Twenty-three years after winning the All-time American Backgammon Tour in 1997, Harvey Mudd College math professor Arthur “Art” Benjamin returned to the playing board to claim his throne as the 2020 ABT Online! champion. For Benjamin, mathematics incorporates twists of fate common to our everyday lives — and backgammon is no different.
First popularized during the ’60s when played by celebrity crowds, backgammon is a two-player board game where players move 15 pieces between 24 triangles according to the throw of two dice, attempting to be the first to move all 15 pieces off the board. Strategic maneuvering is key, but luck — and knowledge of probability — goes a long way.
“Think of backgammon as chess with dice,” Benjamin said. “It’s a game of strategy, but there’s also a large random element, and you have to be able to make predictions and roll with the punches depending on what the dice give you.”
As the captain of the chess team at his high school, Benjamin spent many of his teenage years studying the game through a mathematical lens, fascinated by how he could apply one game of numbers and patterns to master another.
But Benjamin, who has a knack for performing mental math calculations at an almost impossibly fast speed, believes the beauty of math is also meant to be shared, and he applied it to magic.
What started off as a high school stint doing magic shows for children’s birthday parties soon turned into a passion for entertainment. Now, his audience includes not just 5-year-olds, but anyone across the globe. A nationally acclaimed “mathemagician,” Benjamin has performed for audiences on TV shows, written best-selling math books, given three TED talks (one of which has been viewed over 20 million times) and earned the title of “America’s Best Math Whiz” from Reader’s Digest.
Benjamin’s interest in the intersection of math and magic might seem counterintuitive at first. After all, everyone knows mathematicians have to show their work, while magicians keep theirs a secret. Or do they?
Benjamin’s “mathemagics” shows feature him performing impressive tricks, like squaring triple-digit numbers in a matter of seconds, or even telling you which day of the week you were born given the date and year.
But Benjamin’s magic isn’t secretive; it’s accessible. By explaining how he performs these tricks, he subverts that common conception to illuminate how magic can be even more fascinating when explained in everyday terms like simple math, rather than kept distant from its audience.
“I was basically doing math and showing off, but that would only be half the show. The rest of the [show] would be my explaining to the audience how I did it,” Benjamin said. “I actually think understanding what’s going on is as interesting as the effect itself.”
After joining the Harvey Mudd faculty in 1989, Benjamin now serves as the Smallwood Family professor of mathematics at Harvey Mudd. But his career as an entertainer has never shied away from the classroom.
“I try to think about what in my math class will evoke a reaction of ‘Wow, that was cool.’ You know, what’s the punchline that I’m trying to deliver,” Benjamin said. “And I think just by even thinking about those questions made me an effective teacher.”
Magic continues to find its way into Benjamin’s research in combinatorics, where phenomenons like the Fibonacci numbers reveal to him on a daily basis just how otherworldly the field can be.
“These numbers have all kinds of magical properties. There’s so many applications to them, and people have used Fibonacci numbers in art and architecture and game theory and optimization,” Benjamin said.
Backgammon — like most other games, it seems — might not be so far from a simulation of life, where recognizing and applying sequences and patterns can take us as far as our imagination will.
Perhaps that’s the most magical thing about math; as Arthur Benjamin already knows, you can play the game for your entire life using educated predictions and still be left with mysteries to uncover.
If interested in creating or joining a Claremont Colleges Backgammon Club, contact Arthur Benjamin at benjamin@hmc.edu.
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