Zero: The Biography of a Dangerous Idea - Charles Seife
This book contains the sort of ideas that sparked my love of math. Unfortunately, after four years of majoring in it, I got bogged down in the classes and lost sight of how cool math could be. Lucky for you, you don't have to be a math major to enjoy this book—Seife wisely glosses over the nitty gritty and explains the basic concepts in an easy-to-digest format. At the same time, it's not dumbed down (though the sections on Einstein's theory of relativity are pretty slim).
The book follows the concept of zero from its birth (as a placeholder but not a real number) through the ages, and it's surprising where zero turns up. The book is a who's who in science, from Ptolemy to Copernicus to Galileo, from Descartes to Riemann to Cantor. I hadn't realized influence of religion (both Eastern and Western) on the concept of zero; and vice versa: Pascal's famous wager depended on the concepts of zero and infinity. Zero turns up in the strangest places, and for a symbol that means nothing, it has an unusual amount of power.
Zero will most likely be filed under "Math & Science," but it could also be considered history, and a small part religion. Reading it, I got a big picture of the development of mathematics that would have made my college math classes a bit more meaningful—Seife shows how all the pieces fit together, something I didn't get in any syllabus.
It may not be for everyone, but I think most readers will find at least some aspect of the book that fascinates them.