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Lean-GAP introduces a structured dataset of 430 formalized graduate algebra problems, demonstrating that while automated pipelines can handle preprocessing and initial translation, rigorous verification remains a critical bottleneck requiring significant human oversight. The study provides a systematic methodology for formalizing textbook mathematics and analyzes the performance limits of current autoformalization models in bridging informal statements with formal language. For the technical community, this work highlights the persistent gap between scalable automation and the nuanced logic required for reliable mathematical verification.
Lean-GAP: A Dataset of Formalized Graduate Algebra Problems
arXiv:2606.02588v1 Announce Type: cross Abstract: 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.
Abstract: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.
Logic in Computer Science (cs.LO); Artificial Intelligence (cs.AI); Programming Languages (cs.PL)
arXiv:2606.02588 [cs.LO]
(or arXiv:2606.02588v1 [cs.LO] for this version)
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