Magical Mathematics

"I picked this book because I wanted to have a very recent title on my list. Some of the books I have chosen, such as Polya’s, are fairly old. This book just came out within the last year. Persi Diaconis and Ron Graham are two of the most fascinating and fun mathematicians you will ever meet. They both exemplify mathematics as entertainment, even though they also do very serious maths. Persi Diaconis is a great statistician and Ron Graham is an expert in combinatorics. But a lot of their maths is inspired by simple problems, and the enjoyment they take in them really comes through in this book. Diaconis is both a professor of maths and also a skilled magician. As a teenager he completely devoted himself to magic, and learnt tricks from the best in the business. In this book he presents a lot of self-working magic tricks involving cards. This means that the principles involved are not sleight-of-hand but mathematical. For example, he starts the book with something called the Hummer Shuffle – a special way of shuffling cards that anyone can do. You take a deck of cards and cut them anywhere. Then take the first two cards and turn them over. Cut the deck again and turn the top two cards over. Keep doing this as long as you feel like it. After a while, everyone in the audience will agree that the cards have been completely randomised. But amazingly, there are subtle ways in which you are not randomising it. The magician can send a deck of cards out into the audience, which they shuffle like crazy, and then gets the deck of cards back. Through simple procedures he can then undo what the audience has done, and get marvellous tricks out of it. One of them is to hide in the deck a royal flush – an ace, king, queen, jack and 10 of one suit – and make it magically appear even after the audience have shuffled the pack. He will do some more shuffles, then he will spread out the whole deck and you will see that only five cards are face down. Then he asks someone to turn the cards over and – lo and behold! – they are the royal flush. It looks like magic but he is using maths. In the book he explains how this trick and others like it actually work. All of them come from mathematical principles, such as keeping certain patterns intact (as in the Hummer Shuffle) or tricking the audience into revealing information without realising it. The skill of the magician is turning this into a magic trick and not just a boring mathematical problem."