The main goal of this informal paper is to push forward fuzzy set theory as a formal mathematical theory based on mathematical fuzzy logic and, namely, its higher-order version developed by the authors -- \textit{fuzzy class theory}. This is a formal axiomatic theory inside which the concept of fuzzy class is systematically introduced and studied. The authors show in their theory that all principal classical concepts can be directly transferred to fuzzy set theory as their generalization so that proving new properties can proceed in a fairly simple way using formal methods. This makes fuzzy set theory a well-founded concept. The authors announce also the open program to develop or re-develop fuzzy mathematics in the mentioned frame and invite everybody to participate in it.