Introduction

Abstract

Modern mathematical literature is characterized by a far-reaching distinction, which all of you must have noticed: The interests and ways of thinking of the theoreticians differ considerably from the methods that are effectively used in mathematical applications. Not only does the scientific training of the individual suffer from this discrepancy, but also the standing of this science itself. It seems extremely important to try to counteract the grievances arising from this situation. The lecture course that I start here is aimed at providing a contribution to this issue, in that it tries to establish a clear relationship – so to say from an epistemological point of view – between the different kinds of mathematical questions, as they arise in some occasions according to their very nature. You must, on the one hand, try to understand the interests of modern theoreticians, but on the other hand you must form an opinion on which parts of mathematical speculation have a direct meaning in applications.