Structured textbook data improves math proof learning in language models
Scaling Mathematical Proof Supervision from Structured Textbooks
Computation and LanguageArtificial Intelligence
Summary
Mathematical problems and their solutions are often taught in an organized way within textbooks, but machine learning models usually see these problems and solutions as separate, unrelated examples. The authors created a large collection called TOME-Math that keeps all the organization and connections found in textbooks, like chapters and how different propositions relate to each other. By using this well-structured data to train language models, the authors boosted the models' ability to reason mathematically by a significant margin. This work shows that preserving the structure in learning materials helps models understand math better.
What this means in practice
- •For ai model trainers: Improve mathematical reasoning in language models by training on structured textbook data that preserves logical and curricular links.
- •For educational software developers: Build smarter tutoring systems that better understand step-by-step mathematical proofs using models fine-tuned with organized textbook supervision.$Commercial implications: Enables development of advanced math tutoring AI that adapts to curriculum structure and reasoning steps, improving learner outcomes.
Authors
Youqing Fang, Zhouqi Hua, Yinhao Tang, Yuzhe Gu, Lingkai Kong, Bin Liu, Weiming Zhang, Kai Chen, Yanan Sun, Wenwei Zhang
Abstract
Mathematical supervision for language models is typically flattened into isolated problem-solution pairs, discarding the curricular organization and evidential structure of the original sources. We introduce TOME-Math (Textbook-Oriented Mathematical Evidence), a large-scale corpus that converts 2,118 textbooks spanning the core areas of university-level mathematics subjects into approximately 380K structured proof-supervision records while preserving chapter order, proposition-proof links, dependency references, and source provenance. Leveraging these structural signals, we explore curriculum learning across multiple mathematical subjects and characterize scaling patterns with supervision volume and source breadth. At full scale, fine-tuning on TOME-Math raises the unweighted mean score across our held-out evaluations and established public benchmarks by 16.7 percentage points over the base model, while exceeding all three public instruction-data baselines evaluated in aggregate. Our findings highlight structured textbooks as both a scalable source of mathematical supervision and an empirical framework for studying the impact of data organization on mathematical reasoning. We will release the corpus to facilitate further research on structured mathematical supervision.