Here is an analogy.... Set theory is like Abstract Expressionism. People (the non-artists) think that art needs to be nicely drawn (like the Renaissance). In this case People (the non-math) think math needs to have applications. But art does not need to be nicely drawn and can look stupid. Similary math can have absolutely no application and look stupid*.
*)Like in, prove that if: x>y and y>z then x>z. It looks stupid but there is much more to it.