Some do, others don't. There is an interesting dichotomy: much of mathematics does appear to be completely dissociated from reality, and yet in the other direction, reality appears to be entirely mathematics. I think to reach a unification, it is absolutely essential that we have people working in each direction. You aren't likely to develop a theory of (∞,n)-categories by working backward from reality, and yet it turns out to be useful to have done so once you start exploring e.g. topological quantum field theories.
