Formalizing a ring theorem with Lean 4 and Claude

This article describes an experiment testing Claude's ability to generate Lean 4 code to formally prove a theorem about partial fraction decomposition in a principal ideal domain (PID). The author prompted Claude to write a proof without providing a pre-existing proof or calculation. After 11 iterations and handling error messages, Claude produced code with five 'sorry' sections (unproven assumptions). The article discusses the challenges of using AI for formal theorem proving, including issues with Mathlib refactoring and hallucinations. It is relevant to IT/TECHNOLOGY as it covers programming, formal verification, and AI-assisted coding.