Stephen Hawking wrote A Brief History of Time with only a single equation, accepting that more might “scare the punters off”. Bill Bryson wrote A Short History of Nearly Everything with neither equations nor pictures. Ian Stewart is therefore being very brave writing a popular science book which explains the mathematical basis for our modern world, unashamedly focusing on the key equations themselves.

That said, the equations are used more as milestones than intensively studied subjects. This is not a “book full of maths”, and each chapter is largely a textual exploration around the subject starring the featured equation, explaining what it means, and what it led to.

The scope is vast, from Pythagoras through to the underpinnings of quantum theory, chaos and derivatives trading, taking in key scientific developments and their mathematical explanations along the way. Stewart does a remarkable job of compacting this scope into just 17 chapters and about 300 pages.

If you’re a skilled mathematician you will gloss over the maths and still take value from the following discussions. If, however, your maths is more limited or, like mine, rather rusty, you’ll find you don’t need to follow all the mathematical details. You don’t need to really understand about grads, divs and curls, for example, to appreciate the similarity in “shape” between the key equations in several different areas of science. The author does a very fine job of both explaining this structure, and also where the reader must understand, and where detailed understanding is less important.

Some of the explanations are quite complex, especially where Stewart is exploring the most recent applications of older ideas. I did get lost a couple of times and had to re-read short sections, but overall I came away thinking that I had built a decent grasp.

The book has an admirable focus on the practical applications of science, but some of this is presented with such limited detail that in a couple of places it devolves into lists of applications rather than real explanations. As well as positive stories, Stewart is not afraid to show where mis-interpretation of the mathematics or its limitations has failed us, most notably in the last chapter on financial derivatives and how their abuse has caused the current crises.

Although eminently readable and often amusing, this book is best read in chunks of a couple of chapters at a time, allowing the ideas to sink in. Do so, and invest a little effort, and you’ll be well rewarded.