The Magic of Math: Solving for \(x\) and Figuring Out Why

In 2010, I was intrigued and entertained by this author’s appearance and display of calculation gymnastics on The Colbert Report. In more recent years, I found his Joy of Mathematics course, a series of twenty-four half-hour lectures, rich source material for my lectures to first-year college students. Thus, I was immensely pleased to learn that elements of that course along with tricks of the stage used by this “mathemagician” (a title previously held by Benjamin’s inspiration Martin Gardner) were compiled into a book.

The book delivers on all the promise of both aspects of Benjamin’s talent: teacher and performer. Like Gardner, Benjamin telegraphs a joy in surprising mathematical stunts, such as accurate estimates of e from one’s own phone number and the manifold discoveries waiting in Pascal’s Triangle. These are front-loaded in the book, engaging the reader, then trickle off as the work becomes more educational and the topics more sophisticated.

To take advantage of the knowledge imparted, no more than high school algebra is required. The topical chapters cover many topics encountered by the first-year undergraduate, among them fundamental combinatorics, basic proofs including induction, the unit circle and trigonometry, analytical geometry, and some optimization of areas and volumes. Benjamin also gleefully explores the entertaining and eye-opening implications within i, e, \(\pi\), and infinity.

At this level, there are two topics which I feel are both interesting and pedagogically valuable but are rarely explored in first-year algebra texts. Benjamin does a very engaging and enlightening introduction to both: the complex plane and \(\tau\). I recommend this book for the math enthusiast embarking on his or her university career, the high school adept in your life intrigued by math yet bored in class, or someone remembering fondly math as their favorite subject yet lacking time to enroll in courses now.

Tom Schulte gleans lecture-enlivening ideas from Arthur Benjamin for the courses he teaches at Oakland Community College in Michigan.