OpenAI's September 2026 announcement of an AI-generated proof—produced by thousands of internal agents on an advanced model and formalized in Lean—established finite-time singularities for the Navier-Stokes equations under smooth external forcing, addressing Clay statements C and D. This breakthrough, building on prior human-AI work by mathematicians like Buckmaster and Alpöge, prompted the Clay Mathematics Institute to note the problem appears settled while stressing its unhurried review process, which requires peer-reviewed publication, independent verification, and broad community acceptance before any declaration. As of October 2026, CMI still lists the problem as active amid ongoing scrutiny, credit disputes, and questions about extensions to unforced or analytic cases, creating uncertainty around near-term official resolution despite rapid AI progress in mathematical formalization.
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