AI models crack decades‑old math problems, from FrontierMath benchmark to OpenAI's Astra breakthroughs

The FrontierMath benchmark, managed by Epoch AI, has expanded its Open Problems track to about 50 unsolved research‑level mathematics questions. AI systems have solved three of these problems, achieving a 6% success rate on questions that have resisted professional mathematicians for years. The benchmark covers areas such as combinatorics, number theory, algebraic geometry and topology, and each solution is verified by custom checkers. OpenAI announced that its next‑generation core model, Astra, internally solved ten long‑standing problems in mathematics and theoretical computer science, with an estimated token cost of roughly $2,000. The ten advances include new bounds for high‑dimensional sphere packing, improvements to binary and spherical codes, a construction proving the existence of non‑sofic groups, a refutation of Connes's rigidity conjecture, stronger lower bounds for arithmetic circuit complexity, an exponential parallel repetition theorem for two‑player quantum games, hardness results for the closest vector problem, a resolution of Ehrhart's volume conjecture, super‑exponential lower bounds for multicolor Ramsey numbers, and new results on extremal graph theory conjectures. Funding for the FrontierMath Open Problems track comes from Schmidt Sciences, the philanthropic initiative founded by former Google CEO Eric Schmidt, while OpenAI’s Astra work was carried out internally with human researchers assisting in formal verification using the Lean language.