“There is a mistake into which several have fallen, and have deceived others, and perhaps themselves, by clothing some false reasoning in what they called a mathematical dress, imagining that by the application of mathematical symbols to their subject, they secured mathematical argument. This could not have happened if they had possessed a knowledge of the bounds within which the empire of mathematics is contained. That empire is sufficiently wide, and might have been better known, had the time which has been wasted in aggressions upon the domains of others, been spent in exploring the immense tracts which are yet untrodden.”
Source: On the Study and Difficulties of Mathematics (1831), Ch. I.
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Augustus De Morgan 41
British mathematician, philosopher and university teacher (… 1806–1871Related quotes

Quoted by C. S. Hastings in "Biographical Memoir of Josiah Willard Gibbs 1839-1903," National Academy of Sciences Biographical Memoirs, vol. VI (Washington, D.C.: National Academy of Sciences, 1909), p. 390. Complete memoir http://books.nap.edu/html/biomems/jgibbs.pdf
Attributed

Lecture on "Electrical Units of Measurement" (3 May 1883), published in Popular Lectures Vol. I, p. 73, as quoted in The Life of Lord Kelvin (1910) by Silvanus Phillips Thompson

Footnote: In the future by 'mathematics' will always be meant 'pure mathematics'.
The Foundations of Mathematics (1925)
W. V. D. Hodge, Changing Views of Geometry. Presidential Address to the Mathematical Association, 14th April, 1955, The Mathematical Gazette 39 (329) (1955), 177-183.

Source: Adventures of a Mathematician - Third Edition (1991), Chapter 3, Travels Abroad, p. 52

Source: 1950s, Portraits from Memory and Other Essays (1956), p. 53
“The great advances in mathematics have not been made by logic but by creative imagination.”
100 Years of Mathematics: a Personal Viewpoint (1981)
Context: Logical analysis is indispensable for an examination of the strength of a mathematical structure, but it is useless for its conception and design. The great advances in mathematics have not been made by logic but by creative imagination.