Asking "When will I ever use math?" is like jogging and asking, "When will I ever use these calf muscles?"
(The answer to both is "all the time", but that's not the point.)
I was a math major who did independent research in Elementary Number Theory and decided to switch paths and become a computer programmer (many years ago). It's true, I haven't encountered many sigmas, deltas, and derivative signs in all those years, but there's absolutely no doubt in my mind that I'm exercising the same mental muscles built with math.
OP mentions “wondering, playing, amusing yourself with your imagination.” Hell, build something.
Assembling ones and zeros to help real people solve real problems is every bit as wonderful, playful, and amusing as anything I ever did with pure mathematics. And probably even more rewarding...I've discovered that it's much more likely to see a customer do a happy dance with software that never existed before I built it than proving Fermat's Last Theorem or figuring out what Galois was up to on that long last night.
(The answer to both is "all the time", but that's not the point.)
I was a math major who did independent research in Elementary Number Theory and decided to switch paths and become a computer programmer (many years ago). It's true, I haven't encountered many sigmas, deltas, and derivative signs in all those years, but there's absolutely no doubt in my mind that I'm exercising the same mental muscles built with math.
OP mentions “wondering, playing, amusing yourself with your imagination.” Hell, build something.
Assembling ones and zeros to help real people solve real problems is every bit as wonderful, playful, and amusing as anything I ever did with pure mathematics. And probably even more rewarding...I've discovered that it's much more likely to see a customer do a happy dance with software that never existed before I built it than proving Fermat's Last Theorem or figuring out what Galois was up to on that long last night.