This book has been shortlisted for the Royal Society 2015 Winton Prize. When I saw it on the list I thought 'surely that was published more than a year ago', but apparently not. It seems that there is a book with the same title (
Alex Through the Looking Glass), but I don't think I'd seen that. Rather I had probably seen this book in the library this year and not really distinguished it from Bellos' earlier work (
Alex's Adventures in Numberland) - I also probably thought it was aimed at children. I wasn't that impressed with Bellos' earlier book - it will be interesting to see whether this book suits me more.
The introduction suggests that we 'get' maths in the same way that we 'get' a joke. The first chapter looks at the way we think about numbers - how we react to prices, how some numbers are thought to be unlucky. It includes heat maps of the properties we give to the numbers from 1 to 100. It looks interesting, and if the book can continue in this way - looking at the way we think about mathematics, rather than just dealing with its history - then it will definitely be worth reading.
The book covers at many different areas of mathematics, such as power laws, trigonometry conic sections, fractals. There's a look at the nature of negative and imaginary numbers as well as the number
e. The later chapters look at calculus and axiomatics, finishing with a chapter on cellular automata. It's written in an entertaining and accessible way - there are a few equations, but nothing intimidating, and there are plenty of pictures and illustrations.
If I hadn't read about these topics I think I'd find it all very interesting. But I have encountered nearly all of it already. Many authors can make a book interesting even if you know most of its subject matter, but I don't think that Bellos manages to do this. At the start he compares mathematics to comedy, but I suppose if you've heard the jokes before - what made Bourbaki unique amoung his contemporaries? - then they're not so entertaining. At the start Bellos suggested he would illuminate some of the thought processes of mathematicians, but I don't think he did this. OK, so he has a few pages looking at the work of Cédric Villani, but most of the material in the rest of the book is several decades old at least. I wasn't that impressed with his previous book, and this seems to be more of the same. I wouldn't like to put you off reading it if you think it would suit you, but I don't rate it very highly in the list of 2015 Winton prize contenders.