Many branches of math start out as being "meaningless". Number theory was once widely considered meaningless until it was given importance through cryptography. The current head of Microsoft's Cambridge research location literally said to Bill Gates as she was being hired that her work was completely unrelated to computer science; her work was in combinatorial optimization. I think that may be a part of the problem: not enough math professors teach their subjects with any regards to what they are used for. Sometimes, they don't even know themselves.