^Math is not science. Science studies the universe while math is independent of reality just like logic. I can use a hypothetical scenario to make the distinction. If there were an alternative universe that is 30-dimensional Physics in that universe would be different from that in ours. However the math principles would be the same as long as the axioms are the same. In math people talk about k^n, not just R^3 or R^10 that are relevant to the universe.https://www.math.utah.edu/~cherk/mathjokes.html
This can help you understand what math is really about. No we don't care about numbers other than 0 and 1 in general because these two have good algebraic properties. (So in essence we study structures)
I do have one paper on arXiv. The stuff I wrote about is new but it does not seem to have any application IRL however my field is indeed related to quantum mechanics.
I have finished a really short paper as well on a problem that is more popular. Basically many associative algebras are evil in some sense. (I can explain more if you are interested.) My advisor wants to generalize some result from good algebras to evil ones (roughly speaking) and I did make the gap a bit smaller. He has to fill in the rest and publish with others.
Edited 3/24/2017 16:55:25