Curious about Gödel's incompleteness? No?... Well, you can still learn about it -- and its connection to the halting problem and computability -- by reading this post:
lcamtuf.coredump.cxGödel's beavers, or the limits of knowledgeCan you examine infinitely many integers in finite time? Are there numbers you're not allowed to know? Can a monkey beat a beaver in a fair fight?