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Professor Stewart's Incredible Numbers - Ian Stewart ***

Ian Stewart is the most prolific writer in the field of popular maths, sometimes producing absolute crackers of a book like The Great Mathematical Problems and sometimes turning out ones that don't quite hit the mark. Intriguingly, this seems to manage to be both, in the same way as we discover that zero manages to be the same as minus zero.

 The good news is that there's all kind of weird and wonderful mathematical information here. The book is divided into many sections, starting with the small integers, and making it all the way to infinity, via a plethora of different values and climaxing, appropriately enough, with 42. 

 The bad news is that this format means that the book is mostly a collection of facts with limited context and narrative, the part of a popular maths/science book that makes for a truly engrossing read. There are also heavy duty examples of the classic writer's error of 'If it's interesting to me, it must be to you.' So, at one point we read 'On Christmas day 1640 the brilliant mathematician Pierre de Fermat wrote to the monk Marin Mersenne, and asked an intriguing question. Which numbers can be written as a sum of two perfect squares.'

 In fact there are two problems with this particular extract. One is spurious context. Unless there was some relevance to it being Christmas Day, then telling us that makes it sound like we're getting context without actually doing so. But worse is the 'intriguing question' bit - because unless you are a mathematician, there is nothing intriguing about that question. 

 I think a good general test of whether this book will work for you or not is how you react to magic squares - those grids of numbers that typically add up to the same value along each row, column and diagonal. It's a good example of how the book is organised, by the way, that these turn up in the section for number 9, because the smallest magic square is 3x3. If your reaction to magic squares is a mild interest that the earliest known magic square is called the Lo Shu (no date given), but then you get bored finding out about the properties of all sorts of different magic squares you will find parts of the book hard going. On the other hand, if after four pages on magic squares you think 'I wish there was more on magic squares,' rush out and buy a copy immediately. 

 If I am honest I am more in the first camp - but it didn't stop me reading the whole book because there are a good few genuinely interesting bits. The ones that work for me are the historically meaty ones, like the origin of zero, negative numbers and complex numbers - my suspicion is that every reader will find some parts to enjoy. So you pays your money (in real numbers) and you makes your choice. 
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Review by Brian Clegg
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