Product Description

The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questions about the mathematical community (such as "Is it true that mathematicians burn out at the age of 25?")

Product Details

• Amazon Sales Rank: #5339 in Books
• Published on: 2002-08-22
• Number of items: 1
• Binding: Paperback
• 160 pages

Synopsis
The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questions about the mathematical community (such as "Is it true that mathematicians burn out at the age of 25?").

About the Author
Timothy Gowers is Rouse Ball Professor of Mathematics at Cambridge University and was a recipient of a Fields Medal for Mathematics in 1998, awarded for 'the most daring, profound and stimulating research done by young mathematicians'.

Customer Reviews

Making Sense of Mathematics
I have become addicted to the "Very Short Introduction" series, offering the knowledge-hungry layman a great way to gain insight into a wide variety of topics. For me, mathematics is a subject which I was happy to close the book on in upper school, and it seems I was not alone in lacking enthusiasm for the subject which was impressed upon hapless students as being so important (why maths is so dreaded by many is a question this book seeks to answer, amongst many other "FAQ's" of this kind).

Rather than presenting a mass of complex formulae to prove various points, the book takes the approach of explaining the practical applications of mathematics, such as why modelling is relevant in many different situations, and how an understanding of patterns can be of value. Teaching mathematics from such a practical stand-point is a trick modern school education may be missing, yet the book suggests this might be the key for a new generation to understand what's being taught and actually getting excited about the subject.

Rather than being a dry read best left for boffins and insomniacs, this is a book which provokes thought and puts this fascinating subject in a whole new light.

Pragmatic Mathematics
An introduction to mathematics could be just that; elementary arithmetic and geometry, or it could be an outline history or finally, it could introduce the philosophical aspects of the subject. Gowers does none of those, although he does touch on the history and philosophy of mathematics. This is really an introduction to higher mathematics, for readers who have reached what in Britain is GCSE standard, roughly eleventh grade in the US.

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
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