[romwell]

>Every map in existence is but an inaccurate description of the observable universe.

That's the thing though: mathematics can be inspired by the world around us, but more often than not, it does not aim to describe it.

Mathematicians working, say, on exotic 4-manifolds, are not concerned in the least with how well these structure describe anything out there in the "real world" of yours. The short answer is: it doesn't. The longer answer is: 4-manifolds are the real world, or, rather a part of it that, perhaps, the only way you can observe and interact with that part of the real world is through mathematics.