„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.“

Fuente: On the Study and Difficulties of Mathematics (1831), Ch. I.

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Augustus De Morgan8
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„If I have had any success in mathematical physics, it is, I think, because I have been able to dodge mathematical difficulties.“

—  Josiah Willard Gibbs physicist 1839 - 1903

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
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„The great advances in mathematics have not been made by logic but by creative imagination.“

—  George Frederick James Temple British mathematician 1901 - 1992

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Contexto: 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.

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„The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics.“

—  Benjamin Peirce, Linear Associative Algebra

§ 2.
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Contexto: 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.

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„The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future;“

—  Eric Temple Bell mathematician and science fiction author born in Scotland who lived in the United States for most of his life 1883 - 1960

Fuente: The Development of Mathematics (1940), p. 283
Contexto: The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future; and should analysis ever appear to be without or blemish, its perfection might only be that of death.

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