On the top-tier AI math benchmark FrontierMath, a long-standing open problem that had been posed as a "major breakthrough" since 2017 has been solved — and this time, the hero was a human-AI collaboration of GPT-6Astra and three human researchers. The question asked whether the "core" is empty in a approval-based committee election. The original intention was to find a counterexample where the "core" is empty. However, GPT-6Astra proved the opposite: such a counterexample does not exist at all, meaning that an absolutely fair committee must always exist under any circumstances.

Even more impressive, the model also invented a new voting rule based on "harmonic entropy," providing a polynomial-time algorithm and proving that a local optimal solution already satisfies the requirement of the "core." In this collaboration, humans were responsible for setting direction and logical framework, while AI took over the knowledge base, computational drills, and those sudden inspirations — their division of labor resembled a well-coordinated research team.

This is the first time AI has solved a "major breakthrough" level math problem, and its significance goes beyond solving one problem. It pushes large models one step further from being just "problem-solving machines" to becoming collaborators capable of discovering mathematical patterns. Even Epoch AI, which maintains the ranking list, has added a new "Human + AI" status tag, specifically reserving a place for such human-AI joint research achievements. As mathematicians begin to play the role of "prompt engineers," the way scientific research is conducted is quietly being rewritten.