I wonder how laws of physics, mathematics and logic influence each other. What I mean is the following: In Quantum Mechanics (probably even in general physics), only very few non-linear problems can be explicitly solved. The most important ones are 1.the harmonic oscillator (potential r^2) and 2. the Hydrogen atom (potential 1/r). This is the reason why almost any other non-linear problem is first reduced to a r^2 or 1/r-potential problem.
This seems like lucky coincidence or a divine act or whatever you might call it: 2 very basic physical problems can be expressed and solved in a very basic mathematical way.
Now I keep on wondering: If our mathematics was based on some different algebra than the one it actually is, say, elliptic functions (=objects that are reasonably hard to express in "our" mathematics), would our understanding of physics be different?
(For example: would we better understand physical facts that are now "too complicated" (because of their mathematical complexity), and -maybe- fail to really understand the harmonic oscillator, just because there is no means to express this problem mathematically?)