George Frederick James Temple - Mathematical Quotes

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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.

George Frederick James Temple
Logical analysis is indispensable for an examination of the strength of a mathematical structure, but it is useless for its conception and design. The great advances in mathematics have not been made by logic but by creative imagination.

George Frederick James Temple
The history of mathematics throws little light on the psychology of mathematical invention.

George Frederick James Temple
What would geometry be without Gauss, mathematical logic without Boole, algebra without Hamilton, analysis without Cauchy?

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.

George Frederick James Temple
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.

George Frederick James Temple
The concept of 'number' in its most elementary sense as the signless integer appears to be an immediate abstraction from quantitative reality subjected to processes of counting and measurement. Vulgar fractions arise from division of a quantity into equal parts. But in what sense is zero a number? Are there negative numbers? Are there numbers corresponding to incommensurable ratios? Each question requires for its solution a fresh exercise of that kind of creative imagination which we call mathematical abstraction.

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

George Frederick James Temple
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.

George Frederick James Temple