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The Magic of Math

Colm Mulcahy

There are two types of magic. The first is the most well known and is performed on stages and at parties across the world. It is engineered by sleight of hand and requires the magician to be one step ahead of the audience at all times. Then there is the type of magic in which Colm Mulcahy specializes. Rather than rely on sleight of hand, Mulcahy makes use of his training as a mathematician to transform the performance of street magic.  

Mulcahy, a visiting professor from Spelman College teaching Introduction to Statistics and Great Ideas in Mathematics, often begins his classes with a bit of magic. “When I teach at the beginning of the semester, I invariably do a card trick, usually right after I give out the syllabus and students start to get bored,” Mulcahy says. “It gets their attention, because they often don't believe that the trick is entirely based in mathematics. Depending on the nature of the class, I might explain the trick right away or wait until we cover the topic in class.”  

When they do reach a topic in class—anything from algebra to probability and statistics—Mulcahy will present the card trick again and give students time to work out how mathematics plays a role in it. After students have presented their theories or expressed their frustration at not being able to find the key to the trick, Mulcahy will walk them through the mathematical theories. This allows students to see the workings of math throughout the card trick and gives them a different perspective to what they are learning in class.  

Mulcahy began his practice of mathematical magic about 15 years ago, when he rediscovered the works of Martin Gardner, writer of the hugely influential Mathematical Games column in Scientific American. “His column ran from the mid 50s to the early 80s and it was hugely influential for a whole generation,” he says. “He engaged people with some really amazing stuff, and some of it was mathematical magic.”  

Around the same time as Mulcahy was reintroduced to Gardner and at the beginnings of his interest in mathematical card tricks, he joined Ring 9, a local magic club in his home state of Georgia. “I quickly realized that if I wanted to be good at real magic, I should have started at 12 or 13 like all the other boys and girls in the club,” he says. “The kind of people who can show you a card and show it to you a second time and it's changed from a red ace to a black queen and you have no idea how they did it… I don't have those skills. But I have mathematics, which is my secret weapon.” 

The card trick that started it all, Mulcahy says, goes back to a trick invented in 1950 by William Fitch Cheney. The trick runs like this: the participant picks five cards at random from a shuffled deck and gives them to the magician, who returns a single card to the participant and arranges the remaining four in a face-up row on the table. The magician's accomplice, who has not seen any of the cards before that, now joins the scene. That accomplice is soon able to announce what the hidden fifth card is. The only communication passing between the magician and the accomplice is mathematical: the list of four cards. “I was told about this trick, and I spent three or four days thinking about it and figuring out how it worked,” he says. “When I figured it out, I was hooked.” 

About a month later, Mulcahy had invented his own “mathemagical” spin on the five-card trick. It begins like the five-card trick, except with four cards. “But it's a little different, because rather than display the cards the usual way, which is face up, this time one, two, or even all three of the cards can be face down,” he says. “There is absolutely no verbal or physical communication between the accomplice and the magician; it's entirely based on mathematics.” 

It's the oldest trick in Mulcahy's new book, Mathematical Card Magic: Fifty-Two New Effects, of which 80 percent is Mulcahy's own material from the past 15 years, and it's the last trick presented because Mulcahy thinks it's one of the best.  

On Friday, November 8, from 7-8 p.m. in Ward Hall Room 1, Mulcahy will present a lecture and a performance of his best card tricks. There will be refreshments and a reception afterward, where Mulcahy will be available to sign copies of his book. For more information on the evening of math and magic, curious minds can visit the event webpage. Mulcahy's blog can be found at http://cardcolm.org.