[259]. There is an astonishing imagination, even in the science of mathematics.... We repeat, there was far more imagination in the head of Archimedes than in that of Homer.—Voltaire.
A Philosophical Dictionary (Boston, 1881), Vol. 3, p. 40. Article “Imagination.”
[260]. As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.—Sylvester, J. J.
A Plea for the Mathematician, Nature, Vol. 1, p. 261; Collected Mathematical Papers, Vol. 2 (Cambridge, 1908), p. 717.
[261]. A marveilous newtrality have these things mathematicall, and also a strange participation between things supernaturall, immortall, intellectuall, simple and indivisible, and things naturall, mortall, sensible, componded and divisible.—Dee, John.
Euclid (1570), Preface.
[262]. Mathematics stands forth as that which unites, mediates between Man and Nature, inner and outer world, thought and perception, as no other subject does.—Froebel.
[Herford translation] (London, 1893), Vol. 1, p. 84.
[263]. The intrinsic character of mathematical research and knowledge is based essentially on three properties: first, on its conservative attitude towards the old truths and discoveries of mathematics; secondly, on its progressive mode of development, due to the incessant acquisition of new knowledge on the basis of the old; and thirdly, on its self-sufficiency and its consequent absolute independence.—Schubert, H.