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G. The Mathematical Old Humanists
Pure knowledge, including mathematics, is claimed to originate in societies which separated the work of the hand and brain(Restivo,1985). In societies such as Ancient Greece, intellectual work was dissociated from manual work, becoming the province of the more powerful social class, the elite, closely associated with the rulers of society.
Through the millennia, the study of pure mathematics has been associated with high culture and the liberal education of elite. Plato’s Academy bore a sign over the portal denying entry to any who had not studied geometry. The Roman Boethius made sure of the place given to mathematics in a liberal education. He adjoined the mathematical quadrivium of arithmetic, geometry, music and astronomy to the trivium at the core of liberal curriculum. Beyond the curriculum of his day (c.480-524), Boethius influenced British education for the following millennium, through his textbooks (Howson,1982).
Although its fortunes varied, pure mathematics was a central part of the public school curriculum throughout the Victorian era, largely represented by Euclid’s Elements. It was valued for its contribution to the development of thinking, as the Royal Commission of 1861 reported :
Mathematics at least have established a title of respect as an
instrument of mental discipline; they are recognized and honoured at
the universities.
(Ministry of Education,1958,pages2-3)
The teaching of geometry was criticized by the Taunton Commission of 1868, but there was no threat to the purity of the syllabus in the nineteenth century (Howson, 1982). Indeed, only in the twentieth century did elements of applied mathematics begin to be included in the selective school curriculum, leading to the Applied Mathematics ‘A’ level course in the 1950s (Cooper, 1985).
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