The discussion of curiosity driven discovery in mathematics, especially applied mathematics, is quite good here. I wonder what that sort of curiosity driven experience would do within a software developer environment. In a lot of ways I develop a lot of code, even production code, using a curiosity and more artistic method to getting to a solution. However, project management doesn't seem to want to allow for that sort of discovery as we're writing software. They want solid estimates and firm commitments. It's unfortunate. A lot of good comes from curiosity.
Also, a fabulous article on a brilliant mathematian. A great read!