There are broadly three types of popular maths. There are books like A Brief History of Infinitywhich introduce mathematical concepts and history without actually doing any maths - and these can be fascinating. There are books of recreational maths, like Martin Gardner's classic Mathematical Puzzles and Diversions, or Ian Stewart's Cabinet of Mathematical Curiosities, which explore the weird and wonderful of maths, with a need for a bit of practical working out, but almost always provide plenty of fun along the way. And there are book like the Magic of Maths. (Could I say, by the way, how grateful I am that the UK edition has that 's' on 'maths'.) Almost always written by mathematicians, such books set out to prove to the masses who think that actually getting your hands dirty and doing mathematics is too hard or too boring that it's really easy and enjoyable too.
To give him his due, Arthur Benjamin makes a good stab at this - one of the best I've seen. He tells us we're going to learn clever little tricks that will allow us to do amazing things with mental arithmetic - for instance multiplying surprisingly big numbers in our heads. And he delivers. It really works, and we can amaze ourselves, though probably not our friends, because if other readers are anything like me they will have forgotten most of the techniques by the time they finish the next chapter.
Benjamin also takes on the likes of algebra, Fibonacci numbers, geometry, trigonometry, imaginary numbers, calculus and more. And going on the pages of testimonials from maths professors in the front, this is the kind of thing maths-heavy people love. And that's fine. But for most of us I'd say 80 per cent of the book is not going to be appreciated. Early on, Benjamin tells us we shouldn't mind skipping pages or even chapters. But when you find yourself skipping most of the content, it begins to feel as if it wasn't a great thing to read in the first place.
In one of those fruitless exercises in saying the whole world is your audience, Benjamin comments that the book is for anyone who will one day take a maths course, is taking a maths course or is finished taking maths courses. I'd say the audience is a lot tighter. It's for people who one day will take a maths degree, or took one years ago and wants to reminisce. It's just too number heavy and narrative light to work for me. And I have taken a maths course. But I certainly don't want take another - and this has reminded me why.
I have to emphasise that the book is by no means all bad. Benjamin does introduce some fun, and weird and wonderful stuff, like the apparent demonstration that infinity is equal to -1/12 (though I've seen better explanations of why this demonstration falls apart). But far too often what Benjamin thinks is fun is just 'So what?' to us lesser mortals.