MATHEMATICS QUOTES

The essence of mathematics lies in its freedom. –– Cantor, Georg, Mathematische Annalen, Bd. 21, p.564.

The object of pure Physics is the unfolding of the laws of the intelligible world; the object of pure Mathematics that of unfolding the laws of human intelligence. –– Sylvester, J.J., On a theorem connected with Newton's Rule, etc., Collected Mathematical Papers, Vol. 3, p. 424.

[Mathematics] is that [subject] which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causation. –– Huxley, T. H., The Scientific Aspects of Positivism, Fortnightly Review (1898); Lay Sermons, Addresses and Reviews, (New York, 1872), p. 169.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry. What is best in mathematics deserves not merely to be learned as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement. Real life is, to most men, a long second-best, a perpetual compromise between the real and the possible; but the world of pure reason knows no compromise, no practical limitations, no barrier to the creative activity embodying in splendid edifices the passionate aspiration after the perfect from which all great work springs. Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the natural world. –– Russell, Bertrand, The Study of Mathematics: Philosophical Essays (London, 1910), p.73.