AIMO-2 Winning Solution: Building State-of-the-Art Mathematical
  Reasoning Models with OpenMathReasoning dataset
Authors: name: Ivan Moshkov, name: Darragh Hanley, name: Ivan Sorokin, name: Shubham Toshniwal, name: Christof Henkel, name: Benedikt Schifferer, name: Wei Du, name: Igor Gitman

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.