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Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics. - [Abstract] It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences. - [Mathematics] "Obvious" is the most dangerous word in mathematics. - [Arithmetic] The Handmaiden of the Sciences. - title of book, about mathematics [Mathematics] I have always hated machinery, and the only machine I ever understood was a wheelbarrow, and that but imperfectly. - "Mathematical Circles Adieu" by H. Eves [Machines] Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. - "Return to Mathematical Circles" by H. Eves [Assumptions] The longer mathematics lives the more abstract--and therefore, possibly also the more practical--it becomes. - "The Mathematical Intelligencer" (vol. 13, no. 1) [Abstract] Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos. - Mathematics, Queen and Servant of Science (p. 164) [Groups]
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