Abstract
Recently we have heard that "today is the age of information," and informational materials have been carried into mathematical education. But what is the information? If we do not look it only at the surface, but make a deep study into it, we must discover that there is after all the way of thinking which creates the system at the root of fundamental mind of information. The author thinks that this thinking is similar to the thinking of Structure of J. Piaget. And the thinking of Structure is the very thinking of mathematics. (a) The whole is determined not by the peculiarities of constituent elements but by the law of relation between the elements. (b) Even if we replace the constituent elements for anything, the law is the same. (c) The Structure produces only the element which holds the law. In this paper, these properties are shown not only by group, probability and metamathematics as examples of mathematics but also by combinatorial circuit and Wiener's Differential Space as examples of System. Especially, in the Wiener's example the agreement of Structure and Process is discussed.
