Automating Mathematical Proof Generation Using Large Language Model Agents and Knowledge Graphs

Abstract: LLMs have demonstrated remarkable capabilities in natural language processing tasks, including mathematical problem-solving that requires multi-step logical reasoning. However, challenges persist in automating the identification of key mathematical concepts, understanding their interrelations, and formalizing proofs within a rigorous framework. We present a novel framework that leverages knowledge graphs to augment LLMs to construct and formalize mathematical proofs. Our results demonstrate significant performance improvements across multiple datasets, with using knowledge graphs, achieving up to a 34% success rate on the MUSTARDSAUCE dataset on o1-mini and consistently outperforming baseline approaches by 2-11% across different models. We show how this approach bridges the gap between natural language understanding and formal logic proof systems and achieve elevated results for foundation models over baseline.