OpenAI published a solution to the Navier–Stokes problem, one of seven Millennium Prize Problems. An unreleased internal model produced it, working through coordinated groups of software agents. The proof shows smooth fluid motion can break down in finite time. OpenAI released a written proof and a machine-checked version in Lean. The same system also disproved smoothness for the related unforced Euler equations. Work began on 1 September after rumours that two prize problems had been solved. OpenAI says the internal model is far more capable than GPT-6 Astra, and is still training. It will not claim the Clay Institute prize money. Levent Alpöge of Anthropic and NYU's Tristan Buckmaster separately resolved the forced Euler case, and OpenAI recognises their priority. OpenAI says its researchers and agents saw none of that work before its public release.
What changed
The question of whether smooth 3D fluid motion can break down had stood unresolved for about 90 years.
- ~10,000 concurrent agents on the problem
- 88 hours to reach the resolution
- 2.7m messages, ~130bn output tokens
- 17 hours for Lean verification
Sources