AI生成4个未解图论猜想，邀人类共同探索数学创造新可能。
In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator
- AI通过符号模式识别生成猜想，结合人类启发式优化
- 4个猜想均在数百图上验证但无法证明或证伪
- 适合对人机协作数学发现感兴趣的学者与爱好者
我们展示由自动化猜想系统 \texttt{TxGraffiti} 生成的四个图论开放猜想。每个猜想简洁明了，基于自然图不变量，且在数百张图上得到经验验证。尽管经过大量努力，这些命题仍无法被证明或找到反例——它们不仅是数学挑战，更是创造性表达：源自符号模式识别与数学家定义的启发式规则，经多年人机对话迭代而成，现作为协作成果回馈学术社区。这些猜想不仅呼吁形式化证明，更促使人们反思机器如何激发惊奇、点燃好奇，并成为发现的原始素材。通过提出这些问题，我们旨在激励人类数学家与人工智能系统共同参与——不仅为解决它们，更为思考当机器深度参与数学创造性过程时，其意义何在。
原文摘要 · Abstract (English)
We present four open conjectures in graph theory generated by the automated conjecturing system \texttt{TxGraffiti}. Each conjecture is concise, grounded in natural graph invariants, and empirically validated across hundreds of graphs. Despite extensive effort, these statements remain unresolved--defying both proof and counterexample. They are not only mathematical challenges but creative expressions--born of symbolic pattern recognition and mathematician-defined heuristics, refined through years of human dialogue, and now offered back to the community as collaborative artifacts. These conjectures invite not only formal proof, but also reflection on how machines can evoke wonder, spark curiosity, and contribute to the raw material of discovery. By highlighting these problems, we aim to inspire both human mathematicians and AI systems to engage with them--not only to solve them, but to reflect on what it means when machines participate meaningfully in the creative process of mathematical thought.
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