Can LLM generate interesting mathematical research problems?
This work addresses the challenge of automating mathematical problem generation for researchers, though it is incremental as part of a series on LLM creativity.
The authors investigated whether large language models (LLMs) can generate valuable and cutting-edge mathematical research problems, specifically producing 665 problems in differential geometry, with human verification showing many were unknown to experts and had unique research value.
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.