## Friday, September 25, 2015

### Q&A with Arthur Benjamin

Arthur Benjamin is the author of the new book The Magic of Math: Solving for x and Figuring Out Why. His many other books include Secrets of Mental Math. He is the Smallwood Family Professor of Mathematics at Harvey Mudd College, and is also a magician. He lives in Claremont, California.

Q: What do you think are some of the most interesting connections between math and magic?

A: Mathematicians and magicians both want their audience to wonder: How did you do that? The magician keeps the method secret, but the mathematician wants you to understand. Math is not just solving for X. It's also figuring out why.

Q: You write that 9 is the most magical number. Why is that?

A: As a kid, I loved the fact that the multiples of 9: 9, 18, 27, 36, and so on, had the magic property that their digits would always add to a multiple of 9.

Here's a magic trick based on this fact. Think of any two digit number. Add their digits together. (So if you were thinking of 42, the digit sum is 6.) Now subtract that sum from the original number. (Example: 42 – 6 = 36.) Now add your digits together. (Example: 3 + 6 = 9.) You should now be thinking of the number 9.

Q: What are some of your favorite strategies to encourage people who are scared of math or don’t like it?

A: I like to motivate math with puzzles, magic, humor, and mental math strategies that anyone can learn that are very empowering. The main secret to math success is persistence. A good teacher or tutor can make all the difference in the world.

Q: In the book’s last chapter, “The Magic of Infinity,” you write that “when you enter the twilight zone of infinity, very strange things can happen…” What are some of the strangest things?

A: Here are some fun facts about infinity:

The infinite decimal 0.999999.... = 1. They are not just close; they are equal.

The sum 1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 + ... is equal to pi/4 (where pi is the irrational number 3.14159...).

When adding and subtracting infinitely many numbers, it is possible to get different sums with the same numbers, depending on the order that they are added. For example, the sum above can be rearranged to get pi or 9 or negative 2!

Although 1 + 2 + 3 + 4 + 5 + ... is infinite, a case can be made that the sum is equal to –1/12. (What's more disturbing: the negative sign or the fraction?)

Q: What are you working on now?

A: My next book will be on Math for the Fun of It, which will show how math can improve our ability to play games, solve puzzles, and have a better understanding of the randomness in our lives.

Q: Anything else we should know?

A: Schools today put so much emphasis on testing that all the joy has been taken out of the subject. In my book, I want students to see the important math explained in a clear (and fun) way, but I also want them to appreciate the beautiful aspects of mathematics, which is seldom seen in schools.

--Interview with Deborah Kalb