It's not that math isn't useful (pragmatic) and it's not invalid
   as a descriptive, useful language to describe the universe with,
   make predictions, build things. It's VERY useful. Extremely so.

   But it's a closed system. Mathematics can be derived from Set
   Theory and Logic. But what is the origin of Logic? Geometry.
   What is the origin of Geometry? Axioms and Proofs.

   At the root of Set theory, at least generally, is the Axiom of
   Choice. It _does_ complete the circuit, as it were which is
   great, but it works out to being a closed system.

   It is a beautiful structure, entirely capable of describing much
   of the Universe in great detail.

   But does it have an independent existence? I don't think it
   does. Being pragmatic doesn't make it fact but it _does_ make it
   extremely useful and I wouldn't want to try replacing it with,
   say, English. The algorithms of grammar and the communicating of
   concepts via words is a bit sloppy at best.

   Considering we don't have a better replacement at the moment,
   it's the best we can do. And.. .it's a pretty good system
   honestly.