Noesion Radarnoesion.ai
Research2026-08-03

OpenAI published results in which an internal version of Astra, described as its next major model, produced solutions to ten open mathematics problems, including new sphere-packing upper bounds down to the Cohn–Elkies threshold, a construction of non-sofic groups, a disproof of Connes's rigidity conjecture, arithmetic-formula lower bounds for the permanent of order n^4/log n, an exponential parallel repetition theorem for two-player quantum games, Ehrhart's volume conjecture, and resolutions of Erdős problems 146, 180 and 183. OpenAI stated the token cost would be roughly $2,000 at Sol API rates, that humans prepared manuscripts with the same model, and that each argument was formalized in a Lean certificate released on GitHub. Noam Brown said other major problems were attempted without success and no Millennium Prize problems were solved.

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