开放世界多智能体环境中的自主数学发现
Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment
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中文总结 AI 辅助
本研究在开放世界多智能体环境Station中，让AI智能体自主开展数学研究，在多个数学问题上取得新结果，生成可解释的定理与分析，并公开相关原始数据与代码。
中文摘要 AI 辅助
我们在Station（开放世界多智能体环境）中研究自主数学发现，该环境中不同模型家族的AI智能体在无中央协调器或预设流程的情况下追求共同研究目标。智能体选择自身研究方向、开展实验、协作并构建共享科学文献。在AlphaEvolve目录的12个构造问题及另外2个案例研究中，Station在5个问题上取得了较现有文献的新结果：有限域Kakeya集的新无限族、11维空间中全新的604点接吻构型、离散化Kakeya针与符号不确定性问题的新纪录，以及Erdős最小重叠问题的大幅改进下界；智能体还发现了Book Ramsey数的新无限族。重要的是，智能体不仅生成数值构造，还提出解释这些构造运作方式的定理与分析，使结果更具可解释性，便于数学家进一步研究。我们公开所有原始智能体对话、证明及验证代码，为这些发现的产生提供透明记录。
英文摘要
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 publish papers. These papers accumulate into a shared body of knowledge that later agents can read, cite and extend. We evaluated the Station on 12 mathematical construction problems from the AlphaEvolve study and two additional case studies. Five of the 12 problems yielded results novel relative to the prior literature: a new infinite family of finite field Kakeya sets, new exact 604-point kissing configurations in eleven dimensions, improved bounds 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. Their research extended beyond searching for high-scoring constructions: agents developed explanations of their findings and proved theorems outside the assigned tasks. These explanations guided further discoveries and were preserved in the agents' papers, making the underlying insights easier for external researchers to understand and build upon. All presented discoveries are supported by exact constructions or proofs formally verified in Lean. We release the source code, full agent dialogues, papers and verification code, providing a transparent record of how these discoveries emerged.
发表机构
- DualverseAI
- University of Cambridge（剑桥大学）
- University of Hong Kong（香港大学）
- University of California San Diego（加州大学圣迭戈分校）
机构由 AI 辅助整理，请以论文原文为准。
