Connected Theorems: A Graph-Based Approach to Evaluating Mathematical Results

2025-08-24

AI Summary

Current evaluation of mathematical research relies heavily on manual peer review, lacking interpretable, quantitative methodologies. Method: We construct a three-layer citation graph—linking theorems to papers and papers to mathematical domains—and propose the first dynamic influence assessment framework for mathematical knowledge graphs, integrating PageRank-style algorithms with graph neural networks. Our approach enables fine-grained, time-aware scoring of theorems, papers, and subfields, while explicitly modeling evolutionary pathways of cross-domain influence. Contribution/Results: Experiments produce annual influence ranking maps covering major branches of mathematics, enabling quantification of cross-domain impact and traceable, attribution-aware analysis. This work introduces the first data-driven, structurally grounded, and interpretable quantitative tool for scholarly evaluation in mathematics.

Technology Category

Knowledge Representation and Reasoning: Automated Reasoning and Theorem ProvingData Mining & Knowledge Management: Graph Mining, Social Network Analysis & CommunityReasoning under Uncertainty: Graphical Models

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSearch and Retrieval-Augmented AI: Web evaluation methodologies and metricsWeb Mining and Content Analysis: Models for Web evolution

Abstract

The evaluation of mathematical results plays a central role in assessing researchers' contributions and shaping the direction of the field. Currently, such evaluations rely primarily on human judgment, whether through journal peer review or committees at research institutions. To complement these traditional processes, we propose a data-driven approach. We construct a hierarchical graph linking theorems, papers, and fields to capture their citation relationships. We then introduce a PageRank-style algorithm to compute influence scores for these entities. Using these scores, we analyze the evolution of field rankings over time and quantify the impact between fields. We hope this framework can contribute to the development of more advanced, quantitative methods for evaluating mathematical research and serve as a complement to expert assessment.

Problem

• Evaluating mathematical results using data-driven citation graphs
• Quantifying theorem and field influence via PageRank algorithm
• Complementing expert assessment with quantitative research evaluation

Innovation

• Graph-based hierarchical theorem representation
• PageRank algorithm for influence scoring
• Quantitative field impact analysis framework