OpenAI’s Navier-Stokes Proof Faces Pushback From Mathematicians

OpenAI presented a 166-page potential solution to the Navier-Stokes problem and said it followed an approach associated with Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa. Several groups of experts now dispute that characterization, saying the actual proof appears to use a different approach. The key takeaway for readers: the issue is not only whether the proof is correct, but whether OpenAI can accurately explain how it got there.

The proof is written in Lean, a formal verification language that can check logical steps. But formal verification does not automatically make a proof clear or readable to human mathematicians. The Clay Mathematics Institute has been reviewing the potential proof since its release, making expert interpretation and validation central to what happens next.

Before publication, NYU mathematician Tristan Buckmaster accused OpenAI of building on work he and Anthropic’s Levent Alpöge had done with publicly available models. OpenAI denied using Buckmaster’s data. Because large language models are widely described as black boxes, the article notes that a definitive answer about where the underlying ideas came from may be impossible.

OpenAI reportedly used about 10,000 model instances for roughly 88 hours and 130 billion tokens in developing the potential solution. OpenAI researcher Noam Brown said no one actually knows what the large agent swarm contributed. Brown put less than 10 percent of the success down to the multi-agent setup, pointing instead to the base model’s ability to work through tasks over long periods and in parallel.