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By Howard W. Eves

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The first use of undecidable properties of effectively presented objects (such as the decimal expansion of π) occurs in Brouwer (1908 [/1975]). ” is the unsolicited exclamation. The response is not to a painting, a breathtaking view or a flawless musical performance, but rather to a mathematical statement or a mathematical proof. What brings such aesthetic pleasure to a mathematician or to those who wish to appreciate mathematics and engage in it? Beautiful Statements A simple, yet profound statement can evoke awe.

24 Mathematics and the Aesthetic Hardy’s Apology Correspondingly, G. H. Hardy, the leading British analyst of the first half of the twentieth century, was also a stylish author who wrote compellingly in defence of pure mathematics. He observed that: All physicists and a good many quite respectable mathematicians are contemptuous about proof. (1945/1999, pp. 15-16) His memoir, entitled A Mathematician’s Apology, provided a spirited defence of beauty over utility: Beauty is the first test. There is no permanent place in the world for ugly mathematics.

P. 210) However, in conclusion, and to avoid possible accusations of mawkishness at the close, I also quote Jerry Fodor (1985): It is, no doubt, important to attend to the eternally beautiful and to believe the eternally true. But it is more important not to be eaten. (p. 4) Notes [1] This quotation is commonly attributed to Gauss, but it has proven remarkably resistant to being tracked down. Arber, the citation I give here, a philosopher of biology, acknowledges in a footnote (p. 47) that, “the present writer has been unable to trace this dictum to its original source”.

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