O związkach matematyki z filozofią na przykładzie projektu Archipelag Matematyki

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 (available at www.archipelagmatematyki.pl). They seem to be effective due to different interconnections between mathematics and philosophy (both historical and contemporary).After describing methodological assumptions, goals, methods and the structure of Archipelago, I present two, designed by me, examples of its contents: (1) quasi-internet chat with the ghost of G.W. Leibniz (on metaphysics, philosophical aspects of calculus, and artificial intelligence); and (2) 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.