ChatGPT represents a significant milestone in the field of artificial intelligence (AI), finding widespread applications across diverse domains. However, its effectiveness in mathematical contexts has been somewhat constrained by its susceptibility to conceptual errors. Concurrently, topological data analysis (TDA), a relatively new discipline, has garnered substantial interest in recent years. Nonetheless, the advancement of TDA is impeded by the limited understanding of computational algorithms and coding proficiency among theoreticians. This work endeavors to bridge the gap between theoretical topological concepts and their practical implementation in computational topology through the utilization of ChatGPT. We showcase how a pure theoretician, devoid of computational experience and coding skills, can effectively transform mathematical formulations and concepts into functional code for computational topology with the assistance of ChatGPT. Our strategy outlines a productive process wherein a mathematician trains ChatGPT on pure mathematical concepts, steers ChatGPT towards generating computational topology code, and subsequently validates the generated code using established examples. Our specific case studies encompass the computation of Betti numbers, Laplacian matrices, and Dirac matrices for simplicial complexes, as well as the persistence of various homologies and Laplacians. Furthermore, we explore the application of ChatGPT in computing recently developed topological theories for hypergraphs and digraphs. This work serves as an initial step towards effectively transforming pure mathematical theories into practical computational tools, with the ultimate goal of enabling real applications across diverse fields.

翻译：ChatGPT代表了人工智能领域的一个重要里程碑，在多个领域中得到广泛应用。然而，其在数学语境中的有效性因易受概念性错误影响而受到一定限制。与此同时，作为一门相对较新的学科，拓扑数据分析近年来引起了广泛关注。然而，理论研究者对计算算法及编程技能的有限理解阻碍了TDA的发展。本文旨在通过利用ChatGPT，弥合理论拓扑概念与其在计算拓扑中实际实现之间的鸿沟。我们展示了如何在ChatGPT的协助下，一位缺乏计算经验和编程能力的纯理论研究者有效地将数学公式与概念转化为计算拓扑的功能性代码。我们的策略提出了一种高效的流程：数学家首先训练ChatGPT理解纯数学概念，引导其生成计算拓扑代码，随后通过已知实例验证所生成代码。具体案例研究包括单纯复形的贝蒂数、拉普拉斯矩阵和狄拉克矩阵的计算，以及多种同调与拉普拉斯算子的持续性。此外，我们探索了ChatGPT在计算超图和有向图的最新拓扑理论中的应用。这项工作迈出了将纯数学理论有效转化为实用计算工具的第一步，其最终目标是实现跨学科领域的实际应用。