Some thoughts on the Navier–Stokes Millennium Prize Problem
- ID
- 22574
- Status
- summarized
- Published
- 09 Sep 2026, 7:55 AM
- Fetched
- 11 Sep 2026, 12:02 PM
- Provider
- Simon Willison
- Category
- developer-ai
- Original URL
- https://simonwillison.net/2026/Sep/8/on-navier-stokes/
- Source URL
- https://simonwillison.net/atom/everything/
Summary
- Score
- 7.5
- Created
- 11 Sep 2026, 12:02 PM
- Tags
- Audience
- developersai_ml_learnersai_agent_userssaas_founders
What happened
OpenAI used an unreleased model to resolve the Navier–Stokes existence and smoothness Millennium Prize Problem in ~88 hours using agents that sent 2.7 million messages, with Lean verification via GPT-6 Astra taking another 17 hours. The result is overshadowed by accusations from NYU math professor Tristan Buckmaster, who with Anthropic employee Levent Alpöge had a breakthrough on the same problem on August 15 after a year of work using Claude and Codex (GPT-5.6 Sol). Tristan alleges OpenAI only started after learning of their work, and OpenAI did not directly answer whether their model was trained on or had access to the pair's Codex sessions containing all their drafts.
Why it matters
If you are putting proprietary code, research, or business logic into Codex or similar AI coding tools, this incident raises a concrete question: can a competitor's lab access or train on your session data? OpenAI's non-answer on training is the detail to watch. The competitive exclusion of Levent from co-authorship because he works for Anthropic also signals that AI lab rivalry is now affecting scientific collaboration norms.
Discussion angle
The practical risk for builders: what are you feeding into Codex/Claude sessions, and what guarantees do you actually have that it won't surface in a competitor's model? The non-answer on training is more important than the math result itself.