Is Maths Real? - Eugenia Cheng ****

As soon as I saw this book, I knew I had to read it, if only because I wrote a book called Are Numbers Real?. The maths content of Eugenia Cheng's book is brilliant: where I was covering the history of mathematics, she focuses on what real, pure mathematicians do. (Funnily, I had called my book Is Maths Real?, but it was changed to the less accurate Are Numbers Real? so we wouldn't need different covers for the UK and US editions.)

The mathematical journey that Cheng takes us through is mesmerising. She starts by showing the power of abstraction - how by thinking about the nature of, say, something basic like addition or multiplication it is possible to extend the concept into something other than numbers. We also discover that, in some ways, the answer '2' is the least interesting response to 'What is 1 + 1?' - real maths isn't about the answer per se, but about digging into the processes, mechanisms and definitions to get a deeper understanding of the underlying logic.

From these simple beginnings, we are then helped to get over what has proved a stumbling block for many: the abstraction of what we'd call variables in computing. Using an x (say) instead of a specific number. I loved algebra at school, because it felt like code breaking, but I absolutely understand why this step is one that defeats many young people in their exposure to mathematics. We then get on to formulae and their relationship to other mathematical structures like geometric ones, and different visual representations. And this was all a delight.

I wouldn't entirely agree with Cheng on why so many people aren't interested in, or openly dislike, maths. I suspect a lot of it is about the very thing that makes it attractive to her - that abstraction. If we look at the rest of STEM, engineering and medicine give us practical things. Physics and chemistry tells us how the world works. Biology tells us about interesting animals and feeds into medicine. But most of maths is neither useful in ordinary life nor telling us anything about the world, because it exists within its own abstracted universe. This book makes clear how beautiful that can be - but it's a hard sell to teenagers.

Originally, I was going to give this book five stars, because the maths coverage is brilliant, but most of Cheng's books I've read have the flaw of containing (for me, at least) too much about her and her opinions. I want to read about maths, not Cheng's interest in food, her politics or her cultural inclinations. I do want to know about why mathematicians find maths interesting - but that’s a very different thing. This sort of personal content does appeal to some readers, just as, say, reading a magazine about celebrities is fascinating for some, but it puts me off.

Overall, then, do read it if you want to know more about the nature of pure mathematics and about being a mathematician - the mathematical content is great - but you may need to occasionally grit your teeth over the rest.

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