"I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."
"But," says Man, "the Babel fish is a dead giveaway isn't it? It proves you exist, and so therefore, you don't. Q.E.D.."
"Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.
"Oh, that was easy," says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.
This is quite profound. The basic axiom is indeed that proof denies faith, because faith is a belief that stands upon the strength of its own convictions. It's very easy to believe in something that can be proved. In a sense, doing so isn't true belief at all.
I had the opportunity to actually ask Douglas Adams about this passage and how religion influenced his writing. His response was:
I am, as you guessed, fascinated by religion. But I am by conviction an atheist, and a fairly radical one at that. Have a look at this.
The fact that you can pose a question doesn't mean to say that it has an answer, at least, not the sort of answer that the question implies. So saying that religion has the job of asking the underlying "Why?", as you suggest, seems to me to mean as much as asking "What colour is opera?" or "Where is indecision?" or "When is osteopathy?" or "How is blue?". By the time you've done enough clarification of the question to render it meaningful you're effectively got yourself another question. Like "How come things are as they are?"
The link Douglas provided goes to an article he wrote in American Atheist. I find the subtle differences between Douglas' atheism and Steven's to be fascinating. If Douglas is fascinated by religion, then I suppose I am fascinated by its absence. His answer above reveals a worldview that while quite different from mine, still served as a source of inspiration when writing about religion in his books.
Ultimately, religion requires only a single leap of faith at its core. Is there a God? This is the starting point that I share with my Christian and Jewish brothers, all of us sons of Ibrahim (Abraham). That leap can not and must not be a matter of proof, solely of conviction. From there, however, we who believe in God apply the same processes of reason and logic that our atheist cousins do. My own series of conclusions draws me to Syedna Mohammed Burhanuddin TUS, others may be drawn to Pope John Paul II, or even to Qutb.
But can any of us prove our convictions? I believe the answer is no. But I can't prove it.
UPDATE: more on this here.