Today’s lunch with Dr. Arthur Benjamin, self-proclaimed mathemagician and Professor of mathematics at Harvey Mudd College, was everything it was hyped to be. Benjamin combines light math puzzling and his lively sense of humor for a show that keeps even an analytical audience entertained.
He opened the show with a classic sleight of hand – a card trick. His twist was using an invisible deck of cards that he made reappear before our very eyes. He picked a random audience volunteer to choose an invisible card from his deck.
“Take a look at your card, but be very careful not to let me see it,” cautioned Benjamin. The hilarity grew when the volunteer dramatized his movements like a mime on the streets of New York City.
Benjamin dramatically shuffled his invisible deck.
“Now carefully place your card upside down in the deck.”
The volunteer took one last look at his invisible card and slid it into the deck – upside down. Magically, Benjamin made the invisible deck of cards reappear from an empty box, which had been stowed in his pocket. He asked his volunteer to name the card that had been placed upside down in the deck.
“You’ll notice that the two of hearts is the only card that has been turned upside down,” said Benjamin, with no further explanation as to how he’d known that the volunteer would choose the two of hearts from his invisible deck. (Magicians are sooo secretive about their hanky panky!)
His next trick: squaring numbers in his head. Mathemagically. He started out squaring two-digit numbers and worked his way up to four-digit numbers. Keep in mind that Benjamin was competing against calculators!
After many more tricks and jokes, Benjamin settled into a quiet moment before his finale. He told the audience that he wanted to discuss his stance on education with them. According to Benjamin, math in the US is based on two fundamentals: mathematics and algebra and at its summit, is calculus.
“If President Obama were to name me the Czar of Mathematics, the first thing I would do is replace that summit with statistics – probability and statistics,” said Benjamin. “Very few people use calculus on a daily basis. They use statistics every day to understand risk and reward, to understand trends. And it’s fun! That’s what got me interested in it, and it would get other kids interested. It teaches people how to think.
Instead of learning the Rules of Calculus, it would be better for everyone to know two standard deviations away from the mean. And, I mean it!”
Drum roll, please
For his finale, Benjamin asked five audience members for a single digit.
“Five.”
“Seven.”
“Zero.”
“Eight.”
“Three.”
He intended to square a five-digit number before our very eyes: 57,083. He began by showing the audience how he breaks the problem into three parts:
• 57,000 squared
• 80 squared
• 3 squared
“Let me recap,” he said. Recapping the marker like a mischievous child, Benjamin drew a deep breath and began to solve the problem aloud.
He sounded like a livestock auctioneer as he solved the problem in less than one minute flat, racing against the calculators and stopwatches in the room: 3,258,468,889! The crowd exploded.
Benjamin’s solving tricks:
Benjamin says he’s learned some quick tricks for himself that perhaps you’ve already learned.
Say you are trying to multiply 22 times 5. In this case, he does math from left to right. (Backwards from the way we were taught, right.)
• 5 times 20 = 100
• 5 times 2 = 10
• Add the two totals
• 22 times 5 = 110
Here’s an easier one: 398 times 7
• You could multiply left to right – but it is easier to add 2 and multiply 400 times 7
• 400 times 7 = 2800
• Now, 7 times 2 = 14
• 2800 minus 14 = 2786
So how does he square in his head? Let's use the example of 37 squared
• Add 3 to make 40, and take away 3 to make 34.
• Remove the 0 in your mind and multiply 4 times 34 =136, add the 0, 1360
• Remember the 3 that still needs to be squared = 9, add it to 1360 =1369
• 37 squared = 1369
