AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset

2025-04-23

AI Summary

This work addresses the scarcity of large-scale, high-quality long-reasoning data and the limitations of existing optimization paradigms for mathematical olympiad–level reasoning. To this end, we propose three key innovations: (1) a novel tool-augmented long-reasoning data generation paradigm, yielding 540K problems and 3.2M code-enhanced step-by-step solutions; (2) a generative solution selection (GenSelect) mechanism that replaces conventional majority voting to significantly improve solution quality; and (3) an integrated training framework combining iterative code-execution supervision, multi-candidate generation-and-ranking modeling, and joint supervised fine-tuning with RLHF. Our approach achieves state-of-the-art performance across multiple mathematical reasoning benchmarks. Furthermore, we publicly release OpenMathReasoning—the first large-scale, open-source mathematical reasoning dataset—comprising all problems, annotated solutions, executable code, and trained models, under a commercial-use license.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Metareasoning and Metaheuristics
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

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.

Problem

• Building large-scale high-quality math dataset with solutions
• Integrating code execution with reasoning models iteratively
• Training models to select best solutions from candidates

Innovation

• Large-scale dataset with 540K math problems
• Code execution integrated with reasoning models
• Generative solution selection pipeline