This book is meant, first of all, for able school children of 14 and over and first year undergraduates who are interested in mathematics and would like to learn something of what it looks like at a higher level. There exist several books with a similar aim. I remember with particular pleasure from my own childhood the book From Simple Numbers to the Calculus by Colerus with its uncompromising opening:

In Appendix Al.l I list and discuss some of them. However, the aim is so worthwhile and the number of such books so limited that I feel no hesitation in adding one more.

In many American universities there are courses known universally, if not officially, as ‘Maths for poets’. This book does not belong to that genre. It is intended, rather, as ‘Maths for mathematicians’ — for mathematicians who know very little mathematics as yet, but who, perhaps, will one day give lectures which the present author attends open-mouthed with admiration†.

I hope that this book will also be enjoyed by my fellow professionals and by those general readers who value mathematics without fearing it‡.