Weyl Quotes & Sayings

Weyl curvature tensor ... but consciousness was no — Alastair Reynolds

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. — Hermann Weyl

The question for the ultimate foundations and the ultimate meaning of mathematics remains open; we do not know in which direction it will find its final solution nor even whether a final objective answer can be expected at all. "Mathematizing" may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalization. — Hermann Weyl

the problem is then to develop a theory of invariance with respect to arbitrary linear transformations, in which, however, in contra-distinction to the case of affine geometry, we have a definite invariant quadratic form, viz. the metrical groundform once and for all as an absolute datum. — Hermann Weyl

Before you generalize, formalize, and axiomatize there must be mathematical substance. — Hermann Weyl

No mathematician of equal stature has risen from our generation ... Hilbert was singularly free from national and racial prejudices; in all public questions, be they political, social or spiritual, he stood forever on the side of freedom. — Hermann Weyl

Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold. — Hermann Weyl

One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant, sharp but cold ... thus we are clearest where knowledge matters least: in mathematics, especially number theory. — Hermann Weyl

The little individualist, recognizing his individual impotence, realizing that he did not possess within himself even the basis of a moral judgement against his big brother, began to change his point of view. He no longer hoped to right all things by his individual efforts. He turned to the law, to the government, to the state. — Walter Weyl

We must not forget that these men and women who file through the narrow gates at Ellis Island, hopeful, confused, with bundles of misconceptions as heavy as the great sacks upon their backs these simple, rough-handed people are the ancestors of our descendants, the fathers and mothers of our children. — Walter Weyl

We must here follow the first course so as to be able to pass on later to generalisations which extend beyond the limits of Euclidean geometry. — Hermann Weyl

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

Our mathematics of the last few decades has wallowed in generalities and formalizations. — Hermann Weyl

Or, we may use Cartesian co-ordinate systems from the outset: — Hermann Weyl

Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that by their very nature refer to the infinite. This is his glory. — Hermann Weyl

You can not apply mathematics as long as words still becloud reality. — Hermann Weyl

But it seems an irony of creation that man's mind knows how to handle things the better the farther removed they are from the center of his existence. Thus we are cleverest where knowledge matters least ... — Hermann Weyl

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

By refraining from reducing multiplication to addition we are enabled through these axioms to banish continuity, which is so difficult to fix precisely, from the logical structure of geometry. — Hermann Weyl

God exists because arithmetic is consistent - the Devil exists because we can't prove it! — Hermann Weyl

The surplus of society overrides all our traditions and shapes all our philosophies. — Walter Weyl

Not only in geometry, but to a still more astonishing degree in physics, has it become more and more evident that as soon as we have succeeded in unraveling fully the natural laws which govern reality, we find them to be expressible by mathematical relations of surprising simplicity and architectonic perfection. It seems to me to be one of the chief objects of mathematical instruction to develop the faculty of perceiving this simplicity and harmony. — Hermann Weyl

Besides language and music mathematics is one of the primary manifestations of the free creative power of the human mind. — Hermann Weyl

It is impossible to discuss realism in logic without drawing in the empirical sciences ... A truly realistic mathematics should be conceived, in line with physics, as a branch of the theoretical construction of the one real world and should adopt the same sober and cautious attitude toward hypothetic extensions of its foundation as is exhibited by physics. — Hermann Weyl

Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the universal organ for world understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation. — Hermann Weyl

Professor Weyl,* the mathematician, gave an excellent definition of symmetry, which is that a thing is symmetrical if there is something that you can do to it so that after you have finished doing it it looks the same as it did before. That is the sense in which we say that the laws of physics are symmetrical; that there are things we can do to the physical laws, or to our way of representing the physical laws, which make no difference, and leave everything unchanged in its effects. It is this aspect of physical laws that is going to concern us in this lecture. — Richard Feynman

For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number. — Hermann Weyl

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

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] — Hermann Weyl

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

The whole is always more, is more capable of a much greater variety of wave states, than the combination of its parts ... In this very radical sense, quantum physics supports the doctrine that the whole is more than the combination of its parts. — Hermann Weyl

Two possibilities present themselves for the analytical treatment of metrical geometry. — Hermann Weyl

We must learn a new modesty. We have stormed the heavens, but succeeded only in building fog upon fog, a mist which will not support anybody who earnestly desires to stand upon it. What is valid seems so insignificant that it may be seriously doubted whether anlaysis is at all possible. — Hermann Weyl

The objective world is, it does not happen. Only to the gaze of my consciousness, crawling along the lifeline of my body, does a section of this world come to life as a fleeting image in space which continuously changes in time. — Hermann Weyl

The introduction of numbers as coordinates is an act of violence. — Hermann Weyl

With mathematics we stand precisely at that intersection of bondage and freedom that is the essence of the human itself. — Hermann Weyl

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

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

Our generation is witness to a development of physical knowledge such as has not been seen since the days of Kepler, Galileo and Newton, and mathematics has scarcely ever experienced such a stormy epoch. Mathematical thought removes the spirit from its worldly haunts to solitude and renounces the unveiling of the secrets of Nature. But as recompense, mathematics is less bound to the course of worldly events than physics. — Hermann Weyl

Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature. — Hermann Weyl

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. — Hermann 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

We are developing new types of destitutes-the automobileless, the yachtless, the Newportcottageless. The subtlest luxuries of today reaches very high in the social scale ... The end of it all is vexation of spirit. — Walter Weyl