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Numbers: a very short introduction – Peter M. Higgins ***

Part of the massive ‘a very short introduction’ range of pocket books, this book sets you straight immediately if you thought it was going to be about mathematics – no, it’s about number, which is quite a different thing. This is both true and not true, which really sets the pattern for the whole little book. Number is a quite distinct concept from maths, yet in discussing number, Peter Higgins inevitably brings in quite a lot of mathematics.
The mixed feel continues with the presentation. The writing style is light and accessible for what can be quite an indigestible topic, but bits of the book are better than other in this respect. I wanted to keep reading, but I found myself feeling a strong urge to skip bits that seemed to be getting bogged down.
After an introduction to what numbers are we’re plunged into prime numbers in some detail. From here we go on to the various labels mathematicians have for numbers, from perfect to deficient – this is faintly interesting, but it does generate an urge to ask ‘Yes, but why does it matter?’ We go on to the likes of cryptography and the use of large primes to perform encryption/decryption, the various fractions, infinity and more. (Yes, you can have more than infinity, and you know what I mean anyway).
There seemed a couple of strange omissions. I think we could have done with significantly more on the philosophy of number – just what numbers are, why human beings use them, whether they have a real existence outside of mathematics etc. I was also surprised by the near-absence of set theory – it comes into the infinity chapter, but there is none of the use of set theory to establish the basics of number and operations, which seemed odd. I’d have expected it up front.
In the end it’s a book that falls between two stools. It isn’t consistently readable enough to be good popular science, but it isn’t detailed enough to be a textbook. I’m not really sure what it’s for. But it’s certainly not a bad addition to the series – and ‘number’ certainly deserves its place there.

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Review by Jo Reed
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