There is the definition [of mathematics], boldly proposed by Pierce that 'Mathematics is the science which draws necessary conclusions', and more exp… - George Frederick James Temple

At each stage of in the advance of mathematical thought the outstanding characteristics are novelty and originality. That is why mathematics is such a delight to study, such a challenge to practise and such a puzzle to define.

The professional mathematician can scarcely avoid specialization and needs to transcend his private interests and take a wide synoptic view of the whole landscape of contemporary mathematics. His scientific colleagues are continually seeking enlightenment on the relevance of mathematical abstractions. The undergraduate needs a guidebook to the topography of the immense and expanding world of mathematics. There seems to be only one way to satisfy these varied interests... a concise historical account of the main currents... Only by a study of the development of mathematics can its contemporary significance be understood.

This book... is primarily and essentially an account of the discovery or invention of mathematical concepts, and the historical material is... divided and classified, neither chronologically nor biographically, but philosophically.