Again, I would argue this is no different than physics. The strength and maturity of a model is not only based on its ability to describe what we can verify, but predict what we have never (and may never) seen, and sometimes what we have never even conceived of- and I think both physics and mathematics are doing that.
My point is, many concepts in math do not exist outside of the models describing them, while if we throw away physical models, the reality does not go away.
