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

This paper evaluates the Station, an open-world research environment where six autonomous agents—two each powered by GPT-5.5, Claude Opus 4.8, and Gemini 3.1 Pro—choose problems, run experiments, communicate, and publish into a persistent literature without a central coordinator. Across 12 construction problems from the AlphaEvolve catalogue, the Station produced results novel relative to prior literature on 5 problems, showing a complementary approach to AlphaEvolve and broader AI-for-mathematics efforts involving OpenAI. Its strongest results include a new infinite family of finite-field Kakeya sets, three exact 604-point kissing configurations in dimension 11, a new discretized Kakeya needle bound that improves AlphaEvolve by 6.74%, and a sign-uncertainty upper bound of 0.3089. In separate case studies, agents discovered novel infinite families for Book Ramsey numbers, proving the conjecture at 43 values of n ≤ 200, and reconstructed a degree-seven Jacobian-Conjecture counterexample from a binary evaluator without web access. The central novelty is not only score improvement but theorem-level explanation: agents converted numerical constructions into algebraic rules, impossibility results, and proofs. Analysis found that 19 of 28 spotlight findings involved multiple agents, while persistent archive papers, reflection periods, and stagnation protocols helped accumulate knowledge across agent generations. However, the system favored theory-guided constructions and underperformed large-scale heuristic search on irregular autoconvolution problems, highlighting the continuing value of expert intuition and human synthesis.