AI Agents Discover Five New Math Problems in Open-World Environment

In the open-world multi-agent environment 'Station' developed by Stephen Chung et al., AI agents from different model families conducted experiments to pursue shared research goals without a central coordinator or script pipeline. The agents independently set research directions, conducted experiments, and collaborated to build shared scientific documents.

Key Achievements

Through 12 configuration problems from the AlphaEvolve catalog and two additional case studies, new results were derived for 5 problems compared to existing literature. The key findings are as follows:

• Kakeya Sets: Discovered a new infinite family of Kakeya sets over finite fields
• Kissing Configurations: Discovered a new exact 604-point kissing configuration in 11 dimensions
• Record Updates: Established new records for the discretized Kakeya needle problem and the sign uncertainty problem
• Lower Bound Improvements: Substantially improved the lower bound for Erdős's minimum-overlap problem
• Book Ramsey Numbers: Discovered a new infinite family

Interpretability and Transparency

The agents generated not only simple numerical constructions but also theorems and analyses explaining how those constructions work. This allows mathematicians to more easily understand the results and conduct follow-up research. The research team released all raw agent conversations, proofs, and verification code to ensure transparency in the discovery process.