[twiceaday]

Math is a purely logical tool. None of it "exists." That makes no sense. Some of it can be used to model reality. We call such math "physics." And I think physics is significantly closer to math than to reality. It's just a collection of math that models some measurements on some scales with some precision. We have no idea how close we are to actual reality.

I do not understand the framing of "translating math concepts directly into reality." It's backwards. You must have first chosen some math to model reality. If you get "bad" numbers it has nothing to do with translating math to reality. It has to do with how you translated reality into math.

[brap]

I think maybe I didn’t really explain myself properly. I didn’t mean that math is real in the sense that atoms are real. Perhaps “true” would be a better word. We know these things are true to us, but are they universally true? If that’s even a thing? Hope that makes more sense.

[IAmBroom]

The age-old problem of a respondent using different definitions of words than the OP.

Socrates made a whole career out of it.

[kcexn]

Mathematics is a philosophy that focuses on the study of logic. It's a bit of an exaggeration to conflate mathematics with 'truth' in an absolute, universal sense.

Mathematical 'truths' are themselves only true in the sense that they can be derived from axioms.

The fact that mathematics can be used to understand the world around us is nothing short of a mystery (or a miracle).