OpenAI said on Sept. 8 that an internal model ran about 10,000 agents to resolve the Navier-Stokes problem, a claim two mathematicians dispute.
Key Points:
- An unreleased OpenAI system produced a written proof and a Lean formalization for one of the seven Millennium Prize problems.
- Tristan Buckmaster and Levent Alpöge, who released a related result a day earlier, question how the company reached the same approach.
- Terence Tao says AI labs are mining famous open problems for publicity rather than for mathematical insight.
OpenAI Navier-Stokes Proof Details
The company published a write-up and a Lean formalization arguing that an initially smooth fluid at rest can develop a singularity in finite time. Researchers described the internal system as significantly more capable than GPT-6 Astra, and said the model remains in training with performance still climbing. Mathematicians have chased that question for roughly 90 years, since Jean Leray showed in 1934 that solutions exist in a looser, generalized sense.
OpenAI began training the model on Aug. 28, then aimed it at every open Millennium Prize problem on Sept. 1, after rumors said two of them had already fallen. Executives told reporters the compute bill reached millions of dollars.
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Buckmaster And Bubeck Clash Over Credit
Tristan Buckmaster, a mathematician at New York University, and Levent Alpöge, an Anthropic researcher working in a personal capacity, had spent close to a year on related fluid equations. They built on earlier work by Diego Cordoba and Luis Martinez-Zoroa, and released Lean-verified proofs for the forced Euler problem a day before OpenAI went public. Buckmaster then asked whether his private Codex drafts had steered the rival effort, and said he got no answer about training.
He also said OpenAI researcher Sebastien Bubeck pushed to drop Alpöge from a paper because of his employer, then warned him against going public.
Bubeck rejected that account as false and inflammatory.
The company said neither its researchers nor its agents saw the pair's work before publication, while conceding that de-identified usage data may have helped improve its models. It does not plan to claim the $1 million award attached to the problem. The Clay Mathematics Institute, which set the seven problems in 2000, still lists Navier-Stokes as unsolved.
Terence Tao Questions AI Math
Terence Tao, widely counted among the greatest living mathematicians, warned that AI companies are treating famous open problems as marketing proof points for their newest systems. He argued that stripping those problems for answers can wreck the ecosystem that produces the next generation of techniques, questions and working mathematicians, and likened the practice to looting an archaeological site.
The scale of the effort escalated fast. Roughly 100 agents first cracked a simpler unforced Euler question in about 50 hours. Its Navier-Stokes group then reported an answer on Sept. 5, some 88 hours after launch, and Lean verification of that proof took 17 hours more.
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