Wonders of Numbers

For a deep, but deeply entertaining introduction to extraordinarily high-level concepts that remain useful tools of thought forever - Godel, Escher, Bach. That belongs on everyone's bookshelf. For a kind of "cabinet of curiosities", I endorse "Wonders of Numbers" by Clifford Pickover. This book was pivotal in my relationship with mathematics, containing as it does brief excursions into all manner of fascinating topics like cellular automata, and the Collatz Conjecture, as well as a host of more obscure oddities. It's a perfect book to have around when learning programing as well, since it has a nearly bottomless well of interesting things to code. Nor is it dry, thanks to Pickover's whimsical style.