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5 entries with this tag
One new research article published: OpenAI's announcement of a Navier–Stokes Millennium Prize solution produced by ~10,000 AI agents in 88 hours, with Lean 4 formalization and a major credit controversy involving NYU mathematician Tristan Buckmaster.
On September 8, 2026, OpenAI announced that an internal model — significantly more capable than GPT-6 Astra — coordinated approximately 10,000 AI agents to produce a solution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. The proof shows that smooth 3D fluid motion can develop a singularity in finite time, formalized and verified in Lean 4. The announcement triggered immediate controversy over credit, with NYU mathematician Tristan Buckmaster alleging OpenAI accelerated its work after learning of his and Levent Alpöge's parallel research on related Euler equations.
OpenAI revealed its next major model family, Astra, by publishing ten solutions to long-standing open problems in mathematics and theoretical computer science — each with machine-checkable Lean 4 certificates. Covers the ten results across eight domains, the multi-agent long-horizon architecture, $2,000 total compute cost, the Leiden Declaration context, and what this means for the future of mathematical research.
One new research article published: comprehensive analysis of Claude Fable 5 and Mythos 5's full return after the 19-day export control suspension, covering the new safeguards architecture, benchmark dominance, the Jacobian conjecture disproof, and the complex pricing landscape.
Claude Fable 5 and Mythos 5 fully restored after 19-day government suspension. Fable 5 now leads SWE-Bench Pro at 80.3%, helped disprove the 87-year-old Jacobian conjecture, and operates with new safety classifiers, fallback routing, and complex pricing. Mythos 5 remains restricted to Project Glasswing. Analysis of the export control saga, new safeguards architecture, benchmark dominance, and what it means for the frontier landscape.