Mathematical training often turns textbooks into isolated question-and-answer examples. That loses the order in which ideas are taught and the links showing which results support later proofs.
The team converted textbooks into training examples that connect statements to proofs and show how proof steps depend on earlier results. They trained a language model, software that generates text, on these examples and tested it on mathematics tasks.
The model’s average score rose by 16.7 percentage points over its starting version, and it outperformed the tested public instruction-data sets overall. This suggests that organizing mathematical examples as a connected course can improve proof reasoning.