Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving math problems and proving theorems has garnered significant interest in the fields of machine learning and natural language processing. For example, mathematics serves as a testbed for aspects of reasoning that are challenging for powerful deep learning models, driving new algorithmic and modeling advances. On the other hand, recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning. In this survey paper, we review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. We also evaluate existing benchmarks and methods, and discuss future research directions in this domain.

翻译：数学推理是人类智能的基本方面，广泛应用于科学、工程、金融及日常生活等诸多领域。开发能够解决数学问题并证明定理的人工智能系统，已在机器学习和自然语言处理领域引起广泛关注。例如，数学为深度学习模型中具有挑战性的推理方面提供了测试平台，推动了新算法和建模方法的进展。另一方面，大规模神经语言模型的最新进展为利用深度学习进行数学推理开辟了新的基准和机遇。本综述回顾了过去十年间数学推理与深度学习交叉领域的关键任务、数据集及方法。我们还对现有基准和方法进行了评估，并探讨了该领域的未来研究方向。