokes problem in 88 hours, but mathematicians allege the result was built on their unpublished work.

OpenAI claims its artificial intelligence has resolved the 200-year-old Navier-Stokes equations, a challenge tied to a $1 million reward from the Clay Mathematics Institute, according to ColombiaOne. The company reportedly deployed roughly 10,000 AI agents working simultaneously for about 88 straight hours, first tasking 100 of them with the related Euler equations, where genuine blowups were found after roughly 50 hours. The final proof was verified using Lean, software that checks every logical step of a mathematical argument, and the effort consumed 2.7 million messages and roughly 130 billion computational tokens. RBC-Ukraine reports the verification in the Lean 4 language took another 17 hours, and that OpenAI says it is declining the Clay cash prize.

The breakthrough's timing is the heart of the dispute. According to ColombiaOne, NYU mathematician Tristan Buckmaster and Levent Alpoge of Anthropic had independently pursued the same obscure smooth-forcing strategy, originally developed by Madrid mathematicians Diego Cordoba and Luis Martinez-Zoroa, achieving their own blowup results on August 15. Buckmaster says he learned by September 3 that OpenAI had caught wind of their progress and adopted the identical method shortly afterward, a coincidence he called "a bright red flag." RBC-Ukraine reports Buckmaster suspects OpenAI may have used private training logs, and that OpenAI said its developers and agents did not have direct access to user data but acknowledged it "cannot completely rule out the use of de-identified data."

Tensions escalated in a September 6 meeting where, per ColombiaOne, an OpenAI employee warned Buckmaster, "Why would you ruin your career?" Buckmaster further alleges that OpenAI's math research lead pushed to remove Alpoge from co-authorship because Alpoge works for rival company Anthropic, an accusation OpenAI has flatly denied as "false and inflammatory." According to RBC-Ukraine, OpenAI CEO Sam Altman acknowledged the company knew of Buckmaster and Alpoge's work before announcing its results, though he insisted the approaches "appear to be different" — a claim Buckmaster directly disputes. Buckmaster also revealed he had used OpenAI's Codex tool throughout his research and never received a clear answer on whether his sessions trained the model that later solved the problem.

The stakes extend well beyond one proof. Terence Tao, the UCLA mathematics professor and Fields Medalist, warned that the episode could push researchers toward hiding promising work rather than sharing it openly, reversing centuries of collaborative scientific tradition, as ColombiaOne reports. RBC-Ukraine similarly reports Tao's deep concern that when rumors of research prompt technology giants to spend millions on computing power to get ahead of academics, the tradition of open science is undermined, potentially harming mathematics' long-term development. The Clash also illustrates the raw scale now possible: RBC-Ukraine notes OpenAI used a previously unannounced model more powerful than GPT-6 Astra, and ColombiaOne reports OpenAI estimates an outside customer would need roughly $15 million to replicate the effort.