Why is math so adept at describing the world?

I was actually working on a problem yesterday that reminded me of your comment, GLG. In Statistical Mechanics you often encounter problems where energy surfaces in phase space are higher dimensional hyperspheres. Doing mathematics on this surface requires some knowledge of the volume and surface area elements of these hyperspheres. The mathematics of such higher dimensional geometries was worked out well before the modern formulation of Statistical Mechanics, or even of Hamiltonian mechanics (which is a reformulation of Newtonian mechanics upon which Statistical Mechanics depends).