Famous Quotes & Sayings

Hermann Weyl Quotes & Sayings

Enjoy the top 37 famous quotes, sayings and quotations by Hermann Weyl.

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Famous Quotes By Hermann Weyl

Hermann Weyl Quotes 731356

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

Hermann Weyl Quotes 174533

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

Hermann Weyl Quotes 2196626

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

Hermann Weyl Quotes 621040

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

Hermann Weyl Quotes 670635

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

Hermann Weyl Quotes 280852

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

Hermann Weyl Quotes 1453956

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

Hermann Weyl Quotes 1797576

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

Hermann Weyl Quotes 1402860

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

Hermann Weyl Quotes 1490416

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

Hermann Weyl Quotes 1516530

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

Hermann Weyl Quotes 1605300

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

Hermann Weyl Quotes 1618670

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

Hermann Weyl Quotes 1652815

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

Hermann Weyl Quotes 1795132

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

Hermann Weyl Quotes 1128120

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

Hermann Weyl Quotes 1939256

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

Hermann Weyl Quotes 1995711

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

Hermann Weyl Quotes 2103109

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

Hermann Weyl Quotes 2140102

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

Hermann Weyl Quotes 2166659

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

Hermann Weyl Quotes 133161

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

Hermann Weyl Quotes 1264353

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

Hermann Weyl Quotes 236595

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

Hermann Weyl Quotes 1111024

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

Hermann Weyl Quotes 939632

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

Hermann Weyl Quotes 856128

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

Hermann Weyl Quotes 801971

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

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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

Hermann Weyl Quotes 233257

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

Hermann Weyl Quotes 627102

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

Hermann Weyl Quotes 556516

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

Hermann Weyl Quotes 532742

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

Hermann Weyl Quotes 400510

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

Hermann Weyl Quotes 375815

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

Hermann Weyl Quotes 303011

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

Hermann Weyl Quotes 260938

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