Known to many as NPR’s “The Math Guy”, Keith Devlin has at present count twenty-four books, the majority of which are on popular mathematics. He is most likely known to anyone reading this review by his FOCUS Online column, Devlin’s Angle. Each of his books presents mathematics in a new and interesting light. His topics roam the mathematical landscape from the cognitive aspects of mathematics to the underpinnings of mathematics in patterns. In his latest work The Math Instinct: Why You’re a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs), Devlin takes a light hearted look at how all creatures, from humans to spiders, do math daily.
Devlin sums up his premise early on when he states, “For nature turns out to be the greatest mathematician of all. Through evolution, nature has endowed many of the animals and plants around us with built-in mathematical abilities that are truly remarkable.” To show this, Devlin gives examples from roughly three categories: human babies and animals, humans, and how humans learn. To give only one example, I found his discussion of how children of only a few months can distinguish between one, two and three objects truly interesting. Though this is a work for non-scientists, he gives enough details of the current research to satisfy the reader that this is for real. His other examples in this first part include ball retrieving Corgis (Elvis the calculus dog who graced the cover of the May 2002 issue of The College Mathematics Journal), dead reckoning of Tunisian desert ants, the migration of birds and butterflies, the sonar of bats, the distribution of leaves on plants, and several others.
Next he moves on to humans. Here he describes the mathematics behind how our brains turn the two-dimensional signal received from the eye into the three-dimensional image we perceive and the "street mathematics" of young vendors in Brazil. This leads to a discussion of how school mathematics differs from the mathematics people use in every day life. He closes the book with a discussion of learning. In these last chapters he briefly looks at the evolution of counting and mathematics education, and ends with his four steps to better mathematical ability.
Devlin describes the mathematics learned in school as abstract mathematics and the mathematics done by animals, babies, street venders and the like as natural mathematics. This is a very important distinction. Another distinction that is made in the book, but needed to be made more emphatically, is that between doing mathematics and doing an activity that can be described using mathematics. In essence, this book is really about the physics of nature. That bats can fly into a bush to catch their dinner without getting tangled is a matter of the amazing physics of their sonar. While the mathematics needed to describe these natural actions is interesting and intriguing.
Devlin’s examples are interesting, well presented, and thought provoking. However, the book changes gears too often. Given the title, I expected the whole book to be like the first few chapters. I would have been very happy reading about the “mathematics” of animals and babies in more detail. The final chapters on learning seemed out of place as well as cursory. In particular, his third step to improving math skills is for one to figure out the reason behind why school mathematics is taught in its abstract form. This is key, in my opinion, to really learning math and not simply mastering the steps. This important topic is given only one paragraph, however. But to vindicate himself in the eyes of this math teacher, his fourth step, which he goes into in more detail, is to practice, practice, practice.
As usual, Devlin has found a new and interesting “angle” to present the beauty of mathematics to the general public. The Math Instinct was enjoyable and I would recommend it to anyone who asks, “What is math used for anyway?” And those people might be relieved to find out that there is no “math” in this book, and only one graph.
Amy Shell-Gellasch is currently a freelance math historian living in Grafenwoehr Germany while her husband is on a three year tour of duty in Germany. She received her bachelor's degree from the University of Michigan in 1989, her master's degree from Oakland University in Rochester, Michigan in 1995, and her doctor of arts degree from the University of Illinois at Chicago in 2000. Her dissertation was a biographical piece on mathematician Mina Rees. Most recently, she conducted research with V. Fredrick Rickey on the history of the Department of Mathematical Sciences at the United States Military Academy, where she was an Assistant Professor.