The main application of Pure Mathematics is to make you happy.

A math lecture without a proof is like a movie without a love scene. This talk has two proofs.

Recreational number theory [...] is that part of number theory that is too difficult to study.

Music is part of Number Theory. Nowadays when a number-theorist applies for a grant, he says that it is good for security, but in those days, way before America, he would say that it's good for music. I will not comment whether we have progressed.

The main application of Pure Mathematics is to make you happy.