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Weyl, Hermann (1885 - 1955)
We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.
Unterrichtsblatter fur Mathematik und Naturwissenschaften, 38, 177-188 (1932). Translation by Abe Shenitzer appeared in The American Mathematical Monthly, v. 102, no. 7 (August-September 1995), p. 646.
Weyl, Hermann (1885 - 1955)
A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details.
Unterrichtsblatter fur Mathematik und Naturwissenschaften, 38, 177-188 (1932). Translation by Abe Shenitzer appeared in The American Mathematical Monthly, v. 102, no. 7 (August-September 1995), p. 646.
Weyl, Hermann (1885-1955)
The constructs of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow mathematician interested in the constructs of his imagination. We cannot help the feeling that certain mathematical structures which have evolved through the combined efforts of the mathematical community bear the stamp of a necessity not affected by the accidents of their historical birth. Everybody who looks at the spectacle of modern algebra will be struck by this complementarity of freedom and necessity.
Weyl, Hermann (1885 - 1955)
My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful.
In an obituary by Freeman J. Dyson in Nature, March 10, 1956.
Weyl, Hermann (1885 - 1955)
... numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.
"Mathematics and the Laws of Nature" in The Armchair Science Reader, New York: Simon and Schuster, 1959.
Weyl, Hermann (1885 - 1955)
Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or achievements of mathematics in the last 50 years.
[Said in 1950]
The American Mathematical Monthly, v. 100. p. 93.
Weyl, Hermann (1885 - 1955)
Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
The American Mathematical Monthly, November, 1992.
Whewell
Nobody since Newton has been able to use geometrical methods to the same extent for the like purposes; and as we read the Principia we feel as when we are in an ancient armoury where the weapons are of gigantic size; and as we look at them we marvel what manner of man he was who could use as a weapon what we can scarcely lift as a burden.
In E. N. Da C. Andrade "Isaac Newton" in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Whitehead, Alfred North (1861 - 1947)
The science of pure mathematics ... may claim to be the most original creation of the human spirit.
Science and the Modern World.
Whitehead, Alfred North (1861 - 1947)
Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.

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