I love math and I love reading so, naturally, I have some favorite math books:
If you are a math teacher, or interested in math education, I recommend Out of the labyrinth: Setting mathematics free by Robert and Ellen Kaplan. These two are the most impressive math teachers I’ve ever seen. I wrote about them in the joy of participatory learning. Their book isn’t as good as their teaching, but…. well, nothing would be.
I also very highly recommend A Mathematician’s Lament: How school cheats us out of our most fascinating and imaginative art form by Paul Lockhart. Lockhart was a research mathematician, but he quit that to become a math teacher (K-12) at St. Ann’s School in Brooklyn. This book is really wonderful, and short, and anyone connected with teaching and math should read it. Full review.
If you want to know what a mathematician’s world is like, but don’t know a lot of math, then one book is the idiosyncratic conversations with a mathematician: Math, art, science, and the limits of reason by Gregory Chaitin. Chaitin is very smart, and he’s not shy about letting us know. But somehow, it’s not annoying. He seems like he’s having enormous fun with his brain, and he wants us to share.
On the other hand, if you want a taste of what math is like and don’t have a lot of math, then there’s Proofs and Refutations: the Logic of Mathematical Discovery by Imre Lakatos. Really fascinating, and uses a basic geometrical theorem that anyone who passed 8th grade math can understand.
If you do have some math training (say, at least a year or two of calculus) then the Art of Mathematics: Coffee Time in Memphis is a lot of fun. Interesting puzzles that mathematicians pose to each other.
My field is statistics, and, if ever need to understand statistics, a great book is Statistics as Principled Argument this is a stats book like no other. It’s about what the title says: Principled argument. Highly recommended for those who have had one statistics course, some time, even long ago.
Graphics are important in statistics. A graphic can be worth more than 1,000 words…. but which words? If you want to see some ‘great speeches’ and some things that are worthy of George Bush, then the works of Edward Tufte are great. If you actually want to produce some good speeches, then I like the works of William Cleveland: the Elements of Graphing Data and Visualizing Data
Keith Devlin has written a lot about math, and what I’ve read, I’ve liked: Mathematics: the New Golden Age and the Millenium Problems
Alfred Crosby wrote the fascinating book: the Measure of Reality: Quantification and Western Society 1250-1500
A fun book of short essays that all involve math is Group Theory in the Bedroom by Brian Hayes. You don’t need a lot of math training to follow these essays, which span topics from clock making to the genetic code. Full review.
On game theory, there is Prisoner’s Dilemma by William Poundstone, which is very nontechnical and the recent Insights into Game Theory by EinYa Gura and Michael Maschler. I am reading this one now. It goes a long way to giving a flavor of math, without many formulas.
A book that I got in advance, but which should be out soon is Hidden Harmonies: The Lives and Times of the Pythagorean Theorem also by Robert and Ellen Kaplan. Long before the Greeks, someone noticed that a triangle with sides 3, 4, and 5 would have a right angle. The Greeks took the monumental step of generalizing and proving this. Since then, all sorts of things have been done. Full review
and I’ll close with
The magnificent Godel, Escher, Bach: An eternal golden braid by Douglas Hofstadter. An amazing book. I’ve read it three times. I will get more out of it if I read it again. It’s a book to read slowly and think about and discuss.