Why is mathematics so good at physics?

Keeps me up at night

When I was a student, I was pretty good at math, and enjoyed the logic and “elegance” of solving problems and proofs in geometry, trig, calculus, probability, etc. But it all existed “in my head”, a concept space, no reality in everyday existence required: it would all be just as true without it. The truth of 2 + 2 = 4 requires no apples to be counted. Approaching a limit at infinity doesn’t need the universe to establish it.

In college, I studied physics in its various forms - - classical mechanics, relativity, electromagnetism, quantum mechanics, etc. Later I became interested in cosmology. In all cases, mathematics not only describes those realities, but also predicts behaviors that are not obvious. It has been said that math describes quantum mechanical behavior to 8 decimal places. We have discovered a new planet, described the behavior of the universe an instant after the Big Bang, predicted the Higgs boson, derived the masses of some fundamental particles, explained economic behaviors, described the shape of some flowers and shells, and much much more, using “abstract” mathematics developed entirely independentaly in both space and time. Why does this application of knowledge in one sphere empirically work so well in another?? In other words, why is the universe so mathematical?

Surely this is not a coincidence. I have asked this question of many bright people, including a Nobelist in physics, only to receive answers equivalent to “I don’t know“.

One idea with substance — that our existence is just a mathematical computer simulation by some advanced alien — isn’t very satisfying. (Or maybe it offends my ego). It seems to me that a better explanation is that physical reality and mathematics have a common root, they are both manifestations of something more fundamental, and hence fundamentally related. But what is that root??

I am not religious, and find explanations in that dimension intellectually weak, but welcome other ideas…..