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
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!