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The Spirit of Mathematics - David Acheson ****

The subtitle of this slim book is 'algebra and all that', presumably in reference to David Acheson's impressively entertaining general mathematics title, 1089 and all that (itself, a reference to 1066 and all that). What Acheson managed with that book was almost inconceivable - an educational book about maths that was genuinely fun to read.

Clearly, the aim here is to take the same approach with a specific focus on algebra, though the book does stray into geometry and one or two other fields occasionally. And the result is again a delight. It feels a little like an old children's book for adults, with a deliberately old-fashioned style, delighting, for example, in giving examples from ancient textbooks. Acheson makes use of illustrations, cartoons, and occasional two page spreads such as 'Playing with infinity' to break up the material, but this is definitely for an older teen/adult audience.

The underlying message is that the book is attempting to 'capture the spirit of mathematics using only simple materials'. This certainly isn't a purely descriptive history of maths book, as there's plenty of actually mathematical content. 'Simple materials' means that there's nothing here that someone with the basic maths taught to, say, the age of 16 would find difficult. What Acheson does well is to bring out why mathematicians love the subject and some of the tricks of the trade and ways of looking at things that may be different from that of normal folk.

One thing I'm not sure Acheson does entirely address is an implication of his comment 'so far as I can determine, the mystery [of algebra] can often be summed up in one simple question: what is algebra really for?' He points out that the power of algebra is in expressing general statements and ideas in mathematics. The book does show this, but I don't think the question is quite right. Most people, I'd suggest think rather 'What use is algebra to me in everyday life?' and the examples here (including the infamous bath filling problems) don't really address that for fairly obvious reasons. It might, then, have been helpful to also more explicitly demonstrate the indirect lessons we get from that ability to express general statements and ideas. I loved algebra at school as puzzle solving, but I know many people do struggle to see the point.

In practice, this probably isn't much of an issue as the people who are going to buy this book are likely to be in my 'algebra is fun puzzle solving' camp. I really enjoyed reading it, though I wasn't quite as enamoured as I was with its predecessor. However, there's lots of fun stuff, with plenty of links back to the history of maths, some educational material and some practical mathematical tools, so it's still a strong recommendation for the mathematical bookshelf.

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Review by Brian Clegg - See all Brian's online articles or subscribe to a weekly email free here

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