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Professor Stewart's Casebook of Mathematical Mysteries ***

There are broadly two audiences for popular maths books - general readers and maths geeks, and a title can appeal to one, or the other, or a bit of both. I struggle with the pure geek books (I'll give you an example of the sort of thing you have to enjoy for me to define you as a maths geek in a moment), but Ian Stewart is capable of writing a book that really does appeal solidly to general reader, as evidenced by his Great Mathematical Problems.

I haven't read (yet) his two previous books in this trilogy, Cabinet of Mathematical Curiosities and Hoard of Mathematical Treasures, but my suspicion is that Stewart got through most of the really appealing stuff in those, as at least two thirds of this book fell into the 'geeks only' category. This was a real shame, as the other bits were excellent. I was, admittedly, a bit wary on reading the bumf to discover that Stewart was indulging in some Sherlock Holmes pastiche to frame some of the problems. If there's one thing scientists and mathematicians fall for when they try to do funny, it's whimsy - and it can be horribly painful. All the signs were that this would be the case. Stewart's pair, Soames and Watsup have a landlady called Mrs Soapsuds (why?) - the groans were already pilling up. Yet, surprisingly, what he has produced are very palatable pastiches, full of references to the real thing, yet working surprisingly effectively on their own. Nice one.

The fact remains, though, that there are far too many 'mathematical mysteries' that evoke the response 'So what?' For example: 
The cubes of the three consecutive numbers 1, 2, 3 are 1, 8, 27, which add up to 36, a perfect square. What are the next three consecutive cubes whose sum is a square?
Sorry, I neither know nor care - and though I've given a very short example, some of the longer entries are this kind of mathematical trivia that will only turn on the ├╝ber-mathers.

So near, but so far. The good bits are five star greats. I loved, for instance, the Soames and Watsup puzzle requiring you to change the pattern of 8 glasses with only two moves. (Partly, admittedly, because I saw the answer straight away.) In fact the best bits do tend to be logical or lateral thinking problems. I will have to check out the two earlier books to see if the ratio of interest is similar, but for me, in this particular title, there are just too many items that don't raise more than a passing eyebrow.

Paperback (from October 2015):  
Review by Brian Clegg


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