This is one of the few sci-fi short stories that really sticks out in my mind: The Nine Billion Names of God, by Arthur C. Clarke.
Despite the reaction this will provoke from Chris, I will take this opportunity to go off on a tangent on Sir Arthur (probably best known for writing the 2001/2010/2061/3001: A Space Odyssey series). Although I love that short story, and 2001 was pure genious (more elaborate than the movie, and really shines a bright searchlight on Kubrick’s obfuscations), most of his other stuff that I’ve read was really dismal. The book that he’s said he’s most proud of — Childhood’s End — ended about a hundred pages before the back cover.