OpenAI’s blockbuster Navier-Stokes proof isn’t what we thought it was

In early September, OpenAI posted a 166-page solution to the Navier-Stokes problem, one of mathematics' famed "million-dollar problems." Initial accounts, including from OpenAI itself, suggested the proof—produced by an internal large language model—followed an approach devised by Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa, known as the "Spanish program." This sparked a public conflict with mathematician Tristan Buckmaster of New York University, who had been using LLMs to carry out that program alongside Levent Alpöge, an employee of Anthropic. However, closer examination by experts reveals that OpenAI's proof does not actually follow the Spanish program. While both exploit the same "loophole" in the Clay Mathematics Institute's framing of the problem by constructing an unphysical force to cause a blowup, OpenAI's proof builds its force in a totally distinct way. The proof was generated by an "agent swarm" of about 10,000 copies of a math-adept LLM, which spent 88 hours and 130 billion tokens. Even top experts found the proof impenetrable and are now using Lean code to understand it. OpenAI initially used a smaller team of agents that may have followed the Spanish program, but the full swarm took a different path. The black-box nature of LLMs means the exact reasoning may never be known. This incident highlights how OpenAI did not understand its own model's proof, and more than a month later, no one fully does. Last week, OpenAI released 400 more results, some of which could have earned a Fields Medal, raising concerns about the pace of AI-driven mathematical discovery.

(Source：Scientific American)