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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 abstractand therefore, possibly also the more practicalit 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]

