Magical Mathematics: The Mathematical Ideas that Animate Great Magic Tricks

If you wanted to find a perfect book on magic and mathematics, you might look for something written by Persi Diaconis and Ron Graham. The only thing more you might ask would be a preface by the late Martin Gardner. Magical Mathematics is precisely that book.

As the title suggests, Magical Mathematics is indeed a book about magic and mathematics. Not obvious from the title is that the book also contains a significant amount of biography, which we will say more of in a moment. The mathematics in the book is mostly elementary. The book is aimed at a popular audience, not professional mathematicians. However, Diaconis and Graham allude to much deeper mathematical connections that are not explicitly developed in their book.

All the magic in the book has mathematical explanations; none of the tricks depend on slight of hand or tricky equipment. But rather than simply giving dry, mathematical descriptions, each trick is presented with sample patter and notes on showmanship.

The mathematics and the magic are intertwined. Magic tricks suggest mathematical problems, and mathematical solutions suggest magic tricks. Sometimes an innovation on one side spurs an innovation on the other side.

In addition to instruction in magic and mathematics, Magical Mathematics tells stories of mathematical magicians, including some who influenced the authors. Chapter 7, for example, begins with a story from Diaconis’ childhood and ends with a story Graham’s. (The authors do not clearly identify themselves; it takes a little deduction to determine which is speaking when the book includes personal anecdotes.)

Magical Mathematics, like the careers of its authors, blurs the lines between “serious” and “recreational” mathematics.

John D. Cook is a research statistician at M. D. Anderson Cancer Center and blogs daily at The Endeavour.