When I was a student, there was a holy trinity of popular maths authors: Douglas R Hofstadter, Martin Gardner, and Ian Stewart.

Those were the bad old days, before geekery was cool – no Festival of the Spoken Nerd, no Marcus du Sautoy ((Well, there was a Marcus du Sautoy, but he wasn’t on the pop sci shelves.)), no MathsJam… back then, good maths books were furtively swapped among the maths department. If you wanted to buy one in the bookshop, you’d probably try to wrap it in a porn mag just to avoid the embarrassment.

Gardner died in 2010. Hofstadter is still an active researcher and author, but never really regained the popularity of Godel, Escher, Bach. Stewart, meanwhile, has continued to crank out book after article after book.

I think some people suppose there’s a trade-off between quantity and quality, but I’ve never bought into it: I’ve always been more of a ‘throw enough mud at the wall and eventually you’ll get really good at throwing mud at the wall’ sort of guy. And Stewart is really good at throwing mud at the wall.

Seventeen Equations that Changed the World does what it says on the tin – it tells you about 17 equations spanning the history of maths from ancient Greece (or before) to the modern world. He doesn’t just explain what the equations mean (if there’s one weakness in the book, it’s the set-up of the equations themselves – arrows pointing to all the ts saying ‘time’ don’t really help to grok the equation unless you already do), but explores their history, the problems they were aiming solve, and the problems they actually solved.

It paints a realistic picture of maths (and physics), too: a lot of dead-ends and mistaken hypotheses, a lot of assumptions that turned out to be harmful in the end (I’m looking at you, Black, Scholes and Merton), and a lot of correct solutions overlooked because of the prevailing orthodoxy of the day. Science is full of mistakes: it’s just a matter of reducing them.

It’s an engaging book – I (obviously) am pretty good at maths and like to think I have a pretty wide range of understanding and reading; I was expecting to be entertained, or else I’d not have borrowed it (thanks, Barney), but I learned a lot more than I expected to, especially about the topology of space travel – one area that I’d expect to be able to hold my own.

I think 17 Equations works at all manner of levels – if you’re a mathematical beginner, you’ll find enough hooks to get you interested, but you’ll find yourself coming back to it as you develop your skills to understand more deeply.

Good read. Five stars.

* Edited 2014-05-05 to fix a footnote.

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