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Mathematical Magic

William Simon
Dover Publications
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Peter Olszewski
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Magic has always captivated us, made us wonder, and sometimes, left our heads spinning in awe. In William Simon’s 1964 book, Mathematical Magic, every page will make the reader want to learn more about this ancient art form. Simon (1927–1988) has put together a wonderful collection of magic tricks with detailed descriptions of the mathematics making them work. In short, it is a book of “mathematician’s magician’s” tricks that is sure to leave your audience in amazement.

Martin Gardner wrote a preface for the new printing in 1993. He describes Simon’s book as “a nontechnical collection of easy-to-do, self-working tricks based on mathematical principles.” The book is outlined into seven chapters:

  1. Magic with Numbers: In this first chapter, nearly all of the tricks are rooted on the properties of the decimal number system and basic algebra.
  2. The Magic of Shape: This chapter outlines tricks based on topological properties with particular focus on ropes and rubber bands.
  3. Calendar Magic: Each of these tricks is based on calendars, with specific examples given in the year 1963. The basic mathematical properties of the decimal number system and basic algebra are used to explain the tricks in this chapter.
  4. Mental Magic: This is where an audience will begin to feel the wonderment of the tricks. In this chapter, memorization and the use of logic from mathematicians such as Jack Yates, the late Harry Canar, and Bob Hummer are presented.
  5. Magic Squares: As pictured on the front cover of the book, Simon goes through several examples of the famous magic squares.
  6. Magic with Ordinary Objects: The tricks in this chapter make use of watches, cigarettes, napkins, matchsticks, and coins.
  7. Magic with Playing Cards: I believe for many mathematicians, the magic tricks in this chapter will be the most popular. It is fitting to save the most exciting tricks for last!

The tricks in this book require varying degrees of mathematical knowledge, but some are simple enough that one can perform them for friends. For example, “The Linking Clips” used on a dollar bill can be followed by looking at the detailed picture on page 50 of the book. Some of the other tricks require some mathematical thought, like the trick “Horizontal Figuring,” based on the May 1963 calendar, on pages 61–64, or the “Variation on a Theme” where you, the mathematical magician, assume the role of a mind reader but are also preforming mathematics and logic to find what your audience is thinking of.

Some of the tricks require more thought. While reading the book, the reader will be motivated to try out such tricks as Hummer’s “Three Object Divination.” In the example presented in the book, a ring, coin, and watch are used. After reading through the trick, I tried this out on two friends and they were left speechless!

My one comment about the book is that some tricks should have more pictures, as some of the tricks are too complex to preform given the reading. This is evident on the trick “The Jumping Rubber Band” on pages 46–50.

Simon has created a book of exciting tricks that can be used not only for mathematicians but also by anyone who wants to learn tricks that are rooted in mathematics. I can see this book being used for students in grades as low as the 4th grade as a means to motivate interest in students. I believe when Simon was writing this book, he not only wanted his readers to read through the tricks, but to see how much fun mathematics can be. Of course, trying them with others is the ultimate thrill.

Peter Olszewski is a Mathematics Lecturer at Penn State Erie, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Pennsylvania Alpha Beta Chapter Advisor of Pi Mu Epsilon. He can be reached at Webpage: Outside of teaching and textbook editing, he enjoys playing golf, playing guitar, reading, gardening, traveling, cars, and painting landscapes.


1. Magic with Numbers
  2. The Magic of Shape
  3. Calendar Magic
  4. Mental Magic
  5. Magic Squares
  6. Magic with Ordinary Objects
  7. Magic with Playing Cards