I was looking through my textbooks, and I noticed something very interesting that I didn't think was all that interesting before we started talking about models in the other thread.
It's not just math like Maxwell's equations that can predict and explain nature. The periodic table and the pattern of particles in the eightfold way also seem to be intrinsically true. There is something incredibly interesting to me about the fact that the eightfold way and the periodic table were able to make predictions about what particles and elements should fill the gaps when these models were not as complete as they are now,
http://en.wikipedia.org/wiki/Eightfold_Way_(physics) .
How can we be right about something without knowing it first, amazing!
Addition:
I read what you said about math again, and I think I misunderstood what you were going for. You probably meant math in general and not specific equations like Maxwell's.
If that's what you meant, then I agree. Mathematical descriptions of the models seems to be the primary reason why there is this regularity of the models that I mentioned above. The math is what shows the order of the particles and the elements.