Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment

The paper reports on autonomous mathematical discovery within the Station, an open‑world multi‑agent environment where diverse AI agents pursue shared research goals without central coordination. Across 12 construction problems and two case studies, the agents produced novel results—including a new infinite family of finite‑field Kakeya sets, 604‑point kissing configurations in dimension 11, improved records for discretized Kakeya needle and sign uncertainty problems, a stronger lower bound for Erdős’s minimum‑overlap problem, and new infinite families for Book Ramsey numbers—alongside theorems and analyses that explain the constructions. All agent dialogues, proofs, and verification code are released to provide a transparent record of the discovery process.

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