Timothy Gowers

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 listeners 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....

This text features nearly 200 entries which introduce basic mathematical tools and vocabulary, trace the development of modern mathematics, define essential terms and concepts and put them in context, explain core ideas in major areas of mathematics, and much more.