Fixpunkte stetiger Abbildungen Mathematische Theorie und Anwendungen.

The purpose of this paper is to give an idea of modern mathematics and of its contribution to science as a whole. As an example to illustrate this the theory of fixed points of continuous mappings has been chosen, because it allows to explain recent mathematical achievements to non-mathematicians without lengthy preparations and because it has several applications. We shall sketch such applications in biology, numerical computation, economics and hydrodynamics. [ABSTRACT FROM AUTHOR]