The Book of Numbers

This book is excellent. I am not a mathematician; my Ph.D. is in a social science, but my interest in intellectual history made this book worth it for me. The reason that it seems a bit expensive is because the authors use color illustrations. These are really helpful and make the book more exciting. The book is essentially number theory for a lay person. All you need to have is high school level math in order to start enjoying this book, so don't be afraid. Conway and Guy present a fascinating look at what the human intellect can achieve in the realm of abstract thought. Number theory, and mathematics in general, can be mysterioius, artful, and exciting. Highly recommended.

To these "guys", numbers are toys, where the price of possession is nothing but a little knowledge. It is truly astounding, even for veteran mathematicians such as myself, to see how many different sets of numbers there are. They all have a story behind them, and given the multiple uses for so most of them, there are many more yet to be written. Presented in a unique and engaging style that one associates with the authors, the numbers come to life with descriptions that hold your interest and leave you wanting more. The level of demonstration is not extremely technical, being well within the range of anyone who has been exposed to the topics of precalculus. Figures are used extensively, giving a visual interpretation of several ways in which the numbers can be used. Many of the numbers covered in the book are named after the person most responsible for making it famous, an aspiration that most mathematicians would no doubt confess to. In some cases, I was previously unaware of the name assigned to the numbers. When I am in the mood for some light reading in mathematics, my preferred form is some type of listing of the properties of numbers. In this case, I found several hours of enjoyment and recommend it to anyone with similar tastes. Published in Journal of Recreational Mathematics, reprinted with permission.

This is a delightful survey of numbers clearly aimed at as wide an audience as possible. However, as is always the case in such books the book is more formidable than it intends or than it looks. Still it is very friendly especially compared with, say, "Numbers" by Ebbinghays et al. The coverage is wide: primes, reals, Cayley numbers, Eisenstein numbers, polygonal numbers, catalan numbers, Stirling numbers of both types and of course Bell numbers. There are the cardinals and ordinals of Cantor as well as Conway's own surreal numbers. (And an earlier reviewer was correct about misprints and color problems.) I recommend this to anyone whose mathematical maturity is at least as great as basic calculus (and who is interested).

Conway wrote On Numbers and Games. Conway, Guy, and Berlekamp wrote Winning Ways. These groundbreaking books are now hard to find. I hope both will be reprinted soon. The Book of Numbers has a short section on Combinatorial Game Theory -- just a taste. I expected much more about CGT. Still, TBON is an excellent book about numbers. Many diagrams, a lot of top-notch mathematics, and excellent writing fills each chapter. I would recommend this book for any high school student, but it would be quite enjoyable for fans of math at any level.

A personal but fascinating review of numbers: from Egyptian fractions to surreal numbers; from numbers so large they cannot be imagined (and barely be named) to ruler-and-compass; all prefaced by a virtuoso etymologic riff. Beautifully produced, engagingly written, full of new perspectives on old material - and new material too. The book contains so much disparate information that each reader will find something in particular that he or she likes. I do not think I have ever seen a popularization at once so interesting to anyone from bright junior high-school student to a professional mathematician. I have two minor complaints. First, there are some misprints (for example in the description of trisections), and in some of the early diagrams the orange and the red tiles come out looking the same. In view of the extraordinary complexity of the production and in view of the overall visual appeal and clarity of the presentation, these slight errors do not detract from the impact. The more serious problem has to do with the fact that the book is so fascinating that it can be a real time sink. I have personally lost many hours pondering the big (and I mean /big/) numbers Conway and Guy describe, for instance. The book is almost like a CD-ROM game in that one can get completely lost in it for days. It made me wistful, too, that I had not had this book when I was first learning mathematics (also, it could use a few more references to things like Graham's number and surreal asymptotics). Not only that but, despite its fairly hefty price tag, I find myself buying copies for friends - so it can use up not only a lot of time but money too!