# Hermann Weyl

## A Quote by Hermann Weyl on accidents, birth, certainty, community, effort, evolution, feeling, freedom, history, imagination, individuality, mind, necessity, questions, and time

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.

Source: 1951

Contributed by: Zaady

## A Quote by Hermann Weyl on acceptance, aim, feeling, force, ideas, proof, truth, understanding, and virtue

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.

Source: Unterrichtsblätter für 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.

Contributed by: Zaady

## A Quote by Hermann Weyl on generations, mathematics, and understanding

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]

Source: The American Mathematical Monthly, v. 100. p. 93.

Contributed by: Zaady

## A Quote by Hermann Weyl on health, ideas, and logic

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.

Source: The American Mathematical Monthly, November, 1992.

Contributed by: Zaady

## A Quote by Hermann Weyl on machines, principles, proof, and simplicity

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.

Source: Unterrichtsblätter für 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.

Contributed by: Zaady

## A Quote by Hermann Weyl on work

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.

Source: an obituary by Freeman J. Dyson in Nature, March 10, 1956.

Contributed by: Zaady

## A Quote by Hermann Weyl on meaning and simplicity

. . . 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.

Source: "Mathematics and the Laws of Nature" in The Armchair Science Reader, New York: Simon and Schuster, 1959.

Contributed by: Zaady

## A Quote by Hermann Weyl on books, engineering, income, and laws

Our federal income tax law defines the tax y to be paid in terms of the income x; it does so in a clumsy enough way by pasting several linear functions together, each valid in another interval or bracket of income. An archeologist who, five thousand years from now, shall unearth some of our income tax returns together with relics of engineering works and mathematical books, will probably date them a couple of centuries earlier, certainly before Galileo and Vieta.

Source: The Mathematical Way of Thinking, an address given at the Bicentennial Conference at the University of Pennsylvania, 1940.

Contributed by: Zaady