Synopses & Reviews
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.
Synopsis
This book aims to explain, in clear non-technical language,what it is that mathematicians do, and how that differs from and builds on the mathematics that most people are familiar with from school. It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.
Synopsis
Includes bibliographical references (p. 139-140) and index.
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 mathematicians".
Table of Contents
1. Models
2. Proof
3. Algorithms
4. Generalization
5. Sameness and similarity
6. Invariants
7. Orders of Magnitude
8. Numbers
9. Limiting processes
10. Dimension
11. Manifolds
12. Differential equations
13. Probability
14. The life of a mathematician
15. The philosophy of mathematics