Persi Diaconis and Ron Graham are professors of mathematics and, respectively, a magician and a juggler. They're not professional writers; at times it shows. Their book Magical Mathematics (subtitled "The Mathematical Ideas That Animate Great Magic Tricks") occasionally drops the ball (or maybe beanbag, or scarves, or linking rings). But setting aside literary polish, Diaconis and Graham present some amazingly beautiful combinatorics. The core concept: sometimes an apparently-complex situation is far simpler than it seems — specifically, often a mix-it-up operation doesn't actually do a full randomization. Within such subtle order, important information can be conserved, conveyed, and exploited to confuse.
Some of the card tricks and puzzles in MM are startling, but the associated theorems are even more amazing — well, to a mathematically-minded person who studies them for a few hours, that is! Two stand out:
Other chapters of MM deal with de Bruijn sequences, properties of various perfect shuffles, statistical estimates of how many different magic tricks were known at a given time, probability issues in the I Ching, and math related to juggling. MM concludes with fascinating personal biographies of individual "stars of mathematical magic". The last profile is of the inestimable Martin Gardner himself, who died in May 2010, a mere month after writing the Foreword to this book.
(a typo: all the page headers of Chapter 7, "The Oldest Mathematical Entertainment?", read instead "The Olders Mathematical Entertainment?"; and cf. CastingShadows (2000-01-06), SubbookKeeping (2000-06-21), RubikCubism1 (2001-03-16), ...) - ^z - 2013-02-07