数学者はどんなことを考えているのでしょうか。彼らの考える数学とは、私たちが学校で教わる数学とはどのように異なり、どの部分を礎としたものなのでしょうか。このあたりを専門用語を使わずに説明することを試みます。数学についてもっと知りたいけれど難解で…と思っている読者に、数学の本当に大切な部分を説いてくれる格好の入門書です。
  

• A concise explanation of the differences between advanced mathematics and what we learn at school
• Offers the reader an insight into such seemingly paradoxical concepts as infinity, the square root of minus one, and curved space
• Tackles the sociological questions that arise regarding the mathematical community - e.g. 'Do mathematicians burn out at the age of 25?'
• Clear and non-technical language throughout
• The author received a Fields Medal for Mathematics in 1998, awarded for 'the most daring, profound and stimulating research done by young mathematicians'

  
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?")