According to a September 8, 2026 link post by Simon Willison, OpenAI used an unreleased model to produce a claimed resolution of the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems carrying a $1,000,000 prize since May 24, 2000. Willison's account and the cited documents describe a priority dispute. Tristan Buckmaster, an NYU mathematics professor, and Levent Alpöge, a mathematician employed by Anthropic, said they worked on the problem for nearly a year using Claude and Codex (mainly GPT-5.6 Sol) and had a breakthrough on August 15. Buckmaster wrote that OpenAI's first prompt was sent 'in the past few days, after information about our work had reached OpenAI,' and said he did not receive a direct answer about whether the model was trained on their Codex sessions. OpenAI stated it launched its effort on September 1, that agents reached a resolution on September 5 after about 88 hours, with Lean formalization and verification taking 17 additional hours via GPT-6 Astra. OpenAI said its agents sent 4.9 million messages and used about 300 billion output tokens across all attempted problems, and stated it did not access user data, though it 'cannot rule out' that de-identified data helped improve its models.
- OpenAI claims an unreleased model resolved the Navier–Stokes Millennium Prize Problem ($1M prize since 2000)
- Buckmaster (NYU) and Alpöge (Anthropic) say they worked on it nearly a year and had a breakthrough August 15
- OpenAI says its effort began September 1 and reached resolution September 5, ~88 hours after launch
- Agents used ~300 billion output tokens across all problems; ~130 billion for Navier–Stokes
- OpenAI says no user data was accessed but 'cannot rule out' de-identified data helped its models
What it means for you
Two AI labs are fighting over who first cracked a famously hard math problem, and the mathematicians who used OpenAI's tools for a year say they were scooped by the company whose products they were using. The verification of the proof is still pending — this is a claim in dispute, not a settled result. The part that matters for ordinary users is the unanswered question at the center: when a company says your data 'improves model performance,' nobody can tell you exactly what that means.
Try this
If you put sensitive or original work into an AI tool, check that product's data settings this week and turn off training/data-sharing where the option exists (many business and enterprise tiers offer it).
Who should care
Researchers, founders, and anyone entering proprietary or unpublished ideas into AI chat tools who assumes that content stays private.
Skip this if
You only use AI for routine, non-confidential tasks and don't care about the mathematics or the lab rivalry.
Sources: Simon Willison — read the original