OpenAI's internal model produces an AI-generated solution to the Navier–Stokes Millennium Problem

OpenAI announced an AI-generated solution to the Navier–Stokes existence-and-smoothness Millennium Prize Problem, with a writeup and a formal proof in Lean. The work came from an internal model described as significantly more capable than GPT-6 Astra, in training since 2026-08-28 and still ongoing. A multi-agent system of roughly 10,000 concurrent agents ran from 9/1 to 9/5 (~88 hours to the resolution); the effort totals 4.9M messages and ~300B output tokens across all attempted problems, 2.7M messages and ~130B output tokens for Navier–Stokes, and GPT-6 Astra produced the Lean formalization in 17 hours. The proof shows initially smooth, at-rest fluid can develop a singularity in finite time (statements C and D); the unforced Euler regularity problem was also resolved (~100 agents, ~50 hours). OpenAI states it will not claim the Clay Millennium Prize.

This is the first demonstration that long-horizon multi-agent harnesses can carry an open Millennium-scale problem end to end, with Lean formalization acting as the trust layer for AI-generated mathematics. It also discloses an internal frontier model stronger than GPT-6 Astra, and the concurrent-work dispute (ev-20260908-15) makes harness-mediated data leakage a first-class governance concern for every vendor-run agent platform. Willison estimates the token volume at ~$15M at public Astra prices, putting a hard cost number on frontier-scale agent compute.