In this book we treat mathematical ideas in a historical setting. Our principal themes are the concepts of number (Chapters 1-7) and infinity (Chapters 8-11). Within this context we have selected a number of topics for discussion with an eye to their history. Mathematical knowledge of roughly A-level standard is presupposed, and the book is addressed primarily to mathematics students in the sixth form at school and the first year at university who have an interest in historical aspects of their subject. The reader is presented with mathematical argument from time to time so that he may rise above the level of generalities and anecdotes. We hope that this will not deter any intelligent layman who wishes to find out about the development of ideas in mathematics. The more technical passages can...