How Close is Creativity to Madness

I can't help but notice that those who are creative also seem more likely to be "eccentric/mad/crazy/mentally ill/different/depressed". We can all think of a long list of "artists" who made wonderful works but were also quite unusual. Painters who cut their ears off or singers who overdosed or people who decide to cut a cow in half. This raises some interesting questions:
Can you only be a creative genius if you are a little crazy?
Does the creative process drive you mad?
Does constantly expressing yourself lead to problems?
Is it a gift or a curse?
If you gave a “sane” person something to make them crazy (e.g. drugs) would they become more creative?