OpenAI says an internal model resolved the Navier–Stokes Millennium Prize Problem
OpenAI published a proof, with a Lean formalization, that an initially smooth fluid can develop a singularity in finite time, produced by agents running on an internal model it says is significantly more capable than GPT-6 Astra.
According to the 8 September 2026 post (updated 10 September), the result shows that a three-dimensional incompressible fluid starting at rest, with a smooth force applied, can develop a singularity in finite time, which OpenAI says establishes statement "C" (and also "D") in the official Millennium Prize formulation. The model has been in training since 28 August. The group that produced the result involved on the order of 10,000 concurrent agents and reached it on 5 September, about 88 hours after the first agents launched; Lean formalization and verification took another 17 hours via GPT-6 Astra. Across all attempted problems the agents sent 4.9 million messages and used about 300 billion output tokens. Along the way they also resolved the unforced version of the Euler blowup question. Anthropic's Levent Alpöge and NYU's Tristan Buckmaster had separately produced a forced Euler result, and OpenAI's 10 September update says an investigation confirmed that Buckmaster's Codex prompts over the prior two months could not have influenced the system. OpenAI says it does not intend to claim the prize.
This reports OpenAI's claim; the announcement alone does not establish acceptance by the mathematics community. Clay's rules require three conditions before a proposed solution is considered: publication in a qualifying outlet, at least two years since publication, and general acceptance in the global mathematics community. The Lean formalization provides material for independent mechanical checks, whose results remain worth following. Operationally, OpenAI has disclosed an unreleased model beyond Astra and a run with roughly 10,000 concurrent agents, providing a reference point for reading the next public release.
