Mathematical activity has taken the forms of a science, a philosophy and an art. - George Frederick James Temple

For the great majority of mathematicians, mathematics is... a whole world of invention and discovery—an art. The construction of a new theorem, the intuition of some new principle, or the creation of a new branch of mathematics is the triumph of the creative imagination of the mathematician, which can be compared to that of a poet, the painter and the sculptor.

The brilliant summaries by Bourbaki (1969) and Weyl (1951)... set a high standard of exposition, but... there is room for a history of mathematical ideas which will demand less mathematical expertise and offer a more detailed account of the motivation of research.

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.