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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.

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.

ByA customeron January 10, 1997

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!

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!

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ByJames M. Cargalon September 8, 2000

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).

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ByA customeron September 7, 1998

An interesting review of the world of numbers from a pair of respected mathematicians. I E-mailed John Conway a question related to the book and he responded! The book opens many doors to higher mathematics, particularly number theory, the queen of mathematics.

The historical review makes the book a good addition to public libraries and high school libraries.

I particularly liked the review of Gregory Numbers.

It will wake you up mathematically even with a background of high school mathematics.

Teachers should find it useful to augment ciriculums in high school and college math classes.

Richard Brown Research Director 1248 Institute Charleston, SC

The historical review makes the book a good addition to public libraries and high school libraries.

I particularly liked the review of Gregory Numbers.

It will wake you up mathematically even with a background of high school mathematics.

Teachers should find it useful to augment ciriculums in high school and college math classes.

Richard Brown Research Director 1248 Institute Charleston, SC

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Byunraveleron August 29, 2001

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.

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ByA customeron November 17, 1999

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.

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ByA customeron March 17, 1999

The authors present novel and surprising results about different varieties of numbers, with enough elementary discussions to provide readers with a high school background their money's worth. Prime numbers, Fibonacci numbers, Catalan numbers, Fermat numbers, imaginary numbers, infinite numbers, games, counting, patterns, etc. are included. The range of material includes much that will appeal to the expert as well as the novice.

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ByA customeron March 17, 1999

The authors present novel and surprising results about different varieties of numbers, with enough elementary discussions to provide readers with a high school background their money's worth. Prime numbers, Fibonacci numbers, Catalan numbers, Fermat numbers, imaginary numbers, infinite numbers, games, counting, patterns, etc. are included. The range of material includes much that will appeal to the expert as well as the novice.

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ByA customeron July 11, 1999

I am always fascinated by the occasional use of certain numbers within chapter titles, and this book put me in mind of that writing device. I enjoyed the work and recommend that it be read.

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