Hi, Kyle,
I am glad to find an essay which has followed the requirement that it be written for the lay person. Your writing style is flowing and hence easy to read, so that one can get to your central arguments.
I was quite interested in your characterizations of mathematics and its relation to physics. The first thing I noticed was that you apparently list Newton as a physicist who had to do with mathematics: "While working
on his natural philosophy Newton made contact with this vast realm of math. Before
mathematicians knew of calculus, his mind was ignited by it." Yet Newton is considered (by mathematicians, at least) to have been not only a physicist but also a mathematician. He was not given all the mathematical tools necessary for his physics, but he (and Leibniz) invented the calculus. True, the inspiration came from physics, but that is often the case in mathematics.
Before my next comment, allow me to make sure I have one of your main points clear: you say that the subtleties of quantum mechanics are mathematical formulations for the minute realm but, as measurements are ultimately in the macro realm, one may regard Newtonian mechanics as more fundamental. An interesting viewpoint, but there are phenomena on the macro realm which do not obey Newtonian mechanics, such as the two-slit experiment, tunneling, superconducting, etc.
Also, in your characterization, you seem to say (correct me if I am wrong) that the more abstract the mathematics which characterizes a physical phenomenon, the more tenuous its claim to being fundamental. Yet there are many who would claim the contrary, saying that mathematics is a formulation of the thought processes which provide the framework for our perception of physical phenomena.
Your essay raises a number of other philosophical questions -- which is the mark of a good essay. I enjoyed reading it.
All the best, David