An enthusiastic celebration of the beauty of mathematics.
Benjamin (Mathematics/Harvey Mudd Coll.; co-author: The Fascinating World of Graph Theory, 2015, etc.) brings to this book the stage presence of a video lecturer who has contributed math programs to the Great Courses series. Indeed, the book is a distillation of one of those courses and is filled with the patter, puns, and occasional poetry of the stage performer. Presumably because he also loves magic and has learned tricks of the trade, the author compares the workings of math to magic. This is misleading because, as he well acknowledges, math is based on logic and proofs—not magic at all. Benjamin does a fine job of explaining the variety of proofs that math uses (by contradiction, induction, etc.). He begins with a chapter on numbers, number patterns, and tricks on doing mental arithmetic. He then moves on with what is essentially a high school syllabus on algebra, Euclidean geometry, and trigonometry, with a few chapters on Fibonacci series, pi, and probabilities. The author provides several different proofs of well-known results like the Pythagorean theorem. The going gets tougher as Benjamin moves on to more advanced math in the form of complex numbers, e, and calculus. Here, the author is more skilled at telling rather than showing as he introduces how e, for example, appears in odd places and amazing equations. He does a better job at explaining differential (but not integral) calculus, but he devotes much of that chapter to how to differentiate certain functions—a nice tutorial for a test crammer, perhaps, but not of interest to general readers. A final chapter on infinities is better articulated and interestingly shows how performing a few illegal tricks with infinite series can yield astonishing answers.
Forget magic. Benjamin delivers a primer generously filled with insights and intuitions that make math approachable, interesting, and, yes, beautiful.