There’s been a trend for a couple of years in popular science to produce ‘n greatest ideas’ type books, the written equivalent of those interminable ’50 best musicals’ or ‘100 favourite comedy moments’ or whatever shows that certain TV companies churn out. Now it has come to popular maths in the form of Ian Stewart’s 17 Equations that Changed the World.
Stewart is a prolific writer – according to the accompanying bumf he has authored more than 80 books, which is quite an oeuvre. That can’t be bad. He is also a professional mathematician – a maths professor – and that potentially is a problem. The trouble is that, much more so than science, mathematicians are not ordinary people. They get excited about things that really don’t get other people thrilled. And it takes an exceptional mathematician to be able to communicate that enthusiasm without boring the pants off you. It’s notable that the most successful maths populariser ever, Martin Gardner, wasn’t a mathematician.
So how does Ian Stewart do here? Middling well, I’d say. The equations he provides us with are wonderful, fundamental ones that even someone with an interest in science alone, who only sees maths as a means to an end, can see are fascinating. In most cases he throws in quite a lot of back story, historical context to get us interested. So the meat of the book is excellent. But all too often there comes a point in trying to explain the actual equation where he either loses the reader because he is simplifying something to the extent that the explanation isn’t an explanation, or because it’s hard to get excited about it, unless you are a mathematician.
The section on the Schrodinger equation, for example, is presented in such a way that it’s almost impossible to understand what he’s on about, throwing around terms like the Hamiltonian and eigenfunctions without ever giving enough information to follow the description of what is happening. (I also always get really irritated with knot theory, as the first thing mathematicians do is say ‘Let’s join the ends up.’ No, that’s not a knot any more, it’s a twisted or tangled loop. A knot has to be in a piece of string (or rope, or whatever) with free ends.)
Inevitably, to give the book real world interest, many of the equations are from science, and Stewart proves, if anything, better at getting across the science than he is the maths (probably because it is easier to grasp the point). The only section I’d argue a little with is the one on entropy, where he repeatedly says that entropy always increases or stays the same, where it’s more accurate to say that statistically it is very, very likely to do so. But there is always a small chance that purely randomly, say a mixture of gas molecules will partly unmix. (He also uses an unnecessarily complex argument to put down the creationist argument that uses entropy to argue for divine intervention, as it’s easiest to explain that you aren’t dealing with a closed system, something he doesn’t cover.)
Overall, then, I am not sure who will benefit from this book. There’s not enough detail to interest people studying maths or physics at university, but it becomes too obscure in a number of places for the general reader. A good attempt, but would have benefited from having a co-author who isn’t a mathematician and who could say ‘Sorry, Ian, I don’t get that. Let’s do it differently.’ Bring back Simplicio. (One for the Galileo fans.)
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Review by Brian Clegg
When I bought a second hand copy the first section I read was a formula not an equation. My first thought was that the formula looked wrong and it was - the standard deviation was inside a square root. Re-prints also reprint this error and the publisher didn't acknowledge my e-mail. Perhaps too embarrassed?
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