Overview
- OpenAI reported that an unreleased internal model produced a proof showing finite-time singularity for an initially smooth stationary fluid under the Navier–Stokes 'C' and 'D' cases, and supplied a Lean formalization that its released model GPT-6 Astra later checked.
- The company said about 10,000 cooperating AI agents generated the argument over roughly 88 hours and that GPT-6 Astra completed the machine verification in about 17 hours, and OpenAI added it will not claim the Clay Mathematics Institute's $1 million prize.
- Researchers Tristan Buckmaster and Levent Alpöge, who published related fluid-equation work days earlier, questioned whether OpenAI shifted resources after their progress and whether material stored in OpenAI's Codex influenced the result, prompting public scrutiny.
- OpenAI denied that researchers or the AI accessed specific user data but acknowledged it does not rule out anonymous user data having helped model training, and independent peer review and community validation of the proof remain pending.
- Observers note the estimated large compute cost for the work and say the announcement highlights growing tensions over credit, reproducibility and the role of proprietary, high-cost AI systems in producing major mathematical results.