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Hermann Weyl
(9 Nov 1885 - 8 Dec 1955)
German-American mathematician who made contributions to differential geometry, the theory of continuous groups, differential equations, relativity, quantum mechanics and the philosophy of mathematics.
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Science Quotes by Hermann Weyl (14 quotes)
~~[Misattributed]~~ It was Galileo who said, “Measure what is measurable, and make measurable what is not so.”
— Hermann Weyl
No, Galileo did not “say” or write these words, from transcript of a radio talk 'Mathematics and the Laws of Nature', collected in Warren Weaver (ed.), The Scientists Speak (1947). Reprinted in Isabel S. Gordon and Sophie Sorkin (eds.), The Armchair Science Reader (1959), 301. Weyl is perhaps the source of the quotation marks that have resulted in the quote being attributed to Galileo. It is, in fact, a translation of the original French, “Galilée … déclare que dans tous ces phénomènes il faut mesurer tout ce qui est mesurable, et tâcher de rendre mesurable tout ce qui ne l’est pas directement,” in Thomas-Henri Martin, Galilée: Les Droits de la Science et la Méthode des Sciences Physiques (1868), 289. In English: Galileo … asserts that in all these phenomena we must measure all that is measurable, and try to make measurable all that is not directly measurable. Notice the origin statement is not enclosed in quotation marks; they are the biographer’s own words, not Galileo’s. These words do not come verbatim from any known work by Galileo, and should only be used without quotation marks as Martin’s description of Galileo’s method. Nevertheless, quotation marks have been - erroneously - added in many books, and some of those reference Weyl.
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.
— Hermann Weyl
Unterrichtsblätter für Mathematik und Naturwissenschaften (1932), 38, 177-188. As translated by Abe Shenitzer, in 'Part I. Topology and Abstract Algebra as Two Roads of Mathematical Comprehension', The American Mathematical Monthly (May 1995), 102, No. 7, 453.
Before you generalize, formalize, and axiomatize there must be mathematical substance.
— Hermann Weyl
In Eberhard Zeidler, Applied Functional Analysis: main principles and their applications (1995), 282.
In geometric and physical applications, it always turns out that a quantity is characterized not only by its tensor order, but also by symmetry.
— Hermann Weyl
Epigraph in Charles W. Misner, Kip S. Thorn and John Archibald Wheeler, Gravitation (1970, 1973), 47. Cited as “(1925),” with no source.
Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
— Hermann Weyl
As quoted, without citation, in Morris Kline, 'Logic Versus Pedagogy', The American Mathematical Monthly (Mar 1970), 77, No. 3, 272.
My work always tried to unite the true with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.
— Hermann Weyl
As quoted by Freeman Dyson in Obituary for Hermann Weyl in Nature (10 Mar 1956). In James Roy Newman, The World of Mathematics (2000), Vol. 3, 1831.
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.
— Hermann Weyl
In Obituary by Freeman J. Dyson, 'Prof. Hermann Weyl, For. Mem. R.S.', Nature (10 Mar 1956), 177, 458. Dyson notes that this was told to him personally, by Weyl who was “half joking”.
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.
— Hermann Weyl
In 'Mathematics and the Laws of Nature', The Armchair Science Reader (1959), 301.
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 archaeologist 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.
— Hermann Weyl
From Address (1940), given at the Bicentennial Conference at the University of Pennsylvania, 'The Mathematical Way of Thinking'. Collected in Hermann Weyl and Peter Pesic (ed.), Levels of Infinity: Selected Writings on Mathematics and Philosophy (2012), 67.
Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.
— Hermann Weyl
Symmetry (1952), 5.
The constructions 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.
— Hermann Weyl
In 'A Half-Century of Mathematics',The American Mathematical Monthly (Oct 1951), 58, No. 8, 538-539.
The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church, which had been maintained through the Middle Ages, had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science “more geometrico.”
— Hermann Weyl
In Space,Time, Matter, translated by Henry Leopold Brose (1952), 1.
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.
— Hermann Weyl
Unterrichtsblätter für Mathematik und Naturwissenschaften (1932), 38, 177-188. As translated by Abe Shenitzer, in 'Part I. Topology and Abstract Algebra as Two Roads of Mathematical Comprehension', The American Mathematical Monthly (May 1995), 102, No. 7, 453.
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 fifty years.
— Hermann Weyl
In 'A Half-Century of Mathematics', The American Mathematical Monthly, 58, No. 8, 523.
See also:
- 9 Nov - short biography, births, deaths and events on date of Weyl's birth.
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- 
