Artificial Intelligence
OpenAI’s Navier-Stokes proof faces expert doubt
OpenAI’s 166-page proposed Navier-Stokes solution drew challenge from mathematicians who said the method differed from the company’s account, while its extra releases and multi-agent setup also came under scrutiny.
- OpenAI presented a 166-page proposed solution to the Navier-Stokes problem in early September.
- The company said the proof followed work by Diego Córdoba and Luis Martínez-Zoroa, but Gonzalo Cao-Labora said the detailed method was different.
- The proof was written in Lean and has been reviewed by the Clay Mathematics Institute since release.
- Tristan Buckmaster said OpenAI had built on work he and Anthropic’s Levent Alpöge did with public models, and OpenAI denied using Buckmaster’s data.
- OpenAI later posted about 400 more results on GitHub, and Noam Brown said the project used around 10,000 model instances for about 88 hours and that nobody knows exactly what the swarm contributed.
OpenAI presented a 166-page proposed solution to the Navier-Stokes problem in early September and said it followed the approach of Diego Córdoba and Luis Martínez-Zoroa. Several experts disputed that account, and Gonzalo Cao-Labora said the detailed method pointed elsewhere.
The draft was written in Lean, a formal verification language that checks each logical step. The Clay Mathematics Institute has been reviewing the submission since it was released.
Before publication, Tristan Buckmaster said OpenAI had drawn on work he and Anthropic’s Levent Alpöge had done with public models. OpenAI denied using Buckmaster’s data, while Camillo De Lellis said a definitive answer was probably impossible because large language models are opaque.
In early October, OpenAI posted roughly 400 further results on GitHub, which drew criticism from many mathematicians. They said the release format made the field look diminished.
Noam Brown said OpenAI used about 10,000 model instances for roughly 88 hours and 130 billion tokens to develop the result. He said nobody knows precisely what that agent setup contributed, and that the base model did most of the work.
Named in this story
People
- Diego Córdoba
- was named by OpenAI as part of the approach it said it followed
- Luis Martínez-Zoroa
- was named by OpenAI as part of the approach it said it followed
- Gonzalo Cao-Labora
- said the detailed method differed from the claimed one
- Tristan Buckmaster
- said OpenAI had built on work he and Levent Alpöge had done
- Levent Alpöge
- was named in Buckmaster’s claim about earlier work
- Camillo De Lellis
- said a definitive answer was probably impossible because models are opaque
- Noam Brown
- said nobody knows what the agent swarm contributed
Companies
- OpenAI
- presented the 166-page proposed solution and described its method
- Anthropic
- was Levent Alpöge’s employer
Organisations
- EPFL
- is Cao-Labora’s institution
- Clay Mathematics Institute
- has been reviewing the submission since its release
- Institute for Advanced Study
- is De Lellis’s affiliation
Products and systems
- Lean
- was the formal verification language used for the proof
- GitHub
- was where OpenAI posted roughly 400 additional results
How the source tells it
The register is sceptical and combative, with repeated doubt about OpenAI’s account and irritation from mathematicians over how the work was presented.
- scepticism expert disagreement and a direct challenge to OpenAI’s description of the method
- irritation the loose release of extra results and the complaint that it diminished the field
- uncertainty claims that nobody knows what the model swarm contributed and that a definitive answer may be impossible