开源1400万数学题数据集，让大模型数学推理能力提升16%。

Mathematical reasoning continues to be a critical challenge in large language model (LLM) development with significant interest. However, most of the cutting-edge progress in mathematical reasoning with LLMs has become \emph{closed-source} due to lack of access to training data. This lack of data access limits researchers from understanding the impact of different choices for synthesizing and utilizing the data. With the goal of creating a high-quality finetuning (SFT) dataset for math reasoning, we conduct careful ablation experiments on data synthesis using the recently released \texttt{Llama3.1} family of models. Our experiments show that: (a) solution format matters, with excessively verbose solutions proving detrimental to SFT performance, (b) data generated by a strong teacher outperforms equally-sized data generated by a weak student model, (c) SFT is robust to low-quality solutions, allowing for imprecise data filtering, and (d) question diversity is crucial for achieving data scaling gains. Based on these insights, we create the OpenMathInstruct-2 dataset, which consists of 14M question-solution pairs ($\approx$ 600K unique questions), making it nearly eight times larger than the previous largest open-source math reasoning dataset. Finetuning the \texttt{Llama-3.1-8B-Base} using OpenMathInstruct-2 outperforms \texttt{Llama3.1-8B-Instruct} on MATH by an absolute 15.9\% (51.9\% $\rightarrow$ 67.8\%). Finally, to accelerate the open-source efforts, we release the code, the finetuned models, and the OpenMathInstruct-2 dataset under a commercially permissive license.