I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics.
We don't read and write poetry because it's cute. We read and write poetry because we are members of the human race. And the human race is filled with passion. Medicine, law, business, engineering: these are noble pursuits and necessary to sustain life. But poetry, beauty, romance, love...these are what we stay alive for.