LLM能生成具有前沿价值的数学研究问题。
Can LLM generate interesting mathematical research problems?
- 构建智能体自动生成微分几何领域的未知问题
- 产出665个经专家验证的未被发现的研究问题
- 为评估大模型数学创造力提供新方法，适合数学研究者参考
本文是关于大语言模型数学创造力系列工作的第二篇。在前作中，作者提出了评估数学创造力的三项标准，并构建了基准数据集进行衡量。本文进一步探索大模型的数学创造力，重点考察其能否生成有价值的前沿数学研究问题。我们开发了一个智能体，用于生成未知问题，在微分几何领域共产生665个研究问题。经人工验证，发现其中许多问题尚未被专家所知，具有独特的研究价值。
原文摘要 · Abstract (English)
This paper is the second one in a series of work on the mathematical creativity of LLM. In the first paper, the authors proposed three criteria for evaluating the mathematical creativity of LLM and constructed a benchmark dataset to measure it. This paper further explores the mathematical creativity of LLM, with a focus on investigating whether LLM can generate valuable and cutting-edge mathematical research problems. We develop an agent to generate unknown problems and produced 665 research problems in differential geometry. Through human verification, we find that many of these mathematical problems are unknown to experts and possess unique research value.
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