Research progress on the integrated development of applied mathematics and artificial intelligence
应用数学与人工智能融合发展的研究进展

摘要

当前，应用数学与人工智能融合发展是科学技术得以持续进步的重要推动力量，应用数学作为人工智能发展不可或缺的理论、算法基础，在模型构建等多个方面具有不可忽视的价值；而人工智能的发展则可为数学研究范式的改变提供支撑，使其能够朝着数字化、智能化方向不断进步。本文对应用数学与人工智能融合的内在逻辑进行深入分析，着重探讨数学赋能人工智能及人工智能赋能数学的实践路径，希望能够对两者融合发展做好铺垫。

Abstract

The integrated development of applied mathematics and artificial intelligence (AI) currently serves as a vital driving force for the sustained advancement of science and technology. As an indispensable theoretical and algorithmic foundation for AI, applied mathematics holds significant value in areas such as model construction. Conversely, the evolution of AI provides support for shifting research paradigms in mathematics, steering the field toward greater digitalization and intelligence. This paper presents an in-depth analysis of the inherent logic underlying the integration of applied mathematics and AI, with a focus on the practical pathways through which mathematics empowers AI—and, reciprocally, how AI empowers mathematics—thereby laying the groundwork for their continued integrated development.