TITLE: Is there any branch of Mathematics which has no applications in any other field or in real world?
QUESTION [65 upvotes]: Is there any branch of Mathematics which has no applications in any other field or in real world ?
for instance , maybe : number theory ? mathematical logic ? 
is there something like this  ?

REPLY [12 votes]: The field of nondefinable numbers (which studies a subset of the noncomputable numbers for which no human representation exists or can exist) has at it's topic an ontology for which existence may be asserted and really nothing else.  This is about the most meaningless (in the sense of a semantic association) of seriously discussed mathematical topics, and I've heard that the poor souls who brave this field have loose morals and should not be trusted.