The essence of Gauss' law is that the total flux through a closed surface only depends on the charge inside the surface. So two spheres with different radii will have the same flux. This is of course due to the 1/r2 property of coulombs law. Because, since the area increases with r2 this precisely makes up for the force getting weaker proportional with 1/r2. But in my book, I can read that Gauss' law holds for all kinds of surfaces. How do you show that, i.e. that any topologically closed surface has the same property as the surface of the sphere? Or is it actually something very mathematical, which physicists tend to be less rigourous about?