Textbook structure improves math reasoning in language models

The key insight isn't just that structure helps, but that pedagogical ordering itself encodes mathematical relationships that models can learn to exploit. Prior work treated textbook problems as interchangeable data points; TOME-Math preserves the dependency graph between proofs, making the curriculum itself a training signal.

This work sits directly in the emerging consensus that structured supervision outperforms raw scale. The H2R paper from the same day uses hierarchical decomposition to shorten reasoning paths via intermediate hints, and 'The Structure Gap' paper from October 27th formalizes why raw data cannot replace explicit structural knowledge in domains governed by known constraints. TOME-Math extends that principle to proof generation by showing that textbook organization isn't pedagogical scaffolding alone, but learnable signal. The OpenAI and Anthropic results on formal verification and proof discovery suggest the field is converging on the idea that mathematical reasoning requires more than pattern matching from flattened datasets.

If TOME-Math gains replicate when models are fine-tuned on randomly shuffled versions of the same proofs (breaking the dependency graph), then the wins come from data quality or scale, not structure. If they persist, watch whether downstream reasoning benchmarks (MATH, GPQA) show corresponding improvements when models trained on TOME-Math face problems outside the textbook domain, confirming transfer rather than memorization of the curriculum.