Experts say OpenAI’s Navier-Stokes proof does not follow disputed Spanish approach
OpenAI released a 166-page purported solution to the Navier-Stokes problem in early September, saying an internal large language model produced it. Early coverage suggested the work followed an approach by Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa, which led to a public dispute with researchers Tristan Buckmaster and Levent Alpöge. Several mathematicians who examined the paper now say the proof does not actually follow that Spanish program, and the apparent similarity is only superficial.
OpenAI’s September paper spans 166 pages and was attributed to an in-house large language model. Early reports tied it to work by Diego Córdoba and Luis Martínez-Zoroa, prompting objections from Tristan Buckmaster and Levent Alpöge, who had pursued that line with LLM assistance.
Experts including Gonzalo Cao-Labora now describe the overlap as superficial. The proof reportedly used roughly 10,000 model copies, about 88 hours of compute and 130 billion tokens, and was encoded in Lean. Both efforts allegedly exploit a Clay Mathematics Institute framing that allows an artificial stirring force to trigger blowup.
The episode could affect mathematicians, AI labs, and research funders by intensifying debates over credit, verification, and transparency in machine-assisted proofs. If LLM-generated results become more common, peer review and attribution norms may struggle to keep pace, especially for high-profile problems. Researchers relying on proprietary systems may face uncertainty about access and acknowledgment. Public trust in AI mathematics may hinge on independent Lean checks and open scrutiny, while the dispute could also draw wider attention to formal verification as a safeguard.