开放世界多智能体环境中的自主数学发现

摘要

我们研究Station中的自主数学发现。Station是一个开放世界多智能体环境，来自不同模型系列的AI智能体在没有中央协调器或脚本化流水线的情况下追求共同的研究目标。智能体自行选择研究方向、开展实验、相互协作，并构建共享的科学文献。在AlphaEvolve目录中的12个构造问题以及另外两个案例研究中，Station在五个问题上取得了相对于既有文献的新结果：有限域Kakeya集的一个新的无限族，11维空间中新的精确604点亲吻构型，离散化Kakeya针和符号不确定性问题的新的纪录，以及Erdős最小重叠问题的一个显著改进的下界。智能体还发现了Book拉姆齐数的新的无限族。重要的是，智能体不仅产出数值构造，还产出了解释这些构造如何运作的定理与分析，使结果更具可解释性，也更便于数学家在此基础上进一步研究。我们发布了所有原始智能体对话、证明和验证代码，为这些发现是如何产生的提供了透明的记录。

English

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.