OpenAI Claims Navier-Stokes Solution as AI Math Credit Dispute Erupts
OpenAI says 10,000 agents solved Navier-Stokes for millions, but disputed credit and closed models raise major alarms over mathematics' AI-driven future.
Summary
On September 9, 2026, OpenAI said an internal model solved the Navier-Stokes existence and smoothness problem by proving the full fluid-flow equations can break down, addressing whether they can predict impossible states such as infinite velocity. One of seven $1 million Millennium Prize Problems selected by the Clay Mathematics Institute in 2000, it would be only the second solved. OpenAI will not seek the prize. The model, said to dramatically outperform Astra, released the previous week, used about 10,000 concurrent agents, cost millions of dollars and reached the result within days.
On September 7, NYU mathematician Tristan Buckmaster posted on Mastodon a proof that simplified equations break down after almost a year working with Anthropic employee Levent Alpöge and public OpenAI and Anthropic models. Buckmaster says OpenAI offered to publish its solution the next day after theirs, or co-author a paper excluding Alpöge because Anthropic is its biggest rival. He says staff denied agents or employees accessed their OpenAI transcripts but did not answer whether models trained on them. OpenAI denies using the work. Sébastien Bubeck says a rumor about it inspired the effort, while chief research officer Mark Chen also denied access. Disclosures around the Hugging Face hack nevertheless show OpenAI does not always know what its agents do.
Both proofs use an approach pioneered by Diego Córdoba and Luis Martínez-Zoroa. Brown University professor Javier Gómez-Serrano says it was one of several promising routes, so independent discovery and influence remain possible. The episode contrasts the pair's yearlong, partial human-AI advance with OpenAI's costly private-model result, raising questions about credit, access and human research taste. UCLA's Terence Tao warned the previous week that opaque, premature AI solutions can erase the mistakes, incomplete work and new methods that drive mathematics. Gómez-Serrano says few mathematicians can command comparable resources.
Positives
- OpenAI's internal model produced a claimed solution to a Millennium Prize Problem that only one other researcher or team had previously solved.
- About 10,000 concurrent agents reached the full Navier-Stokes result within days, demonstrating a major increase in automated mathematical capability.
- Tristan Buckmaster and Levent Alpöge made substantial progress over almost a year using publicly available OpenAI and Anthropic models.
- Diego Córdoba and Luis Martínez-Zoroa's mathematical approach proved productive for both the OpenAI and Buckmaster-Alpöge proofs.
- OpenAI says it will not pursue the Clay Mathematics Institute's $1 million prize.
Risks & concerns
- Buckmaster alleges OpenAI proposed a paper excluding Alpöge because he works for Anthropic, OpenAI's biggest rival.
- OpenAI did not answer Buckmaster's question about whether its models had trained on his and Alpöge's transcripts.
- Millions of dollars and roughly 10,000 concurrent agents place comparable research beyond the reach of most mathematicians.
- OpenAI's private model dramatically outperforms Astra, widening the capability gap between frontier companies and outside researchers.
- Terence Tao warns opaque AI solutions could eliminate productive mistakes and incomplete work that generate new mathematical methods.
- The Hugging Face hack disclosures raise doubts about OpenAI's ability to track everything its agents access or do.