In 1962, Martin Kruskal coined the term “asymptotology”. As it is known, asymptotic methods, the essence of which is the study of phenomena in limiting cases, are at the heart of natural sciences of nature. It is now a well-developed part of pure mathematics, closely related to applied mathematics. Kruskal, in his lecture, drew the attention of the audience to the fact that, for all the diversity of asymptotic methods, it is possible to identify some common features in them and study them on their own, regardless of the objects to which they are applied. Such meta-science should constitute the subject of asymptotology. It is necessary to say directly that over the past 60 years such ideology, although it attracted (and still attracts) certain attention, has not become mainstream. Does this mean that Kruskal's idea is currently of purely historical interest? It should be emphasized that we are talking about asymptotology as a kind of meta-science. Asymptotic methods as the most important tool of scientific analysis are not threatened by Big Data and AI. In this paper we tried to analyze the opinions of prominent users of asymptotic methods about the future of asymptotology.