開放世界多智能體環境中的自主數學發現

摘要

我們研究 Station 中的自主數學發現，這是一個開放世界多智能體環境，來自不同模型家族的 AI 智能體在沒有中央協調者或腳本化管線的情況下，追求共同的研究目標。智能體自行選擇研究方向、進行實驗、相互協作，並建立共享的科學文獻。在來自 AlphaEvolve 目錄的 12 個構造問題以及另外兩個案例研究中，Station 在五個問題上取得了相較於先前文獻的新穎結果：新的有限域 Kakeya 集合無限族、第 11 維中新的精確 604 點接吻構形、離散化 Kakeya 針問題與符號不確定性問題的新紀錄，以及對 Erdős 最小重疊問題大幅改進的下界。智能體還發現了 Book 拉姆齊數的新無限族。重要的是，智能體不僅產出數值構造，還產出解釋這些構造如何運作的定理與分析，使結果更具可解釋性，也讓數學家更容易在此基礎上進一步研究。我們公開所有原始智能體對話、證明與驗證程式碼，提供這些發現如何產生的透明紀錄。

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.