Is there any branch of Mathematics which has no applications in any other field or in real world? 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  ?
Lots of branches of mathematics currently have no application in any other field or the real world. As you get higher up the ivory tower, the object that you're studying becomes so esoteric, that there might not be relevance to other things.

However, that does not preclude the possibility that someone eventually finds a relevance for it. Before the 20th century, Number Theory was considered recreational, 'useless' math. It has since spawned a huge industry of security.

Of course, someone might come along and say "Hey, there's this connection between (this esoteric field) and (that esoteric field)", like what Andrew Wiles did (Andrew Wiles proved Fermat's last theorem using many techniques from algebraic geometry and number theory [Source:Wikipedia]).
Being a matter that deals more with quality and less with experiment than any other; maths is an avant-garde needing a delay for it to be applied. If i did not believe in the necessity of ethics i would say it´s one of the most aesthetical disciplines; but also when you prove a theorem you open a new road ar at least a path and make the task of discovering  new formal landscapes easier to successors; are truth and beauty and harmony and structures in the Universe immediately useful?