This is an oddity of a popular maths book in that the approachable bits of the book aren’t, on the whole, about maths but about magic. Magic is a strange topic – for me, certainly, it has a fascination. When I was at school I briefly flirted with the school’s magical society, but in the end I hadn’t the patience to practice the tricks over and over again until they were slick enough to be worth watching. I wanted instant magic that didn’t require sleight of hand ability. The other interesting thing about magic as a topic is that we seem, mostly, to have lost patience with the traditional forms. On the TV show Britain’s Got Talent, magicians mostly don’t fare well as the audience and judges don’t have the patience to sit through the build. We love Derren Brown’s dramatic showmanship, but not traditional tricks. This means that Persi Diaconis and Ron Graham have a potentially difficult audience.
Magical Mathematics really has three different threads interwoven. There’s biographical information about magicians (this is the smallest part). There are details of how to do tricks. And there’s the maths behind the tricks. These are actual tricks which at first sight should have appealed to my young self because they are worked by mathematics – the magician need have no physical dexterity. This sounds horribly like the kind of recreational maths (you know, magic squares and the like) that mathematicians get all excited about but for most people cause big yawns. However, when you look at some of these tricks in terms of the effect, they are very impressive. I particularly like one where five spectators each cut a pack of cards in turn, then take a card each. They are asked to do a simple thing (everyone with a red card stands up), and the magician then tells each of them which card they are holding. That really is impressive.
Of course there’s no gain without pain, and in the case of this trick, though there is no dexterity required, you do have to remember (or otherwise access) quite a lot of information. Even so it’s a great trick, and the maths behind it, on de Bruijn sequences (don’t ask) is also really interesting, including some real world applications of the mathematical structure that’s used. This is by far the most engaging bit of the book – but even here, the maths isn’t particularly well explained. I didn’t really get the first explanation and it was only because there’s a second chapter dedicated to the applications that I grasped what was going on. It’s not complicated, it’s just that the explanation isn’t particularly well written.
Other sections of the book proved less interesting. The tricks were not so impressive or the maths was obscure, hard to follow and, frankly, more than a little dull. It got even worse when juggling was brought into the mix, something that, along with mimes, should have been banished from the world many years ago. Only jugglers appreciate juggling.
The underlying thesis, that you can do real, entertaining magic driven by maths was interesting (though I wish it hadn’t concentrated so much on card magic, which is one of the less appealing aspects of the business). The idea of combining explanations of tricks with info on the maths was good too. But overall the book (and I’ve no idea why it’s in a near-coffee table format) didn’t really work for me.
Hardback: 
Also on Kindle:
Review by Brian Clegg
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