Street Fighting Mathematics: The art of educated guessing
mitpress.mit.edu
mitpress.mit.edu
http://news.ycombinator.com/item?id=1548013 (many comments)
http://news.ycombinator.com/item?id=1106846 (2 comments)
http://news.ycombinator.com/item?id=2873902 (no comments)
Seriously, just look at the treatment of Gaussian integral. They wonder if the solution is sqrt(pi alpha) or sqrt(pi/alpha). Then they rule out the first possibility. Yeah, that's fine, but why sqrt and pi at all? Why not sin and e? Or gamma function and ... oh well this actually is a gamma function, but nevermind.
Guessing is easy, if you already know the solution.