*Life by the Numbers* is an easy and entertaining read, generously illustrated, and written in an engaging style. Intended for the non-specialist, it paints a picture of modern mathematics using a large brush and broad strokes; details are omitted by design. It aims to demonstrate how mathematics pervades society and—even if we are unaware of it—is essential to our lives. The book revolves around these related themes: (1) mathematics is the driving force behind many aspects of modern life, (2) the role of mathematics is often hidden, (3) mathematics is not merely arithmetic, (4) the study of mathematics was not completed centuries ago, and (5) there is value in basic research even if its applications are not apparent.

In several chapters, the book succeeds magnificently. It has a clever way of asking questions that immediately spark the interest. The questions are on popular topics, but the answers are unfamiliar. *How does a leopard get its spots? What makes a curve ball curve? How does the Global Positioning System work? How does a virus take control of a cell? What is the shape of the universe?* I was hooked. The answers (of course) involve mathematics, but often in surprising and interesting ways.

*Life by the Numbers* was written as a companion book to the eight-part PBS series by the same name. (See the **MAA Online** review of the series.) It was intended to be independent of the television programs, and I felt it was. After all, I have not seen the series, and I enjoyed the book. At times, the transitions between topics did seem a bit artificial and they certainly became predictable (following the template of reiterating the previous section in summary form and providing a glimpse of what was about to be introduced). I suspect that if I had seen the television version there might have been too much overlap to hold my interest in the book. In this case, the book would serve as an excellent reference, particularly for teachers using some of the ideas in class.

To convince the reader that there is *"hardly any aspect of your life in which mathematics does not play a significant—though generally hidden—part*", the author includes a snappy quote from nearly every authority in the book. *"Mathematics is not playing with numbers and doing accounting,"* says computer scientist Przemyslaw Prusinkiewicz, "*Mathematics is dealing with ideas in a creative and yet very precise way.*" In another example, publisher and writer Kevin Kelly comments that *"people believe that mathematics has nothing to do with them. This is because mathematics has succeeded in becoming largely invisible, at the same time it has become essential to our lives."*

More important than the sound bites; however, is the incredible array of examples (I counted nearly fifty) used to illustrate the point that mathematics is an integral part of contemporary society. Would you be surprised to learn, for example, that the film industry is one of the largest employers of mathematicians in the world? I was. The book explores how mathematics is used to create special effects such as Tom Hanks shaking hands with President Kennedy in *Forrest Gump*. "*In the world of computer graphics,"* says moviemaker Doug Trumbull, *"mathematics is behind everything I do."*

Chapter 3 covers topics from knot theory and viruses to fractals and clouds. There are too many topics to mention them all, so I will pick just one. Why is it that a horse breaks into a trot just when it does? The answer is that the animal does so when the stress on its bones reaches approximately thirty percent of the breaking point. Changing the motion greatly relieves this stress. This also predicts when the horse breaks into a canter and then a gallop. Biologist Mike Labarbara uses this pattern to create mathematical models of the movement of many animals, including extinct ones such as dinosaurs. "*Mathematics has become a bigger part of biology,"* says Labarbara, *"We’re just beginning to understand how animals and plants are designed."* Throughout this discussion, the tone was non-technical, but intelligent. The mathematician as well as the general audience could find much to enjoy in this part of the book.

Chapter 4 was particularly successful in that it included a wide variety of examples from sports to appeal to diverse interests: figure skating, sailing, the triathlon, marksmanship, tennis, baseball and golf. We learn why a golf ball with dimples travels four times as far as it would if it were bald, and why a breaking curve ball appears to break. The diversity of examples shows that mathematics is involved in almost every aspect of sports from equipment design to coaching and training. Computerized mathematical models are at the heart of designing yachts for racing in the America’s Cup. *"This sport would not be possible today without mathematics,"* claims America’s Cup racer John Marshall. Mathematics also helped world class figure skating coaches to deconstruct the triple axel. Video taping and creating a computer model of this difficult trick revealed that the key was not to jump higher, but rather to spin faster while in the air.

Most of the topics were discussed in enough depth to give the reader a sense of where mathematics fits in and why it is essential. In a few cases, a bit more explanation would have been helpful. In Chapter 2, there was an interesting discussion of how the Renaissance-era discovery of the theory of perspective revolutionized the artistic world. This theory enabled artists to represent three-dimensional images on a two-dimensional canvas so there is the appearance of depth. It is noted that projective geometry is at the heart of this theory, but then only two sentences are devoted to explaining the "point at infinity" and the "line at infinity" is explained in only one.

In most cases; however, the explanations were clear and well done. The key to success seemed to be in choosing topics that were familiar but where the mathematics behind them was not. The major disappointment in this regard was Chapter 6, *Chances of a Lifetime*. This overview of probability and statistics was not elevated above the ordinary, as was the rest of the book. Probability is an interesting subject, but the tired example of rolling a die is not. Likewise, the fact that the odds are stacked against the gambler in Las Vegas is hardly a revelation. Statistics can be fascinating, but harping on the importance of a random sample is exceedingly dull. It is also likely that the reader is already quite familiar with the basics of insurance policies. Perhaps I found this dull only because the ideas were so familiar to me. I tried to read the chapter by picturing myself as one of my intelligent non-mathematician friends, but I was still bored. I think these ideas were simply too much a part of popular American culture to be as successful as the rest of the book.

Overall, the book achieves many of its goals. It captures the attention and teaches something new while revealing the central importance of mathematics. *"Many people don’t realize that mathematics is not dead,"* says Nate Dean of AT&T Bell Laboratories, *"… there are a lot of things about the world we don’t know, and it seems that maybe the only way we’ll ever know them is through the applications of mathematics."* So do you still wonder how does the leopard gets its spots? That was my favorite part! And for that, you’ll have to read *Life by the Numbers*.

Bernadette Mullins ( bmullins@math.ysu.edu) is an assistant professor of mathematics at Youngstown State University in Youngstown, Ohio.