AI自动提出图论新猜想，能复现定理并发现潜在新规律。
The \emph{Optimist}: Towards Fully Automated Graph Theory Research
- 用混合整数规划与启发式方法生成可验证的图论猜想。
- 通过反馈迭代，无需人工干预即可改进猜想质量。
- 适合对自动化数学发现感兴趣的科研人员参考。
本文提出名为「Optimist」的自主系统，用于推进图论中的自动化猜想生成。该系统结合混合整数规划（MIP）与启发式方法，能够生成既可复现已有定理，又能提出新颖不等式的猜想。通过基于记忆的计算与类代理的自适应能力，Optimist 能在无需人类或机器频繁干预的情况下，通过整合新数据持续优化其猜想。初步实验表明，Optimist 具备发现图论基础结果的潜力，并能生成具有探索价值的新猜想。本文还展望了 Optimist 与另一代理「Pessimist」（可为人或机器）的协同机制，构建对抗性双代理系统，以实现图论研究的完全自动化。
原文摘要 · Abstract (English)
This paper introduces the \emph{Optimist}, an autonomous system developed to advance automated conjecture generation in graph theory. Leveraging mixed-integer programming (MIP) and heuristic methods, the \emph{Optimist} generates conjectures that both rediscover established theorems and propose novel inequalities. Through a combination of memory-based computation and agent-like adaptability, the \emph{Optimist} iteratively refines its conjectures by integrating new data, enabling a feedback process with minimal human (\emph{or machine}) intervention. Initial experiments reveal the \emph{Optimist}'s potential to uncover foundational results in graph theory, as well as to produce conjectures of interest for future exploration. This work also outlines the \emph{Optimist}'s evolving integration with a counterpart agent, the \emph{Pessimist} (a human \emph{or machine} agent), to establish a dueling system that will drive fully automated graph theory research.
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