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(Davis and Hersh,1980,page 85)
The mathematical old humanists celebraic the intrinsic beauty of pure mathematics. Many mathematicians have affirmed the elegance, beauty, balance and depth of mathematical results (Davis and Hersh,1980).
Many pure mathematicians regard their speciality as an art, and one of their terms of highest praisc for another’s word is ‘beautiful’.
(Halmos,1981,page 15)
Beauty is the final test: there is no permanent place in the word for ugly mathematics
(Hardy, quoted in Steen, 1981, page 36)
Like the other humanists, the mathematical varicty often hold elitist views as to who can contribute to high culture. Thus according to the mathematician Adler:
Each generation has its few great mathematicians, and mathematics would not even notice the absence of the others… There is never is any doubt about who is and who is not a creative mathematician, so all that is required is to keep track of the activities of these of there few men
(Adler, quoted in Davis and Hersh, 1980,page 61)
The influence of the mathematical old humanists, and their values, has been evident in a number of official reports on education, such as the Spens Report of 1938:
No school subject, except perhaps classics, has suffered more then mathematics from secondary rather than primary aims, and to emphasise extraneous rather than intrinsic values. As taught in the past, it has been informed too little by general ideas… Ii is sometimes utilitarian, even crudely so, but ignores considerable truths in which actual mathematics subserves important activities and adventures of civilized man…We believe that school mathematics will be put on as footing only when teachers agree that it should be as art and physical science should be taught, because it is one of the main lines which he creative spirit of man has followed in its development.
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