_Presidential Address British Association for the Advancement of Science, Section A, (1897); Nature, Vol. 56, p. 378._ =705.= The nineteenth century which prides itself upon the invention of steam and evolution, might have derived a more legitimate title to fame from the discovery of pure mathematics. --RUSSELL, BERTRAND. _International Monthly, Vol. 4 (1901), p. 83._ =706.= One of the chiefest triumphs of modern mathematics consists in having discovered what mathematics really is. --RUSSELL, BERTRAND. _International Monthly, Vol. 4 (1901), p. 84._ =707.= Modern mathematics, that most astounding of intellectual creations, has projected the mind’s eye through infinite time and the mind’s hand into boundless space.--BUTLER, N. M. _The Meaning of Education and other Essays and Addresses (New York, 1905), p. 44._ =708.= The extraordinary development of mathematics in the last century is quite unparalleled in the long history of this most ancient of sciences. Not only have those branches of mathematics which were taken over from the eighteenth century steadily grown, but entirely new ones have sprung up in almost bewildering profusion, and many of them have promptly assumed proportions of vast extent.--PIERPONT, J. _The History of Mathematics in the Nineteenth Century; Congress of Arts and Sciences (Boston and New York, 1905), Vol. 1, p. 474._ =709.= The Modern Theory of Functions--that stateliest of all the pure creations of the human intellect.--KEYSER, C. J. _Lectures on Science, Philosophy and Art (New York, 1908), p. 16._ =710.= If a mathematician of the past, an Archimedes or even a Descartes, could view the field of geometry in its present condition, the first feature to impress him would be its lack of concreteness. There are whole classes of geometric theories which proceed not only without models and diagrams, but without the slightest (apparent) use of spatial intuition. In the main this is due, to the power of the analytic instruments of investigations as compared with the purely geometric. --KASNER, EDWARD. _The Present Problems in Geometry; Bulletin American Mathematical Society, 1905, p. 285._