I submit that certain forms of mathematical analysis allow us to analyze phenomena which are simply inaccessible to human understanding. Quantum theory, for example, is just one example of many fields where it is possible to describe and predict phenomena which simply make no sense to us on a verbal or spatial level. They are outside our day-to-day experience. This is made possible by formal systems of abstraction which allow us to manipulate symbols according to pre-determined rules with some assurance that we will get reasonable results. Experiment then confirms whether our abstractions are valid or not. This technique has its pitfalls, but it has been very successful and we have a lot of experience with it.

Mathematical modeling, or computation, also allows us to do simple mathematics on a colossal scale. In this case, the math is easily understood or even trivial, but there's so much of it that it is simply not practical for humans to do it without mechanical assistance.
I concede there may be physical phenomena not amenable to mathematical analysis, but mathematics (and to a certain extent, language) allows us to routinely think about the unthinkable.