I read pop math books. Quite a few, in fact. Also, sometimes publishers send me advance copies and ask for reviews. I generally read these too. What makes me a bad reviewer is that I then wait for 6 – 20 months before I actually write anything down.

Time to remedy this situation! Here are a batch of quick reviews for books on or related to math that I’ve read in the past couple of years.

How Not to Be Wrong: The Power of Mathematical Thinking

Jordan Ellenberg has written one of the finest books on mathematics in decades. How Not to Be Wrong belongs in the pop-math canon, alongside Simon Singh’s best works (The Code Book; Fermat’s Enigma) and Robert Dantzig’s Number: The Language of Science.

There are two qualities that make How Not to Be Wrong exceptional. The first is how much news it contains. So many math books are rehashes of classic stories: Zeno, Archimedes, Pythagoras, Newton & Leibnitz, Euler, Gauss, and so on. Read a few accounts of the history of math and the stories, fun as they are, start to run into each other. Ellenberg begins with Abraham Wald studying bullet holes in airplane fuselages during WWII and goes off in all sorts of new directions from there. I was shocked at how much I had never seen before, and how seamlessly Ellenberg ties together statistics, mathematics, and common sense.

The second quality that makes this book necessary reading is the sense of humor. The asides and footnotes are laugh-out-loud funny, and Ellenberg is a masterful and delightful writer to read. Bill Gates picked How Not to Be Wrong as one of his top five recommendations for reading this summer, and it’s at the top of my list too. Don’t miss it.

Love and Math: The Heart of Hidden Reality

How I wanted to like this book. It’s name is almost identical to this website’s, and Ed Frenkel had been on a tear, speaking on the Colbert Report and other TV and radio shows about the book, which promised to share what he loved about math. I started reading hopefully, and the first five or so chapters didn’t disappoint. Frenkel’s story of learning math despite anti-semitism in Soviet Russia is compelling and readable. Soon enough he’s invited to the West, and the story loses its dramatic tension: Frenkel’s career heads up, and the sailing is smooth. Frenkel tries to create dramatic tension around whether an important mathematician might show up at a conference or not, but the stakes just feel too low.

Wisely, with little narrative left to mine from his own story, Frenkel pivots in the second half of the book mainly to explaining the math and the story behind the Langlands Program, an ambitious and collaborative mathematical undertaking. While points of this project are interesting, the complexity of the mathematics exceeds Frenkel’s ability (and possibly anyone’s ability) to explain it to a lay audience. I’d estimate the necessary mathematical background for much of the second half of this book to be roughly graduate school level, and the layperson who tries to read it may find themselves scared off.

Meanwhile, there are two undermining details that become more glaring as the book goes on. First, Frenkel’s presentation of the mathematical world is deeply male. The female characters appear as charming wives who serve tea to their hardworking mathematician husbands, then disappear. Frenkel seems to have no problem with this, and his video project (looking for the equation for love) in the last chapter doesn’t do a lot to present a more positive space for women in mathematics. While professional math continues to be dominated by men, it feels more important than ever to celebrate female mathematicians and make clear that women belong in the field. Frenkel seems happy with his Mad-Men-esque vision of the field.

Second, Frenkel’s self regard unbalances the story. He’s a master of the humble-brag, and the longer you read, the more you have a sense that the story he’s really interested in telling is the one about how great Ed Frenkel is. Frenkel is taking on more and more of a place in the conversation around popular mathematics, and I think he has something important to share about the passion and beauty of mathematics. If he can make a little more room for underrepresented groups and a little less room for himself, I think his contributions will be that much more valuable.

The Math Olympian

This is a peculiar and kind of wonderful book. It reads like a soap opera, almost: a sort of Slum Dog Millionaire for a female Canadian Math Olympian, who, in the course of a 5-question test, flashes back through all her preparation and through important life moments.

There’s some solid math throughout this book, and, compared with Frenkel, a very clear place for women in math, along with a clear-eyed view of some of the specific difficulties they might face. What makes the book exceptional, though, is the diverse picture it paints of great math mentoring, and the emphasis on what really matters in mathematics—not the contests, it turns out, but the work of doing math itself. A wonderful book to read, especially for math teachers and mentors interested in improving their math-educational craft.

The New York Times Book of Mathematics

The Times sent me a review copy of their Book of Mathematics last year, and I’ve been slowly reading it since then. There’s a lot here: over 100 years of reporting on mathematics. Overall, it’s a pretty impressive collection. More than anything else, it’s amazing to see what they got right: in so many articles, they’re interviewing the pivotal players, and capturing the most important breakthroughs just as they’re happening. Reading through the book gives you a sense of what the news was in 20th century mathematics: chaos theory, cryptography, computers, mathematicians and their major breakthroughs (Wiles, Perelman, Erdos, Conway, Godel and others make appearances throughout the book). There are some whimsical sections too, like an interview with the real Monty Hall, who takes the writer to school.

If you want to get a sense of what the news in mathematics actually was this past century, this is a great place to start.

The Mathematics Devotional

Clifford Pickover has written a number of big, beautiful, coffee-table-grade books on mathematics and physics, and I’ve been a fan. But when his publisher sent me this one, I was skeptical. A Devotional? As in, read an inspirational quote and ponder a picture? Indeed, that’s exactly what this book is: one quote and one image per day of the calendar year. And yet, I’ve had it for over a year now, and find myself opening it up all the time, and using it exactly how it’s meant to be used. It’s exactly what it set out to be, and I continue to be a fan.

Here’s today’s quote:

“The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was ‘out there’ all along I just couldn’t see it. And now I can! This is really what keeps me in the math game—the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods.” —Paul Lockhart, A Mathematician’s Lament, 2009

So there’s some reading to check out this summer! I’ll return now to my stack of books and start reading. Next summer is coming fast.