Philosophically, Gowers is a pragmatist. To him, problematic concepts like infinity and irrational numbers have meaning in as much as they are useful, and are true in as much as they give true results. As a European, Gowers credits Wittgenstein with these ideas. An American author would have credited William James. Gowers sidesteps rather than resolves philosophical problems, thus giving reassurance to mathematicians and irritation to philosophers.

The book is a random selection of topics rather than a continuous narrative, but succeeds because each topic is fascinating and the writing is clear throughout.

Under "Further Reading", Gowers includes his own website address, where you can find sections that did not make it into the book. What a good idea! The site is as full of good stuff as the book, and gives links to further sites that will give you as much mathematics as you will ever want.


Great book   December 28, 2004
 4 out of 4 found this review helpful

This book demystifies puzzling concepts such as infinity, curved space, n-dimensional space and fractional dimensions. His emphasis on the abstract method - the focus on what mathetical objects DO rather than what they really ARE - as the key to understanding all these concepts is amazingly powerful, truly an eye-opener.

A basic knowledge of mathematics is an advantage


A Very Very Good Introduction   January 7, 2004
 6 out of 7 found this review helpful

I've recently gotten interested in Mathematics again (after finding it very difficult and boring at school) and was looking for a good general book to serve as an introduction. I really don't think I could have done any better than this. If you have even the slightest interest/curiosity about maths - you should buy this book.