Forward, as quoted by Mario Livio, Is God a Mathematician? (2009)
Ausdehnungslehre (1844)
“There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.”
As quoted in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane, Springer (1998 [1975]), p. 225; also in Stanley Gudder, A Mathematical Journey, McGraw-Hill (1976), p. 36.
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Nikolai Ivanovich Lobachevsky 1
Russian mathematician of Ukrainian origin 1792–1856Related quotes
in What is Mathematics, in [Hilary Putnam, Mathematics, matter, and method, Cambridge University Press, 1979, 0521295505, 60]
1970s, How do we tell truths that might hurt? (1975)
" New Textbooks for the "New" Mathematics http://calteches.library.caltech.edu/2362/1/feynman.pdf", Engineering and Science volume 28, number 6 (March 1965) p. 9-15 at p. 14
Paraphrased as "Precise language is not the problem. Clear language is the problem."
Quote from Van Doesburg's article 'Elementarism as real art', in: 'Painting and plastic art' - Rome, July 1926, in De Stijl', series XIII, 1 75-6, 1926, pp. 35–43
1926 – 1931
Source: 1950s, General Systems Theory - The Skeleton of Science, 1956, p. 197: Opening sentences
Source: "The Latest Attack on Metaphysics" (1937), p. 133.
The Notebooks of Leonardo da Vinci (1883), XIX Philosophical Maxims. Morals. Polemics and Speculations.
§ 2.
Linear Associative Algebra (1882)
Context: The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.