on 13 May 2009
This book is great for dipping into and presents a host of accessible results. The first chapter ("The Romance of Numbers") is tedious and can be skipped if you're more interested in the mathematics itself. What then follows is an interesting tour of geometry, prime numbers, modular arithmetic and imaginary numbers. There are no exercises, but many of the presented results can be self-set as challenges. The book then moves on into transcendental numbers, varieties of infinity and a survey of the surreals. This material is denser and more has to be taken on trust. It is arguably therefore less satisfying as a result.
There are few books on the market that cover this range of material at this level. There is little of the "gee whizz" that makes much of the popular literature so frustrating if you wish to go further but neither is it academic in its approach.
on 22 August 2011
I really enjoyed this book. John Conway is one of the greatest living mathematicians and Richard Guy has also done some very interesting work too. They manage to describe really interesting and often quirky results very clearly and simply. You get a real insight into how they think.
I found the book very readable. It's also well illustrated and produced. Although it does go into some quite deep areas you can start any chapter quite easily and move on if you find your head starting to spin. Unlike some popular science books, this is the real stuff and it will repay the time spent understanding it.