We present Lean-GAP (Lean-Graduate Agebra Problems), 430 formalized graduate-level algebra problems from the textbook Abstract Algebra by Dummit and Foote. We develop a scalable pipeline consisting of PDF-to-LaTeX preprocessing, autoformalization into Lean 4, and verification of informal-formal correspondence. While the preprocessing and autoformalization stages can be largely automated, we find that verification remains the most subtle and labor-intensive component, requiring careful human oversight. Our contributions include (i) the construction of a structured dataset of formalized exercises, (ii) a systematic methodology for formalizing textbook mathematics, and (iii) an analysis of recurring challenges in the formalization process. We also compare the performance of different autoformalization models and highlight key bottlenecks in translating informal statements into formal language.
We present AutoformBot, a multi-agent system for building an Autoformalized Textbook Library At Scale (Atlas) in Lean 4. AutoformBot orchestrates thousands of LLM agents, equipped with formal verification tools, dependency-aware task scheduling, and collaborative version control, to translate informal textbook prose into machine-checked definitions and proofs. We apply our methods to a corpus of 26 open-access textbooks spanning analysis, algebra, topology, combinatorics, and probability, producing Atlas: a verified library of over 45,000 Lean 4 declarations and 500 thousand lines of code. We release two artifacts: (i) AutoformBot, the open-source multi-agent framework; and (ii) Atlas, the resulting formal library. Our results suggest that autoformalizing the core content of graduate-level mathematics at scale is now economically and technically feasible. This opens the door to the automated verification of both human- and machine-generated mathematics at a research level.
Current autoformalization benchmarks are largely focused on olympiad or undergraduate mathematics, while graduate and research-level mathematics remains underexplored. In this paper, we introduce MathAtlas, the first large-scale autoformalization benchmark of in the wild graduate-level mathematics, containing ~52k theorems, definitions, exercises, examples, and proofs extracted from 103 graduate mathematics textbooks. MathAtlas is enriched with a mathematical dependency graph containing ~178k relations, and is the first autoformalization benchmark to include such relations, facilitating evaluation and development of dependency-aware autoformalization systems. Our extensive experiments show that MathAtlas is high quality but extremely challenging: strong baselines achieve at most 9.8% correctness on theorem statements and 16.7% on definitions. Furthermore, we find performance of state-of-the-art models degrades substantially with dependency depth: on MA-Hard, a subset of 700 entities with the deepest dependency trees, the best model achieves only 2.6% correctness for autoformalization on this challenging dataset. We release MathAtlas to the community as a benchmark set for large-scale autoformalization of graduate-level mathematics in the wild.
Formal theorem-proving benchmarks enable mechanically verifiable evaluation of mathematical reasoning in large language models. However, existing benchmarks mainly focus on Olympiad-style problems and algebraic domains, leaving computational and applied mathematics underrepresented. We introduce CAM-Bench, a Lean 4 theorem-proving benchmark of 1,000 Lean proof targets in computational and applied mathematics, with coverage spanning optimization, numerical linear algebra, and numerical analysis. These problems are adapted from textbook exercises and often depend on locally introduced definitions, notation, algorithms, and elementary results. To construct CAM-Bench, we develop a dependency-recovery pipeline that reconstructs the local textbook context needed to state each problem faithfully. It then normalizes each problem into a standalone informal theorem and translates it into a Lean target. We validate the resulting formal problems through Lean compilation and semantic review, checking both formal correctness and semantic alignment with the original exercises. For each problem, we release the raw exercise, recovered context, normalized informal theorem, and final Lean target. CAM-Bench complements existing formal mathematics benchmarks by targeting applied mathematics problems that rely on textbook concepts and elementary theorems, many of which are not directly available as standard Mathlib4 lemmas. We evaluate widely used large language models and formalization agents on CAM-Bench, and analyze common failure modes in tracking local assumptions, applying elementary results, decomposing proofs, and maintaining long-horizon control in Lean.