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

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 seven works by Leonhard Euler (1707-1783) in just 403 papers analyzed from the History category, as well as errors by Peter Gustav Lejeune Dirichlet (1805-1859) and contemporary Fields medalists. In Dynamical Systems (math.DS), we observed the highest error rate of 11.4% (2,347 errors in 20,666 papers), while Numerical Analysis (math.NA) showed 9.6% (2,271 errors in 23,761 papers). History and Overview (math.HO) exhibited 13.6% errors in preliminary analysis, including seven papers by Euler. In contrast, Geometric Topology (math.GT) showed 3.6% and Category Theory (math.CT) exhibited the lowest rate at 6.1% (228 errors in 3,720 papers). 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.