  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.
