MathlibPR: Pull Request Merge-Readiness Benchmark for Formal Mathematical Libraries
Authors: Zixuan Xie, Xinyu Liu, Shangtong Zhang
Organizations: University of Virginia
Abstract
The ecosystem of Lean and Mathlib has become the de facto standard for large language model (LLM) assisted formal reasoning with remarkable successes in recent years. Those successes, however, only consume Mathlib as an essential dependency but do not directly contribute to it. In the meantime, the growth of Mathlib has recently been bottlenecked by the review process, which requires human reviewers to judge whether proposed pull requests (PRs) follow the Mathlib's conventions and are worth integrating as part of a shared mathematical infrastructure. This leads to our central question: can LLMs help review Mathlib PRs? To this end, we introduce MathlibPR, a benchmark built from real Mathlib4 PR histories. We further propose a staged evaluation protocol and use it to evaluate both LLM models (e.g., DeepSeek, Qwen, Goedel, and Kimina) and LLM agents (e.g., Codex and Claude Code). Surprisingly, both LLM models and LLM agents struggle to distinguish merge-ready PRs from build-passing PRs that were revised or never merged. By turning Mathlib PR histories into a supervised signal, MathlibPR provides a step toward reviewer assistants and reward models that could help evaluate PRs and steer LLMs toward producing merge-ready Mathlib contributions.
Within the past few years, the ability of Large Language Models (LLMs) to generate formal mathematical proofs has improved drastically. We provide a comparison of various LLMs' effectiveness in producing formal proofs in Lean 4 with the goal of assisting those seeking to use LLMs to support their own projects. We utilize both pass@k and refine@k metrics as the benchmark for our comparison and evaluate on subsets of both miniF2F and miniCTX datasets. Our testing shows that overall, Gemini 3.1 Pro and Claude Opus 4.7 perform best. Gemini 3.1 Pro achieved a 92% success rate on miniF2F via refine@32 whereas Opus 4.7 achieved a 86% success rate on miniCTX via refine@32. When taking cost into account, NVIDIA Nemotron 3 Super and GPT-OSS 120B were the most efficient, with competitive accuracies and average costs of <\0.01$ per correct proof.
Most of mathematical knowledge has been communicated through so-called informal use of mathematics and natural language. With large language models (LLMs) being highly adept in using natural language, they achieve strong performance, yet not perfect, in informal mathematical reasoning. Restraining LLMs to informal reasoning misses out on the opportunity to use the discrete verification abilities that machines offer through machine-checkable proofs. In this paper, we bridge the gap between informal and formal reasoning by integrating Lean signals into the informal reasoning process. We introduce Magenta, a training-free agentic pipeline that, given only a natural-language problem, produces an answer, expresses it as a Lean 4 statement, and constructs a machine-checked proof. A statement judge verifies whether the formalisation preserves the original problem, while an error-attribution judge routes failed attempts either to mathematical re-derivation or local Lean repair. Magenta achieves 100% accuracy across all evaluated olympiad benchmarks, including AIME 2025, AIME 2026, and HMMT February 2026. When paired with the open-weight K2-Horizon-7B reasoner, it solves all six IMO 2026 problems. Our analysis shows that statement adjudication is essential for preventing false certificates and that feedback-guided correction outperforms independent resampling on difficult problems.
We present a new approach for benchmarking Large Language Model (LLM) capabilities on research-level mathematics. Existing benchmarks largely rely on static, hand-curated sets of contest or textbook-style problems as proxies for mathematical research. Instead, we establish an updatable benchmark evaluating models directly on the latest research results in mathematics. This consists of an automatic pipeline that extracts lemmas from arXiv and rewrites them into self-contained statements by making all assumptions and required definitions explicit. It results in a benchmark that can be updated regularly with new problems taken directly from human mathematical research, while previous instances can be used for training without compromising future evaluations. We benchmark current state-of-the-art LLMs, which obtain around 10-15% accuracy in theorem proving (pass@1) depending on the model, showing that there is currently a large margin of progression for LLMs to reach human-level proving capabilities in a research context.