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?").