A dataset of challenging mathematical problems for reasoning large language models: SD1K

To address the lack of insufficient challenging training data for reasoning large language models, this study constructs a challenging mathematics dataset for reasoning, termed SD1K, using a methodology that integrates concept extraction and model synthesis. The dataset is built upon a collection of 7,500 training samples from the Sky-T1-32B-Preview model, from which 9,054 mathematical concept entities are extracted. Each concept entity includes a formal definition, application scenarios, and usage example. Using large language models, new mathematical problems are generated by randomly sampling these entities, with long-form reasoning chains and corresponding answers automatically constructed for each problem. A filtering process combining predefined rules and model-based verification is applied to select 1,000 high-quality and challenging mathematical problems, forming the final SD1K dataset. The SD1K dataset provides a valuable resource for the training and evaluation of large language models in reasoning tasks and contributes to the advancement of model performance in complex inference scenarios.