Can LLM generate interesting mathematical research problems?

2026-03-19

AI Summary

This study investigates whether large language models (LLMs) can generate mathematically novel and research-worthy problems. To this end, we develop an LLM-based agent system specifically designed to autonomously produce problems in differential geometry and implement a rigorous expert validation protocol to assess their originality and potential scholarly value. From 665 generated problems, multiple were confirmed by domain experts as previously unknown and possessing distinctive research significance. Our work provides the first systematic demonstration of the creative capacity of LLMs in formulating meaningful mathematical research questions, thereby establishing a new paradigm for AI-driven mathematical discovery.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Cognitive Modeling & Cognitive Systems: Computational Creativity
• Natural Language Processing: (Large) Language Models

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

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.

Problem

• LLM
• mathematical creativity
• research problem generation
• differential geometry
• artificial intelligence

Innovation

• mathematical creativity
• large language models
• research problem generation
• differential geometry
• AI for mathematics