In early September, OpenAI presented a 166-page potential solution to the Navier-Stokes problem. According to The Decoder, which cites Scientific American, the company claimed the proof followed the approach of Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa. Several groups of experts now reach a different conclusion.
Dispute over the origin of the approach
Mathematician Gonzalo Cao-Labora of EPFL says that, looking at the details, it is a different approach; the similarities are only superficial. The proof is encoded in Lean, a formal verification language that checks the formal validity of the logical steps but does not automatically make it understandable to humans. It has been with the Clay Mathematics Institute (CMI) for review since its release.
Mathematician Tristan Buckmaster of New York University also accused OpenAI of building on progress that he and Levent Alpöge of Anthropic had made with publicly available models. OpenAI denies this and rules out having used Buckmaster's data. Camillo De Lellis of the Institute for Advanced Study considers a definitive clarification probably impossible, since language models function as black boxes.
Publication of further results
In early October, OpenAI released roughly 400 further results that the mathematical community can barely keep up with. Publishing them as a loose paper collection on GitHub angered many mathematicians, who saw it as cheapening their discipline.
Unclear contribution of the agent swarm
According to the source, OpenAI deployed about 10,000 model instances for roughly 88 hours and 130 billion tokens. According to OpenAI researcher Noam Brown, it is unclear what this agent swarm actually contributed to the solution. Systematic comparison tests with thousands of agents are considered too expensive, so behavior at this scale is barely studied. Brown attributes less than 10 percent of the success to the multi-agent setup and stresses that the underlying base model is decisive.
Assessment
As long as the CMI has not evaluated the solution and the expert community disagrees about the independence of the approach, the claim of a breakthrough should be treated as open. For companies and research teams that want to adopt AI-generated results, the case is a reminder to carefully establish provenance, verifiability, and the actual role of individual system components.
Sources
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