It is not that objects follow our math rules, it is that the rules are tailored to the objects.
Macnerd10 has it right Jon. You have the cart before the horse. Physics is not based on mathematics it is based on observed physical phenomena which in turn can be modeled mathematically. Albert Einstein created his theories, and he was always careful to call them theories, by observing specific physical phenomena, working them out as a "story problem" describing why the phenomena might occur, and only then developing a mathematical formula to model his story. Of course if he could not model it mathematically he might have to rethink his story.
Virtually every physical, and even human activity, can be modeled mathematically. In some cases the model can be devolved into a single specific equation such as E=MC², others require a complex set of related equations, and still others require modeling using a mathematical heuristic. As the mathematics and the phenomena are better understood the more complex formulations tend to become simpler and less complex. I once took a course where we spent an entire semester understanding the implications of a 47 step equation modeling a single process. Two days before the final exam another researcher published a paper that reduced the 47 step equation into a single equation with 4 variables. (My professor humanely elected to hand out a copy of the new formula instead of the final exam and gave everyone in the class a Pass.)
The beauty of this is once the math has been worked out, it is possible to infer from that math phenomena that have not yet been observed and in fact may never be directly observable. The current very exciting theoretical physics work in string theory being a prime example of the latter.
Mathematical modeling is not limited to physics and the {i]hard[/i] sciences, but as macnerd10 has indicated can easily extended into the biological sciences or in fact virtually any field of study. How about modeling the behavior of customers in the line(s) at a MacDonalds -- been there, done that. the ultimate modeling is summed up in General Systems Theory.
If we knew what it was we were doing, it wouldn't be called research, would it?
