Scaling Mathematical Proof Supervision from Structured Textbooks
Scaling Mathematical Proof Supervision from Structured Textbooks
TOME-Math transforms 2,118 university mathematics textbooks into approximately 380K structured proof supervision records, preserving chapter order, proposition-proof links, and dependency references, used for fine-tuning to improve the mathematical reasoning ability of language models by 16.7 percentage points, surpassing all three public instruction datasets. This corpus will be released to promote structured mathematical supervision research.
Abstract
A large-scale corpus of structured proof-supervision records derived from university mathematics textbooks improves language model mathematical reasoning by 16.7 percentage points over a base model when used for fine-tuning.
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.
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