Faced with the beauty and power of a mathematical tool or result, one is sometimes impelled to say that there is Magic behind Mathematics. This poetic feeling becomes a solid statement when it is read conversely: Magic entertainments are crammed with Mathematics. Under this perspective, the literature of the Mathematics of Magic is steadily growing. In particular, the book under review is an excellent work written by two math professors (P. Diaconis and R. Graham) with a long experience in magical activities based on Mathematics. The reader will find full descriptions of many tricks (with which one can play and amaze friends) as well as, and this makes the thing more exciting, the mathematical principles that support them and their relationship with other situations (from DNA decoding to the Mandelbrot set, to give two instances) where the same principles are found. The final result is an exciting work where anyone with some undergraduate math knowledge will definitely enjoy the effects, secrets and explanations of a selected choice of magic tricks.
The first half of the book is devoted to card tricks, surely the main field where Mathematics have proof their full presence among magicians. In particular, the book analyzes the application of Bruijn sequences, the Gilbreath principle are the properties of shuffles. After this extensive part, the reader finds interesting sections about the Mathematics of the I Ching (the ancient Chinese fortune-telling volume) and the theorems behind good juggling. A third part covers a historic visit of the first contributions on mathematical magic and some short biographies of contemporary celebrated American math-magicians, with the exposition of some of their tricks. Among them, the authors selected Martin Gardner who, in addition, wrote the foreword of the book in April 2010, one month before his passing away.