Cracking Mathematics - Colin Beveridge ****

This kind of book is puzzling, though as we shall discover, Cracking Mathematics is a particularly effective example of the genre. Generally, it's difficult to be sure what a book like this is for, a bafflement not helped in this case by the Zen subtitle 'you, this book and 4,000 years of theories'.

The kind of book I'm talking about is a heavily illustrated summary of a big scientific subject - in this case the whole of mathematics - often covering each topic in as little as a pair of pages with sufficient pictures that the text can only ever be very summary. I can see this format would appeal as a gift book, something to give someone who is difficult to buy for, but I struggle to get a feel for why you would want to sit down and read a book like this from cover to cover - yet it's not a reference book either.

Such books are often big coffee table numbers, but the books in this particular series come in a virtually pocket-sized format - smart hardbacks just 17.5x15 centimetres, so they are far more manageable as, say, a loo book, or something to keep in your bag for boring journeys to keep yourself entertained. And perhaps that format is part of the reason why this particular example works so well - that and some genuinely interesting text from Colin Beveridge.

Along the way, Beveridge takes us on a journey through the origins of mathematics, the renaissance, with the introduction of negative and imaginary numbers, calculus and the infinitesimal, powers and logs, the infinite, codes and some of the more exotic modern ideas. Unlike some of the summary maths texts I've read, it isn't a collection of dull facts, but provides plenty of little gems along the way, from the 20,000 year old Ishango bone to the mysteries of elliptic curves and John Conway's Game of Life. Sometimes the format is a little forced - there's a section labelled 'The Curious Maths of Alice in Wonderland' which certainly does contain some Dodgson maths, but equally includes things like quaternions and non-Euclidian geometry, where the connection to Lewis Carroll, let alone Alice, is rather weak.

In other places, the attempt to make the discussion populist overstretches a little. There is some great material on games and probability, with, for instance, an really good description of the famous Monty Hall problem and the controversy it caused in Parade magazine - but quite why there is a double page spread on poker player Chris 'Jesus' Ferguson, even if he did apply game theory to poker, is a little baffling. My general feeling about this was 'So what?'

Maths is often portrayed as a very dry subject - a necessary evil, rather than something to enjoy - and when maths enthusiasts such as Ian Stewart try to make it seem that mathematics is pure fun they can often misunderstand what the general reader actually finds entertaining, or even faintly interesting. Beveridge does not fall into this trap, and consistently gives us interesting material - in part because the book focusses on the people involved and the history of maths as much as it does on the actual mathematics. Because of this, this title lifts itself above the other books of this type that I've read to make it feel that it really is worth popping into your bag to lighten your next wait at the station.

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Review by Brian Clegg