Logical analysis is indispensable for an examination of the strength of a mathematical structure, but it is useless for its conception and design. Th… - 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.

From Pythagoras to Boethius, when pure mathematics consisted of arithmetic and geometry while applied mathematics consisted of music and astronomy, mathematics could be characterized as the deductive study of 'such abstractions as quantities and their consequences, namely figures and so forth' (Acquinas ca. 1260). But since the emergence of abstract algebra it has become increasingly difficult to formulate a definition to cover the whole of the rich, complex and expanding domain of mathematics.

What would geometry be without Gauss, mathematical logic without Boole, algebra without Hamilton, analysis without Cauchy?