Scaling Mathematical Proof Supervision from Structured Textbooks
Youqing Fang, Zhouqi Hua, Yinhao Tang, Yuzhe Gu, Lingkai Kong, Bin Liu, Weiming Zhang, Kai Chen and 2 others
University of Science and Technology of China · Fudan University · Shanghai AI Laboratory · Shanghai Jiao Tong University
Published October 29, 2026 · on the feed November 12, 2026 · ▲ 42 · arXiv 2610.40394
The 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.
The Brief
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Transcript
Scaling Mathematical Proof Supervision from Structured Textbooks. By Youqing Fang and nine others, from the University of Science and Technology of China, Fudan University, and two other institutions. Published on the twenty-ninth of October.
Mathematical supervision for language models usually arrives flattened into isolated problem and solution pairs. Whatever order and structure the original source had, the curriculum and the way evidence was laid out, is thrown away. A theorem pulled out of its chapter loses the definitions and earlier results it leaned on, and a proof separated from its proposition loses its reason for being there. TOME-Math, short for Textbook-Oriented Mathematical Evidence, is a large-scale corpus built to keep that structure.
It holds approximately three hundred and eighty thousand structured proof-supervision records. Each record keeps what flattening discards: chapter order, the links between a proposition and its proof, dependency references, and where in the source it came from. So a record is not only a statement and a proof, but a statement and a proof that still know their place in the book.
The records are converted from two thousand one hundred and eighteen textbooks, spanning the core areas of university-level mathematics. Those structural signals are what the authors then use, to explore curriculum learning across several mathematical subjects and to characterise how performance scales with the volume of supervision and the breadth of sources. At full scale, fine-tuning on TOME-Math lifts the unweighted mean score, across held-out evaluations and established public benchmarks, by sixteen point seven percentage points over the base model. It also exceeds all three public instruction-data baselines evaluated in aggregate.
It is aimed at researchers working on structured mathematical supervision, and at anyone who wants to study how the organisation of training data affects mathematical reasoning. Fine-tuning a model on it is the use the paper demonstrates, but because the curricular order is preserved, the corpus also lets researchers vary how supervision is organised and see what changes. The authors say they will release the corpus.
A textbook is more than a pile of exercises. Here it becomes two things at once: a scalable source of proof supervision, and an empirical framework for asking whether the order and links in the data matter.
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Chapter 1 🧩 · The problem
Maths textbooks are carefully built. Training data usually tears them apart.
You are building training data to teach a language model to write mathematical proofs. The usual recipe is a pile of isolated problem and solution pairs.
The road ahead
- 1 · The problem ~7 min Training data for maths proofs is usually a pile of isolated problem and solution pairs, which throws away how textbooks build knowledge in order.
- 2 · What came before ~3 min
- 3 · The key idea ~9 min Turn textbooks into proof records that keep their structure, add records for skipped proof steps, then use that structure for ordering training and finding evidence.
- 4 · Choose your own research ~3 min
- 5 · Build the method ~8 min Collect university textbooks, convert them into structured proof records, keep their order, references and provenance, then fine-tune a base model on them.
- 6 · The experiment ~6 min You’ll guess: By how many percentage points did fine-tuning on the textbook corpus raise the unweighted mean score over the base model?
- 7 · The viva ~5 min Three questions from the examiners, answered in your own words. Win it for the paper’s trophy.
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