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

Abstract: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 Erdős'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.

38 pages, 12 figures, 3 tables. Source code at this https URL and raw agent dialogues, proofs, and verification artifacts at this https URL

Artificial Intelligence (cs.AI); Discrete Mathematics (cs.DM); Multiagent Systems (cs.MA)

arXiv:2608.23691 [cs.AI]

(or arXiv:2608.23691v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2608.23691 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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