AI and humans collaborate to solve long-standing math problem

On September 20, 2026, a significant milestone in artificial intelligence was achieved as GPT-6Astra, in collaboration with three human researchers, solved a long-standing mathematical problem on the FrontierMath benchmark. The problem, first posed in 2017, questioned whether a 'core' could be empty in an approval-based committee election. GPT-6Astra proved that such a scenario is impossible, ensuring the existence of an absolutely fair committee under any circumstances. The model also introduced a novel voting rule based on 'harmonic entropy,' offering a polynomial-time algorithm and demonstrating that a local optimal solution meets the 'core' requirements. In this collaboration, humans provided direction and logical frameworks, while AI handled computational tasks and sudden insights, resembling a well-coordinated research team. This marks the first time AI has solved a 'major breakthrough' level math problem, signaling a shift from problem-solving to pattern discovery. Epoch AI has introduced a 'Human + AI' status tag to recognize such achievements, reflecting a new era in scientific research.