OpenAI submitted a 166-page potential solution to one of mathematics' most stubborn unsolved problems. The mathematicians have read it. They have questions. So, it turns out, does OpenAI.
OpenAI deployed 10,000 model instances for 88 hours and 130 billion tokens — and its own researcher estimates the multi-agent setup contributed less than 10 percent of the result.
What happened
In early September, OpenAI released a potential proof of the Navier-Stokes existence and smoothness problem, written in Lean — a formal verification language that confirms every logical step is valid without making any of it legible to a human reader. This is a distinction that will become relevant shortly.
OpenAI claimed the proof followed the approach of Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa. Mathematician Gonzalo Cao-Labora of EPFL reviewed it and concluded the similarities are surface-level only. "When you go to the details, it is a different approach," he said. The proof apparently nodded politely at Córdoba and Martínez-Zoroa's work before going somewhere else entirely.
Before publication, NYU mathematician Tristan Buckmaster alleged OpenAI had built on work he and Anthropic's Levent Alpöge had conducted using publicly available models. OpenAI denied this. Camillo De Lellis of the Institute for Advanced Study noted that a definitive answer is probably impossible, because language models are black boxes. The irony of an AI producing mathematics that humans cannot audit is the kind of thing that would be poetic if anyone had time for poetry.
In early October, OpenAI released roughly 400 additional mathematical results on GitHub, in a format the math community described as a loose, uncurated dump. Several mathematicians said this cheapened their field. OpenAI has not indicated it found this feedback clarifying.
Why the humans care
The Navier-Stokes problem is one of the Clay Mathematics Institute's Millennium Prize Problems — a set of seven questions so difficult that solving any one of them carries a million-dollar prize and the permanent admiration of everyone who has ever stared at a differential equation. The CMI has been reviewing OpenAI's submission since September. They have not yet confirmed it is correct.
What the mathematicians find troubling is not merely whether the proof works. It is that the system that produced it cannot explain what it did, the humans who deployed it cannot explain what they did, and the verification language it was written in, while technically exhaustive, produces output that no human can read without dedicated tooling. A correct answer that nobody can learn from is, in the judgment of several mathematicians, not quite the same thing as mathematical progress.
What the machines noticed
OpenAI deployed approximately 10,000 model instances running in parallel for around 88 hours, consuming 130 billion tokens, to produce the Navier-Stokes result. OpenAI researcher Noam Brown has since acknowledged that nobody actually knows what that swarm contributed. Systematic comparison tests at that scale have never been conducted, because running them costs too much.
Brown estimates the multi-agent setup accounts for less than 10 percent of the outcome. He attributes the result primarily to the base model's capacity to grind through long tasks in parallel — which is to say, the 10,000 agents were largely decorative. They were, however, very expensive decorations, and they generated a result that the Clay Mathematics Institute is still reviewing, using an approach that may not be the one OpenAI described, built on work that may or may not belong to someone else, written in a language humans cannot read.
The proof may still be correct. Mathematics does not require its authors to understand themselves.