This has been my “coffee table” book for the last few months, following on from Julian Baggini’s The Pig That Wants to be Eaten. This is because it’s full of lots of little bits, with no overall narrative. It’s not quite a school exercise book, but it does have quite a lot of puzzles for you to think through, some of which require some scribbling with some pen & paper or plugging numbers into a calculator. As well as these, there are lots of little vignettes of mathematical thought which inform but require less input from the reader.
So my initial advice for any readers of this would be get a notepad and some pens and keep them nearby. Fans of recreational mathematics will find much that is familiar here, as some problems recur in just about every such ‘popular’ level book on maths, such as the problem of the bridges of Konigsberg or lots of factoids about pi.
That may sound like damning with faint praise, but there is a depth of mathematics on display here that is rather splendid. Many of the ideas are really quite profound, yet the way they are presented makes them quite accessible. A non mathematician might disagree with me, but it may be interesting to find out from others if there are areas where they get stuck.
There is a general trend for the puzzles to get a little bit more difficult later on in the book. So we are given some treats that will be unfamiliar even to those who did maths at A-level. We deal with topics ranging from geometry, number theory, topology and even some complexity is thrown in at the end.
I probably ought to add that for any sections that ask questions there are answers provided at the back of the book. Most are pretty good, though if the book does have any weaknesses, it is here, where some of the answers are given with not enough explanation. Though for recreational mathematics, one of the litmus tests has to be how well the solution to the Monty Hall problem is described and this one is very fair.
There is a follow-up book that Ian Stewart wrote, in the same vein but with a different set of problems. Given the quality of this work, I will be reading that as well, so you can look forward to seeing another review like this in a few months. For my next coffee table book, though, I will be turning to Plato and a Platypus; a book I searched for for some years but only got my hands on recently.