Mathemagician Art Benjamin visits with
AU Professors Joshua Lansky and
Jeffrey Hakim and a young fan.

For most people, mathematics and fun go together like ... well, like mathematics and fun. The Friday evening before Halloween, however, more than 50 AU students, faculty, and staff filled Ward 1 with excited applause and laughter for a lecture on three-digit multiplication, perfect two-digit squares, and the properties of the factors of nine.

Of course, this wasn't "mathematics"; this was "Mathemagic," a high-energy presentation by renowned magician and human calculator Arthur Benjamin. The evening, sponsored by the Department of Mathematics and Statistics, featured stunts of mental calculation that made math look like magic but ended with Benjamin doing something magicians never do — teaching the audience how to do the tricks.

Passing out calculators, Benjamin began by squaring two- and three-digit numbers and arriving at the correct answers faster than the audience could punch them up. Then he asked separate audience members to shout out the individual digits to random three- and four-digit numbers and multiplied them before the students, faculty, and staff armed with calculators had even finished entering the first number, let alone arrived at an answer. Other feats included instantly figuring the days of the week of audience members' birthdays and filling in the blocks of a magic square (whose rows, columns, and diagonals all added up to the same audience-determined number) as quickly as a volunteer could point to them.

The only boundaries to Benjamin's mathematic feats, in fact, arose not from his inability to get the answers but from the audience's inability to check them. "I would attempt to square a five-digit number, and I can, but unfortunately most calculators cannot," Benjamin explained with a laugh. "There's not enough room on their screens for the answer."

Amazing as the "mathemagic" tricks seemed, Benjamin insisted that they all are actually quite dull when you know their secrets. "That's why magicians never explain their tricks," he said as he segued into the educational part of his show. "It's always such a disappointment when you know how it's done."

Yet that didn't seem to be the case for this audience, who marveled at the simplicity of such feats as multiplying a two-digit number by 11 by doing nothing more than adding a couple of single digit numbers together. The trick, Benjamin revealed, is to separate the two digits, add them, and place their sum in between to construct your answer: 25 times 11, for example, becomes 2(2+5)5, or 275.

To square a two-digit number, you start by simply adjusting the amount to the closest number ending in a zero, "because I like zeros," Benjamin explained, drawing a smiley face inside the digit that simplifies complex mental calculations. If you're squaring 24, he explained, you need to multiply 20 by 28 (since you reduced 24 by 4 to get 20, you need to compensate by adding 4 to 24 to get your second factor). Keeping that result (560) in your head, you then square the amount by which you adjusted your original number (4) and add that result (16) to your first result (560) to get 576.

According to Benjamin, even multiplying three-digit numbers is much easier than it looks. Take 112 times 104, for instance. Before you reach for your calculator, said Benjamin, merely reduce the number that's closer to 100 by the amount needed to reach 100 (104-4=100). Then add the number by which you reduced that number to your other three-digit number (112+4). The result (116) becomes the first three digits of your answer. The last two digits come from simply covering the 1 on both of the original three-digit numbers and multiplying them (12 x 04 = 48), making your answer 11,648.

As the example above demonstrates, even the secrets behind the tricks got rather complicated. For the task of naming people's birthdays based on their birth dates, Benjamin revealed a system in which each year, month, and day of the week is coded with a numeral 1 through 7. Beyond memorizing all of those codes, calculating the day of the week requires a series of numeric manipulations as well as minor adjustments for 10 out of the 12 months to account for leap years.

Still, as remarkable as his tricks seemed even after he revealed their secrets, Benjamin argued that anyone can master fairly complex mental calculations — and, in many cases, they should. "We don't spend enough time in school learning to do mental math, which is sad because you almost never do math on paper in your daily life," he said. "You either use a calculator or try to do it in your head."

In the end, then, the evening's clearest message went beyond the revelation that math can be fun. As deftly as he made math look like magic, Benjamin, whom Reader's Digest has labeled "America's best math whiz," also took the magic out of math. Armed merely with patience rather than an innate mathematical genius, he stressed that anyone could discover that math can also be easy. "Everything I do is purely a matter of practice," explained Benjamin. "I don't want you to think you're seeing something out of Rain Man up here. There's definitely a method to my madness. Definitely ... definitely."