Jon, it could be the other way around: It is not that objects follow our math rules, it is that the rules are tailored to the objects. We definitely are quite advanced in that domain, I guess. But coming back to the original post, we that a lot in biology. The same molecule has different effects on different cell types having the same signaling machinery. The cell type-dependent effects are unexplained in general - this is just the way it is...
Bingo. The math that is used in physics represents a model of the observed facts. We observe the way the physical world behaves, we construct models that match the observed reality, then we use those models to predict the behavior of the physical world and see how closely the world matches the models.
Some of these models are mathematical in nature. That doesn't mean the physical world is mathematical; it means that certain types of math can be used to construct models that match the behavior we see in the physical world. Not all of these models are mathematical, and not all math models the physical world.
