GPT-6 Astra Helps Solve 2017 Voting-Theory Problem, FrontierMath's First Major Advance
kimmonismus · x · 2026-09-19
Epoch AI announced FrontierMath's first "Major Advance": Becker, Greger, and Peters solved "The Core in Approval-Based Committee Elections" with GPT-6 Astra in a lengthy interactive session. The proof shows no committee-election instance has an empty core, so the benchmark problem was unsolvable as stated but is marked solved per policy. The problem, introduced by Aziz et al. in 2017, asks for an approval-voting instance whose core (fair committees not proportionally overturnable by any voter-candidate coalition) is empty. Peters doubts the team would have found the proof without Astra, but notes Astra couldn't solve it with a simple prompt — hence a human+AI solution and a landmark for AI-contributed original mathematics.
Related event: GPT-6 Astra helps crack first Major Advance problem on FrontierMath(8 posts)→
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