Secrets of Mental Math

Secrets of Mental Math
by Arthur Benjamin and Michael Shermer


Having encountered mathematics as the language of physics in my previous life as a Physics grad student, I wasn't too terrible at it. But, numerical manipulations weren't my forte. I just didn't fancy it much. Which is why it amazes me when I encounter brilliant minds who come up with clever tricks to compute seriously involved numerical calculations at lightning speed in their heads. No paper and pencil.

Arthur Benjamin's Mathemagics: How to Look Like a Genius Without Really Trying, now reprinted as Secrets of Mental Math, with a Chapter Zero and a Chapter Infinity (by Shermer), is a book full of tricks to perform clever and quick arithmetic. The tricks or short-cuts work because of our number system, and the book tells us why they work. Of course, that section is optional if we just want to pick up a few nifty manipulations and impress our friends :)

I think this could be a great book for middle through high school kids who struggle with such concepts. It is true that some tricks are hard to remember and will come with practice. Like arriving at the day of the week, given a date. The codes for the Year seem like a lot to remember. But that's just me. The basic problems of finding square roots, cube roots, squares, 2-by-1 multiplication, 3-by-1 multiplication and such are presented very nicely, making it all look easy.

I also like that the book is peppered with interesting facts about people and topics in recreational mathematics - Carl Friedrich Gauss, Zerah Colburn, the Monty Hall Problem, George Parker Bidder, Évariste Galois, Shakuntala Devi, Alexander Craig Aitken and Thomas Fuller. It is amazing how gifted some people are with seeing and manipulating large numbers mentally.

This is one book I am hoping to having in my home library - just for fun - to practice the tricks and see if it inspires me to come up with a few (not necessarily original) of my own :)