OpenAI’s Internal AI Reportedly Solves Navier–Stokes, Triggering a Mathematical Dispute

Summary

The article describes three connected developments: an OpenAI internal model reportedly produced a proof concerning the Navier–Stokes Millennium Prize problem, a dispute emerged over credit and publication, and OpenAI disclosed rapid progress in automating its own AI research. OpenAI reportedly began searching across unsolved Millennium Problems after hearing a false rumor that two had been solved. Its internal agent swarm allegedly used 2.7 million messages and about 130 billion output tokens on Navier–Stokes, with Astra spending another 17 hours on Lean formalization and verification; the broader effort reportedly used 4.9 million messages and roughly 300 billion output tokens. The article does not present the proof itself, and the mathematicians’ earlier work concerned forced blowup results for related fluid equations, while Lean verification of the reported hypo-dissipative Navier–Stokes result was unfinished. Tristan Buckmaster says OpenAI proposed publication arrangements that would have excluded his coauthor Levent Alpoge, who works at Anthropic; OpenAI personnel, including Sebastien Bubeck and Sam Altman, deny wrongdoing and say they sought to collaborate in good faith. The article discusses suggestions that Codex user data influenced the result, but quotes OpenAI and Anthropic figures saying such influence was extremely unlikely or impossible through training, while acknowledging that the author has not independently verified the proof or data history. A joint declaration signed by 25 Fields Medal winners argues that rushed AI-generated proofs can undermine mathematical understanding, attribution and the community’s incentives, even if humans later study the results. Finally, OpenAI says it has reached its goal of an automated research intern and reports that, by mid-August, its research organization used 3.1 agent-workdays for every human workday, with median daily inference spending above $600 at API prices. The author presents these figures as evidence of accelerating AI-assisted research and unresolved questions about safety, human control and cooperation between leading labs.