The numbers have always been a source of wonder, and the sequence of integers whose unending procession is contrasted with the finiteness of human experience is surely the first place where mathematics appears as the product of soaring imagination. Children as well as adults raise many questions about large numbers. It has been my idea to answer these questions and at the same time to reveal a bit of the modern mathematical horizon via such questioning.

I have used the idea of large numbers as a binding theme for this book and, employing only the simplest materials, have tried to produce a feeling for numbers, their magnitude, and their growth. By means of approximate computation and estimation, I have suggested that numbers may be handled lightly and efficiently as friends with whom one discourses rather than as enemies against whom one struggles. In the later sections, large (and small) numbers take their place in mathematics and science, and are presented in a way which anticipates certain developments in abstract algebra and analysis and numerical analysis. I have tried to intimate—and this also has been a major aim—that mathematics is a living thing that grows and changes with the generations.

The problems are an integral part of the book. This does not mean that they must all be worked or be handled in the same manner. Some are meant to be read for they drive home a point or contain additional lore. Some are meant to be grappled with.