Numerical calculation techniques in spaces of high dimensionality

In this paper I will discuss in particular two kinds of numerical calculations which exemplify especially well the various problems inherent in many dimensions, namely numerical integration and goodness-of-fit testing. This does not mean that other fields such as differential equations are not equally important and interesting, but is only a reflection of my personal background and interests. I think also that it is good to consider one field classified as statistics and therefore often ignored by numerical analysts.