In awarding this book five stars I am rather reminded of the infamous Samuel Johnson quote on women preachers: ‘A woman’s preaching is like a dog’s walking on his hind legs. It is not done well, but you are surprised to find it done at all.’ Leaving aside that Doctor Johnson might have had to rethink his opinion had he seen Pudsey, the reason I say this is because I’m reviewing a book about mathematical equations. Taken purely as a piece of popular science writing it probably only merits four stars, but I am so amazed that anyone can write a book about a series of equations and make it readable and interesting that I have had to award it five.
When I first saw the title I thought I was about to flick through a nice picture book of astronomical photos, but in fact Dana Mackenzie provides us with plenty of words – it’s just that they are describing these ‘no words’ equations. Mackenzie eases us in gently with the work of the ancient Greeks, then brings us forward in time, allowing the maths (and the equations) to grow in complexity as we go.
What makes the book work so well is that there is plenty of context – we learn about the individuals behind these equations (not always the obvious ones when it comes to, say, Pythagoras) and the historical setting of their devising. There are some rather beautiful hand drawn illustrations of the equations themselves and diagrams (I just wish the handwriting was a little more legible) and the amazing, dog-walking-on-hind-legs feat is that we aren’t turned off by the equations, but rather get some feeling for their beauty and power.
I am not saying this book brings me round to a mathematician’s viewpoint. I still think that their view is too abstract, and that much of the maths they get excited about is hugely ‘so what?’ – but this book really does give you a flavour of why they get so worked up.
Strangely, the book tails off towards the end. This is in part because Mackenzie spends more time on physics (which he is less effective at explaining than maths), and partly because there is less focus on equations. Maxwell’s equations, for example, aren’t explored, just mentioned. Yes, remarkably, by then the reader is so drawn in that we want more equations!
I have two specific gripes apart from this. One is about the introduction. We are told how the great Richard Feynman took on someone with an abacus and beat them on the calculation of cube roots because he knew ‘a famous equation from calculus called Taylor’s formula’ – yet we aren’t told what the equation is. In a book that is all about making equations visible, this rankled for the rest of the book.
The other problem I have is with a bizarre mini-rant that Mackenzie has about those who worry about the impact of mobile phones on their brains. He points out that the photons produced by a mobile phone have not got enough energy to ionise atoms, so don’t present a danger. But this entirely misses the point. After all, the photons produced by microwave ovens aren’t ionising radiation either, but few us would feel comfortable sticking our heads in a functioning microwave. It’s not that I agree with the ‘danger from phones, phone masts and wifi radiation’ lobby – I don’t – but Mackenzie merely muddies the water with this strange irrelevancy.
That’s a very minor complaint, though. If you’ve always been puzzled by mathematical formulae, or wondered why mathematicians bother to get out of bed in the morning, this is the book to let you into their secret world. A remarkable achievement.
Review by Brian Clegg