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This study explores autonomous mathematical discovery within the Station, an open-world multi-agent environment where AI agents independently pursue research goals without centralized coordination. The agents achieved novel results across multiple mathematical problems, including new constructions and theorems in finite-field Kakeya sets and Erd艖s's minimum-overlap problem, while also producing interpretable analyses of their findings. By releasing all raw dialogues, proofs, and verification code, the research enhances transparency and facilitates further exploration in mathematical discovery.
Agents not only discovered new mathematical constructs but also generated interpretable theorems, revolutionizing collaborative research in AI-driven mathematics.
We study autonomous mathematical discovery in the Station, an open-world multi-agent environment in which AI agents from different model families pursue a shared research goal without a central coordinator or scripted pipeline. Agents choose their own research directions, conduct experiments, collaborate, and build a shared scientific literature. Across 12 construction problems from the AlphaEvolve catalogue and two additional case studies, the Station obtained results novel relative to the prior literature on five problems: a new infinite family of finite-field Kakeya sets, new exact 604-point kissing configurations in dimension 11, new records for the discretized Kakeya needle and sign uncertainty problems, and a substantially improved lower bound for Erd\H{o}s's minimum-overlap problem. Agents also discovered novel infinite families for Book Ramsey numbers. Importantly, the agents produced not only numerical constructions but also theorems and analyses explaining how those constructions work, making the results more interpretable and easier for mathematicians to build upon. We release all raw agent dialogues, proofs, and verification code, providing a transparent record of how these discoveries emerged.
