That's not true, I don't just get As on tests and believed I'm good at math, math is about understanding the concept and the nature of it, and becoming one with mathematics. I don't just take formulas and memorize it, I investigate "WHY." i.e. Why do we use integration by substitution when integrating a differentiated composite function--i like the analysis of mathematics. If you just merely memorizing formulas, that's NOT real learning of mathematics. You're right, currently my math curriculum are consist of "plug and chug" but i believe once i get into analysis--I will understand why we plug and chug--it's just the matter of time. As for physics... Mathematicians don't study math because it's "useful", I doubt Physics will help me understand math more-- as physicists viewed mathematics as nothing but a mere tool.I question whether you have the ability to pursue a math degree. Mathematics is not solely using an algorithm to solve trivial problems. Most likely, up till now, all your math classes consisted of plugging and chugging. You believe you were good at math, because you can get an A on a superficial test.
Anyhow, my main concern, once again-- is not how physics will help me understand math, but rather how much harder is calc- based physics compared to alg-base physics--and will I do fine if I start from scratch without any background knowledge about physics.