Mining Math Conjectures from LLMs: A Pruning Approach

TL;DR

This paper introduces a method for generating and refining mathematical conjectures using Large Language Models by leveraging their ability to produce plausible ideas and counterexamples, focusing on the solubilizer in group theory.

Contribution

The paper presents a novel pruning approach that uses LLMs to generate and validate mathematical conjectures, demonstrating their potential in mathematical discovery.

Findings

LLMs can generate plausible and falsifiable conjectures.

Counterexample generation helps prune and refine conjectures.

Limitations exist in code execution capabilities of LLMs.

Abstract

We present a novel approach to generating mathematical conjectures using Large Language Models (LLMs). Focusing on the solubilizer, a relatively recent construct in group theory, we demonstrate how LLMs such as ChatGPT, Gemini, and Claude can be leveraged to generate conjectures. These conjectures are pruned by allowing the LLMs to generate counterexamples. Our results indicate that LLMs are capable of producing original conjectures that, while not groundbreaking, are either plausible or falsifiable via counterexamples, though they exhibit limitations in code execution.