OpenAI Claims to Solve the Navier-Stokes Millennium Problem

OpenAI announced that an internal AI system solved one version of the Navier-Stokes problem. The same day, Tristan Buckmaster of NYU and Levent Alpöge released results on related fluid equations.

OpenAI says it began training a new internal model in late August (other than GPT Astra) that showed strong mathematical performance. On September 1, after hearing online rumours that two Millennium Prize problems had been solved, the company launched a large multi-agent effort. Roughly 10,000 agents worked on Navier-Stokes and reached a result in about 88 hours. The model is described as significantly more capable than GPT-6 Astra.

Buckmaster and Alpöge’s results cover related equations, not the Navier-Stokes problem itself. Their work is seen by some mathematicians as an important step that could lead further in that direction. Terence Tao, a leading mathematician and Fields Medal winner, called their work a remarkable achievement. He noted that nothing in principle appears to prevent the method from reaching Navier-Stokes, though significant technical difficulties remain.

A dispute followed over timing and credit. Buckmaster stated that OpenAI intensified its effort only after becoming aware of their progress, and that private discussions raised questions around authorship. He also raised concerns about whether drafts and chat logs stored in OpenAI’s Codex tool could have been used, either directly or through training. OpenAI denied accessing specific user data for this work but said it could not fully rule out that de-identified product usage data had helped improve its models in general. The company maintained that the results differ from those of Buckmaster and Alpöge.

Independent verification of both claims is still underway. The Clay Mathematics Institute has not declared the problem solved. Without the surrounding dispute, this would have stood out as a major milestone for AI systems working on open mathematical problems.

There is considerably more to this story, including competing accounts of private conversations, differing views on research norms when using AI tools, and questions about how credit should work when large AI systems produce candidate solutions to open problems.

No single post covers the full picture. The closest compilation I found is here: https://echai.ventures/collections/navierstokes. For the most complete view, it is better to follow the original threads on X and Mathstodon.