Hello from vacation! New York City, as it happens. I’m spending the summer emphatically not working, but that doesn’t mean I can’t enjoy a little math every now and again.

Perhaps that’s true for you, too. So, here are the titles of a few books I read last year, and which I recommend:

The Art And Craft Of Problem Solving is a great book by Paul Zeitz, intended to teach the reader how to think creatively in approaching difficult math problems. Lots of actual math to be done in this one. More a textbook than anything else, but a very good one. Also requires nothing but high school math… and a good helping of enthusiasm, which the book will help to increase. One can earn the (considerable) purchase price in value many times over without finishing even half of it.

The Equation That Couldn’t Be Solved, by Mario Livio, is a great read: it’s the story of the lives and work of Norwegian Niels Henrik Abel and Frenchman Evariste Galois, who created one of the major branches of modern math (group theory) while trying to solve a different problem altogether. The book begins by building up the problems Abel and Galois were trying to solve, and winds up giving the reader a powerful sense of what mathematics really is: the attempt by creative minds to find and explore patterns and symmetry. But it’s the story of the two minds themselves that makes this story so good.

Prime Obsession, by John Derbyshire, is a fascinating account of the history (and the nature) of the so-called Riemann Hypothesis, one of the greatest unsolved problems in mathematics (and for which another (flawed) solution was recently published). It requires a willingness to consider some challenging puzzles. It’s not a quick read; some pages took me ten minutes or more to really think through. But, it doesn’t require anything other than high school math. It reads a bit like a mystery novel, but finishing it makes you feel like you’ve become a mathematician. It was so good (and truth to tell so rich with math) that I read it a second time a few months later.

The Numbers Behind NUMB3RS, by Keith Devlin and Gary Lorden, explains the math in the TV show “NUMB3RS” episode by episode, and is a surprisingly good intro into many branches of modern math for the interested but casual reader. Good starting book, particularly if you know and like the show. For me, it worked the other way around: I like the show considerably better now that I understand how the math they are showing is real.

Enjoy the rest of your summer!