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Each chapter launches into its subject relatively gently but the going gets tough quite quickly and I found, repeatedly, that my very rusty A level maths just didn’t cut the mustard. However, I suspect that’s more down to memory lapse than to anything else – readers with more recent maths knowledge would undoubtedly get far more from this book than those whose knowledge is patchy or, as in my case, decades old. And at times I felt that Professor Stewart jumped a little, assuming particular knowledge that I’m quite sure I never had. This is where a glossary would have helped enormously – a brief explanation of terms that could be referred to when necessary. An index would have been nice, too, although its omission was perhaps deliberate, to provide distance from other, more academic tomes.
The Prof writes engagingly at all times and has a delightful enthusiasm for his subject. As in his other books, he manages here to popularise maths and make it accessible to a wider range of people than has previously been the case - and this is no mean feat. There are some wonderful nuggets of information that would form a great basis for quiz questions. The four colour theorem, for example, states that with only four colours you can colour in any map whatsoever, such that regions with a common border have different colours. There’s also a short – and clearly explained - chapter on the maths of codes, ciphers cyphers and the Enigma machine.
Incredible Numbers makes for fascinating reading, but only for somebody with a good grasp of maths or, at the very least, a decent mathematical brain. To be fair, you probably wouldn’t consider this book if you had neither of these things. To the numerically-challenged, reading this book might seem like rather hard work. But if you’re prepared to make the effort, you’ll find it gives you a far-reaching introduction to the world of maths, from ancient concepts right up to string theory, and you’ll be well rewarded.

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