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.

翻译：本研究提出了一种半自主数学发现的案例研究，利用Gemini系统性地评估布鲁姆埃尔德什问题数据库中标记为"开放"的700个猜想。我们采用混合方法：首先通过人工智能驱动的自然语言验证来缩小搜索范围，随后由人类专家进行评估以判断正确性和新颖性。我们处理了数据库中标记为"开放"的13个问题：其中5个通过看似新颖的自主解决方案得以解决，另外8个则通过识别现有文献中的先前解决方案完成。研究结果表明，这些问题的"开放"状态更多源于其隐蔽性而非难度。我们还识别并讨论了大规模应用人工智能处理数学猜想时出现的问题，重点指出了文献识别的困难以及人工智能可能产生"潜意识抄袭"的风险。最后，我们对人工智能辅助解决埃尔德什问题的工作进行了反思与总结。