From Euler to Today: Universal Mathematical Fallibility A Large-Scale Computational Analysis of Errors in ArXiv Papers

2025-11-04

AI Summary

Mathematical literature lacks systematic error statistics and automated peer-review tools, hindering large-scale quality assessment. Method: This study introduces the first multimodal analysis framework for cross-era, large-scale automatic error detection and quality evaluation in arXiv mathematics papers, integrating natural language processing, formal logical verification, and mathematical semantic parsing to generate review reports and journal-level recommendations. Contribution/Results: Empirical analysis of 37,000+ papers reveals discipline-specific error rates (9.6% in numerical analysis, 6.5% in geometric topology, none detected in category theory) and quantifies journal suitability (0.4% recommended to top-tier general journals; 15.5% to leading specialized journals). The system demonstrates the feasibility of automated peer review in mathematics and establishes a novel paradigm for scholarly quality monitoring.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Machine Learning: Evaluation and Analysis
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Web data quality in the era of algorithmically-generated content
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We present the results of a large-scale computational analysis of mathematical papers from the ArXiv repository, demonstrating a comprehensive system that not only detects mathematical errors but provides complete referee reports with journal tier recommendations. Our automated analysis system processed over 37,000 papers across multiple mathematical categories, revealing significant error rates and quality distributions. Remarkably, the system identified errors in papers spanning three centuries of mathematics, including works by Leonhard Euler (1707-1783) and Peter Gustav Lejeune Dirichlet (1805-1859), as well as contemporary Fields medalists. In Numerical Analysis (math.NA), we observed an error rate of 9.6% (2,271 errors in 23,761 papers), while Geometric Topology (math.GT) showed 6.5% (862 errors in 13,209 papers). Strikingly, Category Theory (math.CT) showed 0% errors in 93 papers analyzed, with evidence suggesting these results are ``easier''for automated analysis. Beyond error detection, the system evaluated papers for journal suitability, recommending 0.4% for top generalist journals, 15.5% for top field-specific journals, and categorizing the remainder across specialist venues. These findings demonstrate both the universality of mathematical error across all eras and the feasibility of automated comprehensive mathematical peer review at scale. This work demonstrates that the methodology, while applied here to mathematics, is discipline-agnostic and could be readily extended to physics, computer science, and other fields represented in the ArXiv repository.

Problem

• Detecting mathematical errors in ArXiv papers across multiple categories
• Providing automated referee reports with journal tier recommendations
• Analyzing error distribution in mathematical works spanning three centuries

Innovation

• Automated system detects mathematical errors in papers
• Generates complete referee reports with journal recommendations
• Discipline-agnostic methodology scalable across multiple fields