Can LLM generate interesting mathematical research problems?

TL;DR

This study investigates whether large language models can generate novel and valuable mathematical research problems, demonstrating their potential to contribute to mathematical creativity and research innovation.

Contribution

The paper introduces an agent that generates unknown mathematical problems, producing 665 differential geometry problems with many deemed valuable and novel by experts.

Findings

Many generated problems are unknown to experts.

Problems exhibit unique research value.

Large language models can produce innovative research problems.

Abstract

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.