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.

Since the day I rescued copies of the original “Mr Tomkins” books from a school library “discard” pile, I’ve always been an enthusiastic reader of books which try to explain advanced science and technology concepts in a fun way, and this book (and it’s newer counterpart about relativity) caught my eye recently.

The concept is simple: Chad Orzel’s dog, Emmy, may be a typical mutt obsessed with walks, squirrels and discarded food, but she’s also intelligent enough to have a basic grasp of quantum concepts, and a view to how they might be exploited in her favour, for example by passing simultaneously around both sides of a tree to catch a squirrel. Each chapter starts with Chad explaining why “it’s not quite like that”, and going on to explain the real physics to her in some detail. This works well, breaking up some quite complex discussions with amusing dialogue between master and hound, and makes the book eminently readable.

The books scores because it’s bang up to date, and goes beyond the basic quantum concepts into more complex areas like decoherence, entanglement and quantum teleportation, supplementing explanations of the basic concepts and “thought experiments” with the details and outcomes of relatively recent experimental verification. Similarly “quantum” is the current buzzword beloved of pseudo-scientific charlatans, and the last chapter is a timely effort to debunk those who abuse it for get-rich-quick schemes and medical quackery.

I also particularly liked the way that the author is not afraid to embrace the concepts of measurement errors and accuracy. These are vital tools to understand how well, or badly, something has been established, and I was very pleased to see such an accessible book using them well.

The explanations themselves are a mixed bunch, some being very complicated and taking me a couple of goes to read and absorb. Given that I probably have rather more background that the target demographic (I do have a good Physics degree, albeit a few years old) this may mean that some readers could struggle with the most complex parts. I suspect a few more diagrams in these areas might have helped. However overall the book succeeds, and will probably prompt keen readers to re-read or seek out secondary explanations where they don’t understand first time.

In the Kindle edition some of the graphics are a page or two adrift of the relevant text, and the footnotes (which often contain important or amusing asides) are presented in a bunch at the end of each chapter, which is not very reader friendly. I suspect the paper version of the book is better in this respect.

This books is well worth reading, and has certainly helped to refresh and update my understanding of a complex field, while giving me a welcome laugh at the dog’s antics. I look forward to reading the relativity volume later this year.