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Maths 1001 [Mathematics 1001] – Richard Elwes ***

Like its sister title Science 1001, this book takes on an enormous task: telling us ‘everything we need to know about mathematics in 1001 bite-sized explanations’.
It’s a handsome, if rather heavy book, somewhere between a typical hardback and a small coffee table book in size (though with floppy covers). Inside, it’s divided into 10 main sections – from the obvious ones like geometry and algebra, through to the exotics from statistics to game theory. Each section is split into topics – so in geometry you might get ‘Euclidian geometry’ and within each topic there may be around 12 entries.
In a sense, then, this is a mini-encyclopaedia of maths, though arranged by subject, rather than alphabetically. I had mixed feelings about the science entry in the series and those feelings are more extravagantly mixed than ever here. There is no doubt whatsoever that this is a useful book. A good marker of this is that, unlike many of the books that come into the review pile, I intend to keep this one. I think I will come back to it time and again to brush up on what some specific aspect of maths is. (As it is, really, a reference book, it would have been more helpful if the topics were alphabetic, but hey, what do you expect from a mathematician?)
However, as a popular science book to read from cover it has a number of deep flaws. Firstly it’s much too broken up into tiny segments. There is a bit of a flow, brought in by the way the topics are organized, but it’s very weak, and certainly doesn’t make for casual reading matter.
Secondly, far too much of the book is definitions. Time after time, a topic consists of defining what a mathematical term means. I feel a bit like Richard Feynman, who was told in a biology class, when explaining what the various bits of a cat were called, that everyone would be expected to memorise these. He said something to the effect of ‘no wonder this course takes so long’ – he didn’t see why people need to keep all those definitions in memory, and I rather feel the same about maths.
Then there’s the difficulty that the structure has in terms of dealing with some of the essentials of maths. Time after time, the author refers to the number e, without telling us what it is until over 200 pages after it is first mentioned. The assumption for a reader who hasn’t come across it might be that e is just a placeholder, the way j is used elsewhere – although many definitions here aren’t necessary, explaining what something like e is, and why it’s important, is pretty crucial.
As someone with a physics background, I particularly struggle to understand why there’s a whole section in here called ‘mathematical physics.’ No, it’s just physics. Newton’s laws don’t belong in a book on maths – there’s much too much to get your head around already without straying into a different subject.
And to top it all, I think the approach taken is often wrong. Popular science/maths, as opposed to textbooks, adds in explanation and context, not just the theory. By being so strong on definitions, there doesn’t seem to be room for this here. We find very little out about all the fascinating people involved. But even if you decide the format doesn’t allow for context and history, there is still far too little explanation. Two example out of literally hundreds: we are told ‘Up until the early 20th century, 1 was classed as prime, but no longer.’ Why? There are good reasons for this, but it is totally counter-intuitive. The number 1 seems like a prime. After all, it is only divisible by 1 and itself. We need explanation, not statement from authority. Another example is the topic on Bayes’ theorem. This is fascinating in its application, but the explanation is almost unreadable, being mostly equations, and there is nothing about its application in that section (a later one does make use of it, but doesn’t mention it is doing so). Highly frustrating.
Overall then, this is a very useful book if you dip into maths and need a quick reminder of what various things mean. It really is a great resource as a reference book. But it just doesn’t work as popular maths.

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Review by Brian Clegg
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