用AI筛选700个数论猜想，发现13个'开放'问题实为已有解或可自主求解。
Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems
- AI先用自然语言分析缩小范围，再由专家验证真伪与新颖性。
- 解决13个标记为'开放'的问题，其中5个为全新自主解答。
- 适合对AI辅助数学发现感兴趣的科研人员参考。
我们开展了一项半自主数学发现的案例研究，利用Gemini系统对Bloom的Erdős问题数据库中700个标注为'Open'的猜想进行系统评估。采用混合方法：先通过AI驱动的自然语言验证缩小搜索空间，再由人类专家判断正确性与新颖性。共处理13个原数据库中标记为'Open'的问题：5个通过看似新颖的自主求解完成，8个则通过在现有文献中识别到先前解决方案而解决。研究结果表明，这些'开放'问题的存在更多源于文献晦涩而非难度本身。我们还指出在大规模应用AI解决数学猜想时面临的问题，包括文献检索困难及AI可能产生'潜意识抄袭'的风险。最后，反思了此次AI辅助探索Erdős问题的经验教训。
原文摘要 · Abstract (English)
We present a case study in semi-autonomous mathematics discovery, using Gemini to systematically evaluate 700 conjectures labeled 'Open' in Bloom's Erdős Problems database. We employ a hybrid methodology: AI-driven natural language verification to narrow the search space, followed by human expert evaluation to gauge correctness and novelty. We address 13 problems that were marked 'Open' in the database: 5 through seemingly novel autonomous solutions, and 8 through identification of previous solutions in the existing literature. Our findings suggest that the 'Open' status of the problems was through obscurity rather than difficulty. We also identify and discuss issues arising in applying AI to math conjectures at scale, highlighting the difficulty of literature identification and the risk of ''subconscious plagiarism'' by AI. We reflect on the takeaways from AI-assisted efforts on the Erdős Problems.
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