ProofJudge: Tool-Grounded LLM Evaluation of Formal Proof Quality in Mathlib
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ProofJudge is an agentic large language model that evaluates the quality of formal proofs in Lean 4 beyond mere correctness. It scores proofs on five dimensions—library leverage, automation fit, structural clarity, statement quality, and Mathlib conventions—using tool access to the relevant repository commit. The system was tested on 218 Mathlib declarations, achieving alignment with human reviewers between 63.5% and 80.8% and releasing its harness, dataset, and traces for open research.
arXiv:2606. 29493v1 Announce Type: new Abstract: Benchmarks for LLM-assisted theorem proving in Lean are often treated as intrinsically reliable because every solved instance comes with a machine-checked proof.
arXiv:2608. 00004v1 Announce Type: cross Abstract: Grading natural-language mathematical proofs is a recurring cost in evaluating math-reasoning systems, and frontier LLM judges are expensive.
Large language models produce outputs presented as discoveries - new proofs, conjectures, or molecules. Whether such an output that appears creative is truly original and effective is hard to establis...
arXiv:2606. 31002v1 Announce Type: new Abstract: Theorem-proving benchmarks evaluate proof search against fixed formal statements, but natural-language-to-Lean formalization must generate the formal statement itself.
LLMs have recently achieved strong results on formal proving benchmarks. However, existing evaluations remain heavily concentrated on competition-style problems and often fail to capture how models behave on longer, more dependency-rich mathematical developments.