This paper presents our winning submission to the AI Mathematical Olympiad - Progress Prize 2 (AIMO-2) competition. Our recipe for building state-of-the-art mathematical reasoning models relies on three key pillars. First, we create a large-scale dataset comprising 540K unique high-quality math problems, including olympiad-level problems, and their 3.2M long-reasoning solutions. Second, we develop a novel method to integrate code execution with long reasoning models through iterative training, generation, and quality filtering, resulting in 1.7M high-quality Tool-Integrated Reasoning solutions. Third, we create a pipeline to train models to select the most promising solution from many candidates. We show that such generative solution selection (GenSelect) can significantly improve upon majority voting baseline. Combining these ideas, we train a series of models that achieve state-of-the-art results on mathematical reasoning benchmarks. To facilitate further research, we release our code, models, and the complete OpenMathReasoning dataset under a commercially permissive license.

该研究解决了数学推理模型普遍存在的高质量数据不足和推理能力不足的问题。研究者提出了一种新颖的方法，通过将代码执行与长推理模型结合，并使用生成性解决方案选择策略，显著提升了模型在数学推理基准测试中的表现。研究结果表明，这种集成方法在提升推理质量方面具有潜在的重大影响。

AIMO-2获胜解决方案：构建最先进的数学推理模型与OpenMathReasoning数据集