OpenAI Says an Internal 'Astra' Model Cracked Ten Decade-Stale Math Problems at Under $2,000 of Tokens Each — and Published the Lean 4 Certificates
OpenAI released 'Ten advances in mathematics and theoretical computer science' on August 1, claiming an internal version of Astra (its next major model) produced new results on ten problems that had 'seen no progress on the main result for at least a decade' — high-dimensional sphere packing, Connes's rigidity conjecture, Ehrhart's volume conjecture, multicolor Ramsey numbers, quantum parallel repetition, arithmetic circuit complexity, the closest vector problem, non-sofic groups, binary/spherical codes, and extremal number conjectures. The openai/ten-proofs repo (Apache-2.0, Lean 4.32.0, ~275 stars) ships machine-checkable certificates alongside an LLM-written PDF reconstructing the derivations from unpublished reasoning traces. Willison's caveat is the important one for calibration: OpenAI discloses cost per success but not the denominator — how many problems Astra attempted and failed.
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