Ein Bourgeois, wer noch Algebra treibt! Es lebe die unbeschrankte Individualitat der transzendenten Zahlen! ["It's a bourgeois, who still does algebr… - Carl Ludwig Siegel

One of the many importants ideas introduced by Minkowski into the study of convex bodies was that of gauge function. Roughly, the gauge function is the equation of a convex body. Minkowski showed that the gauge function could be defined in a purely geometric way and that it must have certain properties analogous to those possessed by the distance of a point from the origin. He also showed that conversely given any function possessing these properties, there exists a convex body with the given function as its gauge function.

Ours, according to Leibnitz, is the best of all possible worlds, and the laws of nature can therefore be described in terms of extremal principles. Thus, arising from corresponding variational problems, the differential equations of mechanics have invariance properties relative to certain groups of coordinate transformations.

I am afraid that mathematics will perish by the end of this century if the present trend for senseless abstraction — as I call it: theory of the empty set — cannot be blocked up.