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Large Language ModelsTHE DECODERPublished: Oct 17, 2026, 19:01 JST

OpenAI's 166-page Navier-Stokes proof uses a different approach, mathematicians say

OpenAI's 166-page Navier-Stokes proof uses a different approach, mathematicians say

3 Key Points

  1. What happened

    OpenAI presented a 166-page potential Navier-Stokes proof in early September, saying it followed the approach of Diego Córdoba and Luis Martínez-Zoroa. Mathematicians including EPFL's Gonzalo Cao-Labora now say that is not the actual approach.

  2. Why it matters

    If the stated method doesn't match the proof, the claimed link to the Spanish mathematicians' work is only surface-level, raising questions about how much of the proof OpenAI can actually explain — a gap that matters because the proof is hard to read on its own.

WHO IT HITSMathematicians and formal-proof reviewers are the first to feel this: they must verify a 166-page proof whose described method may not match its actual steps, and they have no clear way to trace which ideas came from where.

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Context & Analysis

OpenAI's Navier-Stokes effort came with unusually heavy machinery: about 10,000 model instances running for roughly 88 hours and 130 billion tokens. Yet according to OpenAI researcher Noam Brown, nobody actually knows what that massive agent swarm contributed, because behavior at that scale hasn't been studied and running systematic comparison tests with thousands of agents costs too much. Brown himself puts less than 10 percent of the success down to the multi-agent setup, saying these systems are new and flashy and get a disproportionate share of the credit; what really matters, he says, is the base model's ability to grind through tasks over long periods and run in parallel.

The provenance question is separate but related. 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, a claim OpenAI denied. Camillo De Lellis of the Institute for Advanced Study says a definitive answer is probably impossible because language models are black boxes — the same opacity that makes it hard to say where the proof's ideas came from.

Meanwhile, the volume of output is straining the field. In early October, OpenAI released roughly 400 more results as a loose collection on GitHub, which angered many mathematicians who felt it cheapened their field. The Clay Mathematics Institute has been reviewing the original proof since its release, but the dispute over method suggests the review will have to settle not just whether the proof is correct but what it actually is.

FAQ
What did OpenAI claim about its Navier-Stokes proof?
OpenAI said the 166-page potential solution followed the approach of Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa.
Who is disputing OpenAI's account?
Several groups of experts, including mathematician Gonzalo Cao-Labora of EPFL, who says the similarities are only surface-level and the actual approach is different.
How much did OpenAI's multi-agent setup contribute to the proof?
OpenAI researcher Noam Brown puts less than 10 percent of the success down to the multi-agent setup, saying the base model matters more.

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