Math and Magic: The Secrets Behind Amazing Tricks

Course Overview

Course No. 9202

Pick a card! Think of a number! Magic tricks are irresistible to watch and even more fun to perform. A surprising number are based on mathematical principles. In 12 delightful half-hour lessons, Professor of Mathematics Arthur T. Benjamin of Harvey Mudd College—who also performs as a professional magician—explains some of his favorite math-based showpieces.

From card tricks to feats of mental calculation to geometric conundrums, Math and Magic teaches you how to do dozens of tricks that will leave your audiences scratching their heads in amazement. Above all, you will be able to explain the math that’s really pulling the strings, whether it’s an algebraic expression, a computational shortcut, or a strange topological property.

No math background beyond high school is needed to understand these tricks, and most can be performed by those who are much younger. Many professional mathematicians first fell in love with math thanks to magic tricks, and these lessons can do the same for you.

Video Lectures

01: Mathematical Card Tricks (30 min)

Begin with card tricks where mathematics is clearly used, but the secret isn’t obvious. Learn the invariant principle—qualities that stay the same despite card shuffling—and perform the “tear-able” trick (using expendable cards).

02: What’s Your Deal? (36 min)

Explore tricks where shuffled, dealt, and flipped cards lead to surprising outcomes. Discover Hummer’s principle—random mixing combined with a simple procedure that preserves hidden patterns.

03: Look like a Card Shark (40 min)

Win poker with the Jonah principle, count cards telepathically, and master a trick that always reveals four aces.

04: The Deck Is Stacked (25 min)

Learn the cyclic method of card ordering (stacking) dating back to 1593. Perform tricks like “weighing” a deck in your hands.

05: Perfect Shuffles (30 min)

Master the perfect shuffle (faro shuffle) with mathematician Brent Morris. Study in-shuffles and out-shuffles that create fascinating symmetries.

06: Riffle Shuffles (32 min)

Use Gilbreath’s principle to design tricks based on imperfect riffle shuffles, where pre-arranged patterns produce magical effects.

07: Magic with Numbers (35 min)

Guess numbers using the golden ratio, Fibonacci series, and algebra. Includes Professor Benjamin’s first-ever math magic trick.

08: Look like a Genius (32 min)

Mentally multiply by 11, divide by 91, square numbers ending in 5, and more—no calculator needed.

09: The Magic of Nine (34 min)

“Cast out nines” to find missing digits, calculate cube roots, and reveal a volunteer’s age—all leveraging the number nine.

10: Look like a Psychic (28 min)

Decipher scrambled birthdays, predict dice spots, and use the parity principle to “read minds.”

11: Geometric and Topological Magic (31 min)

Explore Möbius bands (twisted paper loops), sliced bagels, and puzzles with disappearing figures like the “vanishing rabbit.”

12: Magic Squares (37 min)

Design grids where rows, columns, and diagonals sum to the same number—even based on a volunteer’s birthday. End with a pi-based magic matrix.