GPT-6Astra Solves 9-Year-Old Open Math Problem, Proving Perfectly Fair Committees Always Exist
新智元 · wechat · 2026-09-20
EpochAI's FrontierMath benchmark hit a milestone: a "major progress" level open problem from 2017 was solved by GPT-6Astra with three researchers (Patrick Becker, Matthias Greger, Dominik Peters). The problem asked for a counterexample where the "core" of approval-based committee elections is empty — instead, Astra proved no such counterexample exists: a perfectly fair committee always exists.
- Astra invented a novel voting rule based on "harmonic entropy," proved local optima lie in the core, and gave a polynomial-time algorithm, written up in a 20-page arXiv paper.
- Collaboration details: starting from Lindahl equilibrium rounding (2.065 approximation), humans pushed the model to improve until Astra proposed the entropy-based framework, ultimately proving the stronger Core+ property. Peters admitted the proof likely wouldn't have been found without Astra, though a single prompt would never suffice.
- This is the first "major progress" tier problem solved on FrontierMath (only 6 exist; 8 of 49 total solved). EpochAI added a new "Human+AI" status label, stating the core ideas came entirely from the AI.
Related event: GPT-6 Astra helps crack first Major Advance problem on FrontierMath(8 posts)→
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