Expert sees an "unprecedented construction"
Scott Armstrong, a professor who specializes in partial differential equations, posted his assessment on X on Oct. 25 (Oct. 26 Japan time) of a paper on the Navier-Stokes equations produced by OpenAI's AI. Armstrong is a professor at New York University's Courant Institute and also serves as a researcher at Sorbonne University in France.
He said the method of using fluid instability to generate force does not exist in the literature and may go beyond what humans could think of. He added, however, that it is not something humans cannot understand. OpenAI President Greg Brockman also posted that it was a technically incredible paper. RuntimeWire cautioned that Armstrong's assessment is an expert's view of the research's ambition, not a peer review judging its correctness.
"Blowup solution" announced in September
The Navier-Stokes equations describe the motion of fluids, and whether their solutions remain smooth indefinitely is an open problem for which the Clay Mathematics Institute in the United States offers a $1 million prize. On Sept. 8, OpenAI released a proof that, under conditions in which an external force is applied, a solution "blows up" to infinity in finite time, as a 166-page paper and as a write-up in Lean, a language for verifying proofs by computer.
It ran an unreleased internal model with 10,000 parallel agents for 88 hours, using about 130 billion tokens on Navier-Stokes alone, according to the company. It has not solved the case without external force, which is considered more fundamental. OpenAI says it will not seek the prize, and the Clay Mathematics Institute has not recognized the result.
Disputes over verification and credit
The proof has not undergone third-party peer review. In October, a paper also appeared questioning whether the Lean write-up truly corresponds to the paper's proof. Conflicting claims over the paper's authorship and credit also continue with researchers in the same field. The prominent mathematician Terence Tao had cautioned against using open problems as material for AI promotion.
