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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?") It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.
About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.
About the Author
Timothy Gowers is Rouse Ball Professor of Mathematics at Cambridge University and was a recipient of the Fields Medal for Mathematics, awarded for 'the most daring, profound and stimulating research done by young mathhematicians'.
Table of Contents
5. Sameness and similarity
7. Orders of Magnitude
9. Limiting processes
12. Differential equations
14. The life of a mathematician
15. The philosophy of mathematics
Most Helpful Customer Reviews
The world of mathematics elicits many different emotions, from fear to reverence, from apprehension to fascination. On a surface this may seem surprising, since mathematics is supposed to deal rational thought, and should be as removed from emotional considerations as it gets. And yet, it is precisely this dispassionate rationality that makes those unaccustomed to mathematical thinking recoil, and those with a mathematical bend of mind rub their hands in glee. For the truth is, mathematical thought relies heavily on emotions, and mathematicians are fascinated with beauty and elegance of mathematical creations. In the book "Mathematics: A Very Short Introduction" the author Timothy Gowers tries to convey some of this beauty. This is a very readable and intelligent short introduction, and probably the best short introduction to mathematics out there. It takes reader through some basic mathematical problems, and showcases the methods and procedures that mathematicians use in their work. If you are math-phobic, you will not have to deal with any complicated mathematical equations, and all of the problems and proofs that are offered in the book are straightforward and intuitive, and require a very minimal level of mathematical knowledge. The fact that the book attempts to "do" mathematics, as opposed to just tell about it, is one of its more rewarding aspects. It makes this an intelligent read, and rewarding no matter whether you are a complete mathematical "outsider" or someone with an advanced degree in a math-intensive field.
An introduction to what mathematics is about and how mathematicians think rather than to mathematics itself. Excellent account. As follow-up Davis/Hersh: Mathematical Experience and Couturat/Robbins are recommended.