“It seems that you can use math to describe things that are simply not possible in this universe.”
And you can use natural language to describe things that are not possible....
What seems to be missing is good predictive value ~ like it is precluded as a rule.
Waiting on the Higgs boson.
Sometime long after I ran into that one (which, of course, justified my not being more adept in topology) I realized that when you look out on the Universe and take a good look at the galaxies there you find big empty zones as well. That emptiness may simply be chunks of a different universe that is invisible to us because the fundamental laws there prohibit light (as we know it), or the existence of the the same forms of matter we know, and even those other visible galaxies might well differ from our own in terms of fundamentals that we don't yet know about.
Rather than that vast array of galaxies being part of a single universe, they may instead be the very frothiness described by the multiverse equations.