SciTech

# Art Benjamin displays power of magic and mental mathematics

Art Benjamin, a math professor at Harvey Mudd College, combines mathematics and magic in his seminars, where he performs feats, and teaches methods, of mental calculation. (credit: Courtesy of Harvey Mudd College)

The Mellon College of Science hosted speaker Art Benjamin, who gave a talk last Monday titled “The Art of Mental Calculation” that explored the mechanics behind complex mental math techniques.

Benjamin is an alumnus of the Carnegie Mellon math department class of 1983, and he currently works as a math professor and guest speaker. His talks have been featured on The Today Show, National Public Radio, and TED. The TED talk he gave in 2005 has over 200,000 hits on YouTube.

In a mix of showmanship and mathematical prowess, Benjamin began the presentation by returning to his roots as an amateur magician. He called up a volunteer to participate in a card trick, and he afterward invited several students with their calculators to challenge him in mental calculations. The audience, consisting of primarily MCS students across all fields of study, called out random digits that became two numbers that would be multiplied together. Within five seconds, every time, Benjamin provided the correct answer.

Taking questions from the audience, Benjamin delved into his mental math techniques. Using pi as an example, he demonstrated a simple mnemonic device in which one could memorize digits. He assigned each of the 10 digits from zero to nine a consonant (or, in some cases, several different consonants). Zero, for example, became the “z” or “s” sound. He then was able to formulate different words using the sequence of pi. For example, the string of digits assigned the letters “MTTR” could be formed into the word “matter.” Using this method, Benjamin could memorize the first 100 digits of pi in a few sentences.

Some of the methods followed a more traditional form of math. Benjamin revealed his ability to square three- or four-digit numbers. By finding a number that is a multiple of 10 close to the value in question, Benjamin could use a combination of addition, multiplication, and finding the squares of smaller numbers to calculate the answer. None of the calculations took him more than about a minute to explain and demonstrate.

Though he was covering a very complicated topic, Benjamin successfully kept the speech from becoming too dry. When discussing pi, for example, he recalled his time as a writer of the musicals put on by the Scotch’n’Soda theater group. He even composed a song for pi, put to the tune of Don McLean’s “American Pie,” and happily gave the audience a demonstration. During the question and answer session, he willingly answered questions about his personal life. He divulged his favorite number, along with his preference for Macs versus PCs.

Benjamin combined all of his math techniques together in the finale, where he squared a five-digit number. Although he warned the audience that a few digits might be inaccurate, he successfully computed the answer amid a whirl of numbers and nonsensical words — and all mentally. The audience was impressed enough to give him a standing ovation.