“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 Morgan41
British mathematician, philosopher and university teacher (… 1806–1871Related quotes
Josiah Willard Gibbs (1839–1903) physicist
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 <br class="br">Attributed
William Thomson (1824–1907) British physicist and engineer
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
Frank P. Ramsey (1903–1930) British mathematician, philosopher
Footnote: In the future by 'mathematics' will always be meant 'pure mathematics'.
The Foundations of Mathematics (1925)
W. V. D. Hodge (1903–1975) British mathematician
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.
Stanislaw Ulam (1909–1984) Polish-American mathematician
Source: Adventures of a Mathematician - Third Edition (1991), Chapter 3, Travels Abroad, p. 52
Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist
Source: 1950s, Portraits from Memory and Other Essays (1956), p. 53
Harold Koontz (1909–1984)
Source: "The Management Theory Jungle," 1961, p. 181
“The great advances in mathematics have not been made by logic but by creative imagination.”
George Frederick James Temple (1901–1992) British mathematician
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.