When I'm feeling down, I just think on how amazing it is that a system of counting and logic that bloomed into an entirely self-consistent body of rules and ideas that, no matter how abstract and born of imagining strange shapes floating in space and derived from suppositions that are outside of reality it seems, has actually been used to describe, form understanding, and even predict things that actually happen in the physical world that would have been absolutely outside the ability of humans to experience without it.
There is much that is experimental and observational about physics: things fall, electricity "zaps" you, iPhones work and gasoline engines fire.
Yet so much of our entirely incomplete and yet surprisingly deep knowledge of how the universe actually does seem to work came from some human beings somewhere thinking really hard about things, and using the logical tools of math to organize and catalog those thoughts. In some case the observation came before the thinking it through, like planetary motion and the photoelectric effect. The weirdness of the experiment helped form what questions to think about. In some cases, the thinking it through is what lead to later experimental observations, like the existence of black holes and the fact that time slows down for an object the closer it gets to traveling at the speed of light. The logical extension of the theory helped design what experiment to run, often some strange thing which we'd never have thought, "hey, let's do this and see what happens!"
It's trial and error, of course. Some observations have led to thinking that has of yet yielded only more questions than answers, like what the heck is dark matter anyway? And some thinking no matter how mathematically sound has lead to no supporting experimental result, like all the many and ever expanding flavors of string theory. The greatest discoveries in physics in the 20th century also lead to the greatest puzzle of physics to date: why do two theories whose rules are fundamentally incompatible with one another: sometimes following the dictates of one means contradicting the dictate of another, both nonetheless show countless and ever-increasing experimental verification? Special and general relativity describe physical rules about objects that are very large or else moving very fast in ways that have been observed in nature and cannot be explained any other way, while quantum mechanics describes what very small things do with equal experimental confirmation, although with the latter field our understanding of "why" is much more open to--often very, very bizarre--interpretation.
"Why" is the question that we have asked over and over again, the answers to which we have answered an astounding number of times after using our brains. It took quite a lot of time, and quite a lot of brains in collaboration, and quite a lot of brains being wrong.
But damn, the fact that collective contemplative analyses has yielded as many results as it has is nothing short of incredible for a universe in which the majority of space seems to be composed of nothing at all but a few scattered neutrinos and mysteriously low-energy photons.
Mathematics is not just balancing your check book. Mathematics is the language which describes the real, tangible universe.