Abstract

Some new, philosophically inspired, methods of teaching mathematics are discussed in this paper. These methods are implemented and embedded in the virtual environment of learning and exploring mathematics, called officially Archipelago of Mathematics. They seem to be effective due to different interconnections between mathematics and philosophy. After describing methodological assumptions, goals, methods and the structure of Archipelago, I present two, designed by me, examples of its contents: quasi-internet chat with the ghost of G.W. Leibniz ; and radio-style interview with a farmer on the mathematical theory of sets and infinity. Presented materials show such a relationships between mathematics and philosophy like: philosophical origin of some mathematical concepts, philosophical implications of some math. ideas and theorems, heuristic function of philosophical discussions in mathematics.