Do structured textbooks teach AI mathematics better than more examples?
TOME-Math turned 2,118 textbooks into 380,292 proof records and raised a 30B model's six-test mean from 29.17% to 45.83%. The corpus is not yet released, evaluation is largely model-judged, and source-book licensing is unclear.
The short version
- What happened
- TOME-Math contains 380,292 generated proof-supervision records from 2,118 textbooks across 29 subjects: 205,861 proof questions and 174,431 generated gap-filling questions.
- Who it affects
- Better mathematical reasoning could improve research and technical tools, but textbook-derived training data also affects authors, publishers and learners. Provenance and licensing determine whether a useful benchmark can be reproduced and responsibly reused.
- What remains unproven
- Unreviewed arXiv preprint submitted 29 October 2026; the promised corpus is not yet available for independent inspection.
Keep in mind
Unreviewed arXiv preprint submitted 29 October 2026; the promised corpus is not yet available for independent inspection.
The main comparison changes corpus content and scale as well as structure, so the 16.7-point gain cannot be attributed to ordering alone.
Long-form answers were primarily scored through repeated language-model judgments, with a smaller human audit.
The paper does not state redistribution licences for the 2,118 source textbook PDFs or resulting records.
No funding or competing-interest statement was identified.
Source analysis · 1 linked source. Primary analysed source date: 29 October 2026.
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Read the full report · 4 min The evidence, methods, implications and limitations
The dataset keeps chapters and proof dependencies intact
A 29 October arXiv preprint from four Chinese institutions reports that mathematical training data may benefit from retaining the structure of textbooks instead of flattening every example into an isolated question and answer. TOME-Math began with 2,118 canonical university-level mathematics PDFs across 29 subjects. An automated pipeline recovered chapter order, extracted theorem–proof units and generated self-contained questions for reasoning steps that source proofs left implicit.
The pipeline produced 489,162 candidate proof records and 918,235 candidate proof-gap records before filtering. The final corpus contains 380,292 examples: 205,861 proof questions and 174,431 gap questions. Each retains book, chapter and source-location metadata, with proposition links where available. Multiple language models performed OCR cleanup, extraction, gap detection and quality auditing. That is scalable, but it also means model-generated errors can survive a model-led validation chain.[1]
A 30B model improved across six tests
For the main comparison, the team reserved 64 books for evaluation and removed their 15,661 associated records, leaving 364,631 training examples. Qwen3-30B-A3B-Base was fine-tuned for one epoch and evaluated on two new textbook-derived sets plus MiniF2F, Proof Net, MATH-500 and AIME 2026. Its unweighted six-test mean rose from 29.17% to 45.83%. The model trained on MathInstruct, the strongest public-corpus comparison, reached 41.10%; TOME-Math led five of the six individual evaluations and ranked second on AIME.
Separate controlled tests support—but do not fully prove—the role of structure. With the base model frozen and a matched context budget, retrieving proposition dependencies raised long-form proof pass@1 from 13.25% without context to 17.38%. Across six subjects and three token budgets, forward textbook order beat shuffled and reverse schedules. At a fixed 0.75-million-token budget, spreading examples across 16 books generally outperformed denser sampling from eight. Those experiments are more informative than the headline comparison, where corpora differed in size, content and licensing as well as structure.[1]
The distinction that matters
Where the reported gain comes from
The study separates a large end-to-end result from smaller tests that isolate structure more directly.
Full corpus
364,631 records from non-held-out books
Six-test mean: 29.17% to 45.83%
Matched retrieval
Same context-token budget, dependency-linked evidence
Long-form pass@1: 13.25% to 17.38%
Independent proof
Public corpus, licences, checkpoints and external scoring
Not yet available
The release and provenance questions matter
This work could help researchers build mathematical models that follow dependencies instead of memorising disconnected solution patterns. The book-level holdout is stronger than a random example split, and the paper documents token budgets, query construction and leakage filters. It also includes a human audit of a response sample, although the main long-form scoring pipeline relied on repeated judgments by another language model. Benchmark gains therefore remain partly dependent on an automated evaluator's error profile.
The paper says the corpus will be released, so independent inspection is not yet possible. It describes source provenance but does not identify a licence for the 2,118 textbook PDFs or explain which books may legally be redistributed as derived records. It also reports no funding or competing-interest statement. The assessment would strengthen if the frozen dataset, source manifest, licences, extraction failures and checkpoints were released; independent teams reproduced the book-held-out gains; and human mathematicians scored a larger, blinded sample. Until then, TOME-Math is promising evidence about training organisation—not proof that more textbook-derived data is automatically lawful, reliable or educationally sound.[1]
Watch the background, then check the evidence
Illustrative photo · not a video frame
Google DeepMind · 1 min 52 sec · Background explainer
Protein folding explained
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A short introduction to why a protein’s shape matters. It provides background for understanding what AI structure prediction contributes to biological research.
Evidence check: This is the developer’s explanation. Predicting a structure does not by itself establish a treatment’s safety or benefit for patients.
Published 2020-11-30. Source checked 14 October 2026. Check captions on the publisher’s video page.
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Read the next reportExplore the full source and evidence record
What this means for people
- Better mathematical reasoning could improve research and technical tools, but textbook-derived training data also affects authors, publishers and learners. Provenance and licensing determine whether a useful benchmark can be reproduced and responsibly reused.
Global context
Textbook-derived AI datasets raise the same reproducibility and rights questions across languages and education systems. TOME-Math's sources span 29 subjects, but the paper does not report a licensing breakdown or demonstrate that its gains transfer beyond the evaluated model and benchmark family.
What the evidence does not yet show
- Unreviewed arXiv preprint submitted 29 October 2026; the promised corpus is not yet available for independent inspection.
- The main comparison changes corpus content and scale as well as structure, so the 16.7-point gain cannot be attributed to ordering alone.
- Long-form answers were primarily scored through repeated language-model judgments, with a smaller human audit.
- The paper does not state redistribution licences for the 2,118 source textbook PDFs or resulting records.
- No funding or competing-interest statement was identified.
What to watch next
- Public release of the frozen corpus and source manifest
- Book-by-book licence and redistribution information
- Independent reproduction with other base models
- Larger blinded evaluation by mathematicians
- Ablations with fully matched corpus size and source content
- Contamination checks against base-model pretraining
Living evidence record
Impact record IAI-1S0HS35
Evidence stage
Studied
Confidence
Supported
Reporting basis
Source analysis
Independent or research support
Present
Record status
Monitoring
Last checked
1 November 2026
Source trail
1 direct source across 1 source type.
People impact
Documented in this record.
Uncertainty
Limits and next checks are explicit.
Stages describe the evidence available—not whether a technology is good or bad. See the public method.
Single-source reporting disclosure
This record analyses one direct source. It can establish what arXiv published or reported, but it is not independent corroboration of every performance claim or predicted outcome. The confidence label will change only when broader evidence is added.
Evidence trail
Sources used for this report
Links checked 1 November 2026
Research question, topics and regions
Structure-preserving textbook supervision for mathematical language models
Topics: Mathematical reasoning · Training data · Textbooks · Benchmarks · Preprint
Regions: Asia · China
This report is labelled source analysis. We summarise and analyse source material in our own words; company statements remain attributed claims until independently supported. Translated summaries preserve the meaning of the original source and link back to it. Read our editorial standards.
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