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，已在多个领域得到广泛应用。然而，其在数学场景中的有效性因其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，拓扑数据分析的发展因理论家对计算算法和编程能力的理解不足而受阻。本研究致力于通过利用ChatGPT，弥合理论拓扑概念与计算拓扑实际实现之间的鸿沟。我们展示了一位毫无计算经验和编程能力的纯理论家如何借助ChatGPT，将数学公式和概念有效转化为计算拓扑的可执行代码。我们的策略描绘了一个高效流程：数学家先训练ChatGPT理解纯数学概念，引导其生成计算拓扑代码，并通过已知示例验证生成代码的准确性。具体案例包括计算单纯复形的贝蒂数、拉普拉斯矩阵与狄拉克矩阵，以及多种同调与拉普拉斯的持久性。此外，我们还探讨了ChatGPT在计算超图和有向图最新拓扑理论中的应用。本工作旨在作为将纯数学理论有效转化为实用计算工具的第一步，最终目标是为不同领域的实际应用提供支持。