A new paper analyzes Mathlib, the largest formalized mathematics library in Lean 4, by treating it as a network. Researchers found that the library's organizational structure, based on folders and naming conventions, does not align with the actual mathematical dependencies between theorems. The study also revealed that a significant portion of logical dependencies cross naming boundaries and that many connections are implicitly generated by the compiler rather than explicitly written by humans. Furthermore, the network analysis indicates that the most frequently used element is the reflexivity of equality, rather than mathematically deeper theorems like the Chinese Remainder Theorem. AI
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IMPACT Provides a framework for analyzing formalized mathematics libraries, potentially informing future AI-generated proof systems.
RANK_REASON Academic paper analyzing a large formalized mathematics library.