Mathematicians dispute OpenAI's account of its Navier-Stokes proof
In early September, OpenAI presented a 166-page potential solution to the Navier-Stokes problem. The company claimed the proof followed the approach of Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa. According to Scientific American, as relayed by The Decoder, several groups of experts now disagree. "When you go to the details, it is a different approach," says Gonzalo Cao-Labora, a mathematician at EPFL. He says the similarities are only surface-level.
The potential proof is written in Lean, a formal verification language that checks every logical step but does not make the argument readable to humans on its own. The Clay Mathematics Institute (CMI) has been reviewing it since its release.
There was also a dispute over provenance. Before publication, NYU mathematician Tristan Buckmaster accused OpenAI of building on work that he and Anthropic's Levent Alpöge had done with publicly available models. OpenAI denied this, saying it never used Buckmaster's data. Camillo De Lellis of the Institute for Advanced Study says a definitive answer is probably impossible because language models are black boxes.
In early October, OpenAI dumped roughly 400 more results, which the math community can barely keep up with. Publishing them as a loose collection on GitHub angered many mathematicians, who felt it cheapened their field.
The second half of the story concerns the compute. OpenAI deployed about 10,000 model instances for roughly 88 hours and 130 billion tokens to develop the potential solution. According to OpenAI researcher Noam Brown, nobody actually knows what that agent swarm contributed to the result. Behavior at that scale has not been studied, because systematic comparison tests with thousands of agents cost too much. No one has tested how long a single agent would take to solve the same problem, and it is nearly impossible to tell what concrete advantage 10,000 agents offer over 1,000.
Brown puts less than 10 percent of the success down to the multi-agent setup. These systems are new and flashy, he says, so they get a disproportionate share of the credit. What really matters, in his view, is the base model itself, which can grind through tasks over long periods and run in parallel.
Key facts
- OpenAI presented a 166-page potential Navier-Stokes solution in early September and claimed it followed the approach of Diego Córdoba and Luis Martínez-Zoroa; per Scientific American, several groups of experts disagree.
- Gonzalo Cao-Labora of EPFL says the similarities to that approach are only surface-level: "it is a different approach" in the details.
- Tristan Buckmaster accused OpenAI of building on his and Anthropic's Levent Alpöge's work with public models before publication; OpenAI says it never used Buckmaster's data.
- The effort used about 10,000 model instances for roughly 88 hours and 130 billion tokens; Noam Brown says nobody knows what the swarm contributed and puts less than 10 percent of the success down to the multi-agent setup.
- The proof is in Lean and the Clay Mathematics Institute has been reviewing it; in early October OpenAI also published roughly 400 more results on GitHub, which angered many mathematicians.
Why it matters
Navier-Stokes is a headline problem, and OpenAI put a 166-page potential solution forward. Two things are now in question: whether the proof really follows the approach OpenAI named, and how much the huge agent swarm actually did. Brown's own admission that nobody knows the swarm's contribution bears on how far claims about multi-agent systems can be trusted. Comparison tests with thousands of agents are too costly to run, so the effect of scale stays unmeasured.
Who it affects
Mathematicians come first: those reviewing the proof, those whose work OpenAI cited or is said to have built on (Córdoba and Martínez-Zoroa; Buckmaster and Alpöge), and those who felt the GitHub dump of roughly 400 results cheapened their field. It also touches the Clay Mathematics Institute, which is reviewing the potential proof, and anyone who builds or judges large multi-agent AI systems.
How to use it
There is nothing to run here; this is reporting on a dispute. The practical reading: treat OpenAI's description of the proof's lineage as contested, and treat the swarm figures (about 10,000 instances, roughly 88 hours, 130 billion tokens) as a description of effort, not of what produced the result. Because the proof is written in Lean, every logical step can be checked, but that does not on its own make it readable to humans.
How solid is it
The account is secondhand: The Decoder relays a Scientific American report. Only Cao-Labora is named among the experts who disagree; the other groups are not identified. The source calls the work a potential solution throughout and gives no verdict from the Clay Mathematics Institute, which is still reviewing it. Brown's remarks come from an OpenAI researcher, and the claim about what the swarm contributed is his, not an independent measurement.
Risks and caveats
Whether the proof is correct or accepted is not settled in this source. De Lellis says a definitive answer on provenance is probably impossible because language models are black boxes, so the dispute with Buckmaster, which OpenAI denies, may stay unresolved. The headline framing that OpenAI does not understand its own proof is The Decoder's; the evidence given is the disputed lineage and Brown's statement about the swarm. The year of the September and October events is not stated in the source.
“When you go to the details, it is a different approach”
— Gonzalo Cao-Labora, mathematician at EPFL, quoted by Scientific American via The Decoder