In modeling any real physical system, we are required to employ inductive reasoning. We can never be completely certain about the state or properties of any system or of any future observation we will make of it. All we can do is attempt to ascertain its properties from past observations, which are themselves imprecise approximations to the true complexities of the system.
It is a law of physics that at the quantum level, no information is completely certain. Everything that is observable exists within a certain probability interval, and there are fundamental limits to how much one can know about any physical state.
Mathematics generally employs deductive reasoning. We postulate that there are certain axioms which are absolutely true, and draw further inferences from those axioms. This is a very different type of reasoning from what I discussed above, as no such certainties exist in nature.
Given these differences, how is it then that our minds are so easily able to conceptualize mathematical certainties, given how contrary to nature they are? If our minds are themselves a part of nature, and have evolved to model and observe natural systems, what is it that gives us the capability to even conceive of things which have so much more precision than we would ever actually see?
Indeed, it is generally far simpler and easier to describe model a mathematical certainty than anything as complex and imprecise as a real system. In modeling physical systems, we generally employ “simplified” models that rely on assumptions about the properties of the system being much more precise and well-defined mathematically than they really are. Why should it be easier for us to, as physical being within this universe, model a physical system in such an aphysical way?
It would be quite simple for me to give a mathematical description of a perfect circle, and we could all, as rational beings, quickly agree on its properties. Yet, if I were to try and construct a circle, anything I constructed would not only be only an approximation to the mathematical ideal, but also much larger and more cumbersome than the mathematical description was. What is it about mathematics that makes it so much easier to communicate and reason about than nature itself?