OpenAI announces Navier-Stokes proof as credit dispute widens

OpenAI said it had produced a resolution to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems set by the Clay Mathematics Institute. According to the company, the proof came from an unreleased model whose training began on 28 August, with roughly 10,000 concurrent agents working for 88 hours; that problem alone consumed 2.7 million messages and about 130 billion output tokens. Formal verification in Lean took a further 17 hours. Research lead Mark Chen put the compute bill in the millions of dollars.

Tristan Buckmaster of New York University and Levent Alpöge, who works at Anthropic, said they had spent close to a year on a similar route and had uploaded their drafts to OpenAI's Codex. OpenAI says no specific user data was accessed in solving the problem, while conceding it cannot rule out that de-identified usage data improved its models. Mathematician Terence Tao warned the episode could damage open science.