Making Lessons Count : When Arthur Benjamin combines his twin loves of mathematics and magic- add- bracadabra!- it's 'mathemagic.' : SCIENCE FILE / An exploration of issues and trends affecting science, medicine and the environment


Arthur Benjamin bounds across the gym at the Clairbourn school in San Gabriel looking like Peter Pan in a penguin suit. In his shiny black shoes, tuxedo and pixie haircut, he gives the impression that any minute, he could break out in a soft shoe.

Instead, he asks a girl in pink--one of 50 or so middle-schoolers perched in the bleachers--to pick a card. He holds out an imaginary deck. Then he asks her to remember her imaginary card, and replace it in the deck upside down.

When she's done, he pulls an unopened deck of (real) cards from his pocket. He spreads them out. One is face down. It's her card--the six of clubs.

But that's only the warm-up. Now the real show begins. He gets four youngsters with calculators to help him out. To help test the accuracy of the machines, the students in the bleachers call out two numbers to multiply: 49, 56. "Make sure it says 2,744," says Benjamin, before his helpers can punch in the numbers.

The students look totally bewildered, like he just landed from Mars. Now there's a race between Benjamin and the calculators to see who can square a two-digit number fastest. The bleachers call out the problems: square 44. 55. 43. 65. He beats the calculators every time.

He asks for a three-digit number and calls out the square of that while the students on the calculators struggle to catch up. Squaring a four-digit number takes a second or so longer. One youngster raises an eyebrow in total puzzlement; another drops her jaw to the ground.

If this seems strange activity for a professor of mathematics, Benjamin can be found at even more exotic locales. To catch his performance at Hollywood's Magic Castle, for example, one needs to don a fancy dress and be prepared to say "Open Sesame" (with feeling) to a wooden owl with glowing red eyes simply to get in the club.

While other magicians performing at the world-renowned house of magic pull rabbits out of hats, Benjamin pulls numbers out of his head. And his audience responds with cheers, catcalls, hoots, standing ovations.

When he's not performing, Benjamin teaches calculus, statistics, probability and number theory at prestigious Harvey Mudd College, where he's a tenured associate professor. He's 34 years old (5 squared plus 3 squared, he's quick to point out.) His research interests are combinatorics ("clever ways of counting things") and operations ("the math of doing things efficiently").

He sees no conflict between his math and his magic. In fact it is through magic that he is able to pursue his goal of "bringing math to the masses." In a time when math abilities of U.S. students and adults alike continue to decline, Benjamin's "mathemagics" provides a welcome--if isolated--antidote to the national disease, mathephobia.

"I've always thought arithmetic was magical," says Benjamin, who married his mathematician wife, Deena, two years ago at the Magic Castle. He loved straight magic even more. Growing up in Cleveland, he performed at birthday parties as The Great Benjamini.

His father, however, felt he should pursue something more practical, so Benjamin majored in math at Carnegie Mellon. But he still loved magic. So his father suggested he put the math and the magic together. "I was dubious," he said. "But they [his audiences] liked it."

Certainly, the youngsters at Clairbourn are mesmerized by his numbers games. Moving on to magic squares, he draws a grid on his paper easel with markers. It looks like a tick-tack-toe board, except it has 16 boxes instead of 9. The idea is to make all the columns and rows add up to the same sum.

Benjamin asks a volunteer to point to the boxes in any random order. Then he asks the stands to call out a two-digit number.

Someone yells: 56. As fast as the volunteer can point to a square, he writes a number. When he's through, every row and column adds up to 56. As a bonus, so do the diagonals. So do the four boxes in the corners. So do the clusters of boxes in the corners.

The children bombard him with questions:"How did you do that?"


"Are you a genius?"

Emphatically: "No."

In fact, he volunteers that he was kicked out of several nursery schools for his hyperactive behavior, and spent much of his childhood on Valium. "My elementary school teachers would remember me not as smart, but as a smart-aleck."

And just about anyone, he says, can do what he can do. "It's a skill like typing or juggling. You just need the incentive."

When he was young, Benjamin's main incentive was getting attention, showing off. Now it's more of a missionary approach.

"I'll do whatever it takes to get the public interested in mathematics," he says. "And if there's one area where you lose people, it's arithmetic. People either think it's easy and therefore boring, or they don't understand how it works."

These days he's especially excited about his educational package being hawked on a popular infomercial. "It's for people who say, 'I never did understand fractions.' "

But for Benjamin, math is more than a numbers game. It also teaches important life lessons: "It's all about logic," he says. "It's understanding that if the DNA doesn't match, the subject is innocent. But if it does match, that doesn't [necessarily] mean the subject is guilty."

Even more important, he says, it teaches that there's more than one way to solve a problem. "There are brute force solutions, elegant solutions, surprising solutions. You can be creative, approach the problem from many different angles. And you always get the same result."

For all his skills as a performer, Benjamin takes teaching very seriously. "When a student loses interest, most teachers figure it comes with the territory. But for a magician, if a kid falls asleep, that's a disaster."

Simply exposing students to a subject is not enough, he says. "It's not like exposing them to a virus, where in a few days they're going to catch it."

Yet there's clearly more than entertainment going on. He tries to build from a strong foundation, finding out where the students are and starting from there. It seems to work: "I'll put my calculus or probability students up against anyone's."

As Benjamin gets ready for the grand finale, an eighth-grade boy in the back row is acting up uncontrollably, so Benjamin asks him to leave. Later, he admits that could well have been him at that age.

But right now, he requires concentration. Squaring a five-digit number isn't easy--even for The Great Benjamini. Only one student in the room has a calculator up to the task--because only one can display a 10-digit solution.

He announces that he will think out loud, so they can follow along. "You're going to hear some strange words and sounds, but I don't want you to think that there's something out of 'Rain Man' here. There's definitely a method to my madness."

Five students call out five numbers: 8,2,5,7,9.

His eyes screw up, fists clench, arms swing, hands fold into prayer and unfold, fingers mow the mop of black hair, sweat pours out along with a bizarre string of words: "Bare. Blush. blush. blush. blush. Nerd if I need it. Take 335 and add that to blush."

Then he asks the girl with the high-powered calculator: "Did you get 6,848,359,049. " She nods, stunned.

A teacher heaves a long sigh: "It leaves you breathless!"

A student offers: "This could take somebody who thought they hated math and make them love it."

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