The Conceptual Infrastructure of Mathematics

By conceptual infrastructure of mathematics I mean the concepts, the terminology, the symbols, and the notations that mathematicians and people who apply mathematics use in their daily professional activities. This is very different from what is often called the conceptual foundation of mathematics, which deals critically with the deeper meaning of these concepts, an activity which only some mathematicians, and these only occasionally, worry about. I believe that the infrastructure of mathematics was and still is being developed in four stages.