Categorizing Mathematical Concepts with LLM Voting Ensembles in Mathswitch

Abstract

Mathswitch is an open-source project that imports mathematical concept records from sources such as Wikidata, Wikipedia, MathWorld, Encyclopedia of Mathematics, nLab, ProofWiki, and Agda-Unimath, and links records that refer to the same concept. It does not reorganize or redefine the imported content; each source retains its own structure. The current focus is on importing concept data from Wikidata and the resources it links to, with plans to expand to further sources and better concept linking. Because the concept set is approximated through queries over Wikidata's collaboratively edited graph, the imported data is noisy: some items are non-mathematical, while others are ambiguous. In this paper, we test whether a voting ensemble of LLM judges can filter this noise. We evaluate it on Wikidata items with known MathWorld identifiers as a positive control, and examine how classification changes when database identifiers are removed from context. We then inspect the cases where the judges disagree with MathWorld and group these disagreements into three categories (degenerate descriptions, narrow scope bias, and editorial-scope mismatches) that suggest different remediation strategies.