[1409]. Since antiquity mathematics has been regarded as the most indispensable school for philosophic thought and in its highest spheres the research of the mathematician is indeed most closely related to pure speculation. Mathematics is the most perfect union between exact knowledge and theoretical thought.—Curtius, E.
Berliner Monatsberichte (1873), p. 517.
[1410]. Geometry has been, throughout, of supreme importance in the history of knowledge.—Russell, Bertrand.
Foundations of Geometry (Cambridge, 1897), p. 54.
[1411]. He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its side.—Plato.
Quoted by Sophie Germain: Mémoire sur les surfaces élastiques.
[1412]. Mathematics, considered as a science, owes its origin to the idealistic needs of the Greek philosophers, and not as fable has it, to the practical demands of Egyptian economics.... Adam was no zoölogist when he gave names to the beasts of the field, nor were the Egyptian surveyors mathematicians.—Hankel, H.
Die Entwickelung der Mathematik in den letzten Jahrhunderten (Tübingen, 1884), p. 7.
[1413]. There are only two ways open to man for attaining a certain knowledge of truth: clear intuition and necessary deduction.—Descartes.