A few comments here:
1) Math can be many things, and it not need be ONLY A) BUT NOT B). It can be BOTH, depending on many factors. Just because is can be ONE does not EXCLUDE the possibility of being the other. Most things in the world are NOT black or white, good or bad, light or dark, as your question suggests; most things are on the continuum of "in-between."
Take for example, from quantum mechanics: the electron can behave as a wave or as a particle, DEPENDING on how it is measured.
2) How did math begin? by simple counting. How many sheep are in my flock? How many rabbits did I kill for dinner? How many apples did I find for my family to eat? Did farmer A bring enough baskets of grain to appease the gods (and feed the priests)?
3) Math has proven to be a valuable TOOL to solve problems. There are numerous examples. That should be self-explanatory.
4) Math can be used to PREDICT things, how nature behaves. It is a fundamental part of science, which attempts to explain AND predict the behavior of things in the world. The Kinetic Molecular theory of gases can rather adequately explain the behavior of REAL gases, based on a few assumptions. Geometry is based on assumptions and can predict the relationships of polygons and numbers.
5) Taken to the extreme, math gets very esoteric and very theoretical and become difficult to grasp. One idea that I could not grasp in calculus was the idea of LIMITS. A similar idea is that of asymptotes, the fact that numbers gets smaller (e.g., divide by 2 continuously, but you can NEVER get to ZERO.....kind of like keep adding one to a number to get to a larger number to get closer to infinity, BUT you never get "there."
6) Nature has a mathematical nature and it is aesthetically pleasing, as in music and harmony and octaves. I really do not understand music well enough to explain better, BUT nearly everyone appreciates the sound of some form of MUSIC.
7) There are certain mathematically constants that keep appearing in many scientific equations, such as pi, e, h (Planck's constant) and R (the ideal gas constant).
To me, #7 points to a fundamental “beauty” and simplicity of nature, based on Math.
9) Albert Einstein had a series of debates with Neils Bohr, one of the major figures in quantum mechanics. Quantum mechanics explain the very small (electrons, photons, strong nuclear force, and such). Einstein did not like the statistical nature (based on probability of dice and other random events….(DOES THIS SOUND FAMILIAR??...). Anyway, Einstein is quoted as saying, “God does not play with dice.” Bohr’s response: “Einstein, stop telling God what to do.” Einstein liked causality, and hated the probability as the basis for quantum mechanics.
10) One of the basic goals of Physics has been to explain the ENTIRE cosmos in a series of a few relatively simple mathematical equations. Will we get there? Is the cosmos really mathematical? Ask a highly respected physicist , like Michio Kaku.
11) I hope this answers the initial question posed, or at least sheds some light on the matter. (There is a pun there.....).
