OpenAI, Navier–Stokes, and a Disputed Breakthrough

Why the problem matters

• The Navier–Stokes equations describe how fluids and gases move. They’re used in applications such as hurricane forecasting, aircraft design, and blood-flow simulations.
• Mathematicians still don’t know whether the equations can “break”—for example, whether a fluid’s behavior can become mathematically singular.
• This question is one of the Clay Mathematics Institute’s Millennium Prize Problems, with a $1 million prize for a proof or counterexample.

The researchers’ work

• NYU professor Tristan Buckmaster and Anthropic mathematician Levent Alpige had been studying the problem together.
• After incorporating Codex and other coding tools into their work, they made progress on a related, simpler system: the Euler equations.
• On August 15, they found a way to make that system break—a result described as a significant step toward the Navier–Stokes problem.

OpenAI’s claim and the dispute

• OpenAI later said it had produced a Navier–Stokes solution using a large effort involving thousands of agents and substantial computing resources.
• Buckmaster says OpenAI’s method appeared to follow the novel approach he and Alpige had been developing. He also says the team had heard rumors of their work before starting.
• According to Buckmaster, a call with OpenAI researcher Sebastian Bubeck raised concerns about credit, Alpige’s involvement, and whether his Codex sessions had been used in training. Buckmaster says his questions about training went unanswered.
• Buckmaster alleges OpenAI proposed either publishing its own proof while crediting him, or having him write a Navier–Stokes paper without Alpige. He says he rejected both proposals.
• OpenAI disputes parts of his account, saying it never asked for Alpige to be removed. Sam Altman said he believed OpenAI’s team acted with integrity; OpenAI also said it did not access user data and that its proof differed substantially from the researchers’ work.
• Both the researchers and OpenAI published papers and statements describing their results and accounts of what happened.

Why it matters beyond the proof

• The dispute highlights concerns about attribution, research data, and the use of AI systems in scientific work.
• Terence Tao congratulated the researchers but warned that AI teams racing to replicate rumored research could discourage mathematicians from sharing ideas, undermining open science.
• The video’s central takeaway: even a genuine mathematical breakthrough could have lasting consequences for trust and collaboration in research.