Enhancing Mathematical Knowledge Graphs with Large Language Models

Abstract

The rapid growth in scientific knowledge has created a critical need for advanced systems capable of managing mathematical knowledge at scale. This study presents a novel approach that integrates ontology-based knowledge representation with large language models (LLMs) to automate the extraction, organization, and reasoning of mathematical knowledge from LaTeX documents. The proposed system enhances Mathematical Knowledge Management (MKM) by enabling structured storage, semantic querying, and logical validation of mathematical statements. The key innovations include a lightweight ontology for modeling hypotheses, conclusions, and proofs, and algorithms for optimizing assumptions and generating pseudo-demonstrations. A user-friendly web interface supports visualization and interaction with the knowledge graph, facilitating tasks such as curriculum validation and intelligent tutoring. The results demonstrate high accuracy in mathematical statement extraction and ontology population, with potential scalability for handling large datasets. This work bridges the gap between symbolic knowledge and data-driven reasoning, offering a robust solution for scalable, interpretable, and precise MKM.