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

TL;DR

This paper introduces a graph-based, data-driven framework for evaluating mathematical research by linking conjectures, theorems, papers, authors, and fields to analyze influence and evolution.

Contribution

It presents a hierarchical graph model and a PageRank-style algorithm to quantify influence and assess the development of mathematical fields.

Findings

The influence scores reveal the impact of individual papers and authors.

The framework tracks the evolution of field rankings over time.

Quantitative influence measures complement traditional peer review.

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 conjectures, theorems, papers, authors 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.