In my opinion the two greatest weaknesses in our present mathematics education are the lack of training in creative thinking and the lack of practice in technical writing. I hope that the use of this little book can help make up for both of these deficiencies.

Famed mathematician Donald Knuth presents the discovery of Conway's "surreal numbers" -- a number system in which each number consists of a set of numbers smaller than it, and a set of numbers greater than it -- as a dialogue between a couple on a secluded beach. The objective is to provide a reasonably accessible example of how mathematical discoveries are made, so Alice and Bill also try incorrect approaches and figure out how to fix them.

Unfortunately, this book is priced as a textbook: a very expensive slim paperback. That said, it's probably the cheapest of all Knuth's technical books, and you'll find it interesting if you know a little bit of mathematical notation and want to understand something of the process of mathematics. It's a pity that the dialogue has fallen out of favour as an explanatory tool; I'd like to read more papers written like this...

ISBN 0201038125.