There is the definition [of mathematics], boldly proposed by Pierce that 'Mathematics is the science which draws necessary conclusions', and more explicitly formulated by Russel that 'Pure Mathematics is the class of all propositions of the form "p implies q"... it was... the purpose of Russell's treatise to provide a complete, exact and convincing justification of this definition... instead, he and Whitehead collaborated to give a magisterial account of the Principia Mathematica.
British mathematician (1901–1992)
George Frederick James Temple (December 2, 1901-January 30, 1992) was an English mathematician. He was President of the London Mathematical Society in the years 1951-1953 and recipient of the Sylvester Medal in 1969.
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As a science mathematics has been adapted to the description of natural phenomena, and the great practitioners in this field... have never concerned themselves with the logical foundations of mathematics, but have boldly taken a pragmatic view of mathematics as an intellectual machine which works successfully. Description has been verified by further observation, still more strikingly be prediction, and sometimes, more ominously, by control of natural forces. Happily, unresolved problems... still remain as challenges.
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.