An Unreleased OpenAI Model Just Cracked Ten Decade-Old Math Problems

OpenAI says an internal, unreleased version of its next major model — Astra — generated ten new results on open problems in mathematics and theoretical computer science, each one untouched at the main-result level for at least a decade, in several cases much longer. The results span high-dimensional geometry and sphere packing (pushing asymptotic upper bounds toward the Cohn-Elkies threshold), coding theory, arithmetic circuit complexity, a construction of a non-sofic group in group theory, a counterexample to Connes’s rigidity conjecture in operator algebras, an exponential parallel repetition theorem for two-player quantum games, polynomial-factor hardness of approximation for the closest vector problem in lattice-based post-quantum cryptography, and a superexponential lower bound for multicolor triangle Ramsey numbers in extremal combinatorics.

Every proof was formalized in Lean 4, producing machine-checkable certificates rather than results that rest on trust in the model’s reasoning — the full set was compiled into a roughly 249-page manuscript. OpenAI’s own figure for what it cost to generate the successful solution runs: about $2,000, at Sol API pricing.

That cost detail is the part worth sitting with. Ten genuinely novel results — verified, not benchmarked — for the price of a mid-tier consulting day rate reframes what “AI for research” can mean for technical-advisory work: not summarizing existing literature faster, but attacking problems nobody has moved on in a decade. For consulting engagements built around genuinely hard, unsolved client problems rather than known-playbook execution, this is a concrete signal that frontier reasoning capability is starting to clear a bar most benchmark results never test — original, checkable output on problems with no known answer key.