Hermann Weyl Quotes

55 Sourced Quotes

The truth as we see it today is this: The laws of nature do not determine uniquely the one world that actually exists.

Hermann Weyl
Not the state of rest, but the states of uniform translation form an objectively distinguished class of motions, and this puts an end to the substantial ether. Finally, and fourthly, the general relativity theory re-endows this metric world structure with the capacity of reacting to the forces of matter. Thus, in a sense, the circle is closed.

Hermann Weyl
The mystery that clings to numbers, the magic of numbers, may spring from this very fact, that the intellect, in the form of the number series, creates an infinite manifold of well-distinguished individuals. Even we enlightened scientists can still feel it, e.g., in the impenetrable law of the distribution of prime numbers.

Hermann Weyl
We still share the belief of a mathematical harmony of the universe. It has withstood the test of ever-widening experience. But we no longer seek this harmony in static forms like the regular solids, but in dynamic laws.

Hermann Weyl
Allow me to express now, once and for all, my deep respect for the work of the experimenter and for his fight to wring significant facts from an inflexible Nature, who says so distinctly "No" and so indistinctly "Yes" to our theories.

Hermann Weyl
Science would perish without the continuous interplay between its facts and constructions on the one hand and the imagery of ideas on the other.

Hermann Weyl
Beyond the knowledge gained from the individual sciences, there remains the task of comprehending. In spite of the fact that the views of philosophy sway from one system to another, we cannot dispense with it unless we are to convert knowledge into a meaningless chaos.

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
Seldom is asymmetry merely the absence of symmetry...

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
You should not expect me to describe the mathematical way of thinking much more clearly than one can describe, say, the democratic way of life.

Hermann Weyl
It is the function of mathematics to be at the service of the natural sciences.

Hermann Weyl
Once and for all I wish to record my unbounded admiration for the work of the experimenter in his struggle to wrest interpretable facts from an unyielding Nature who knows so well how to meet our theories with a decisive No — or with an inaudible Yes.

Hermann Weyl
In mathematics the inquiry into the genuineness or nongenuineness of the inner working of our entire western culture urges towards a more rigorous decision than can be attained in the other hazier fields of knowledge.

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

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
Only he who knows what mathematics is, and what its function in our present civilization, can give sound advice for the improvement of our mathematical teaching.

Hermann Weyl
Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means.

Hermann Weyl
Mathematizing may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalizations.

Hermann Weyl
The conception of tensors is possible owing to the circumstance that the transition from one co-ordinate system to another expresses itself as a linear transformation in the differentials. One here uses the exceedingly fruitful mathematical device of making a problem "linear" by reverting to infinitely small quantities.

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 the achievements of mathematics in the last fifty years.

Hermann Weyl
A scientist who writes on philosophy faces conflicts of conscience from which he will seldom extricate himself whole and unscathed; the open horizon and depth of philosophical thoughts are not easily reconciled with that objective clarity and determinacy for which he has been trained in the school of science.

Hermann Weyl
In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain.

Hermann Weyl
Nowhere do mathematics, natural sciences, and philosophy permeate one another so intimately as in the problem of space.

Hermann Weyl
A picture of reality drawn in a few sharp lines cannot be expected to be adequate to the variety of all its shades. Yet even so the draftsman must have the courage to draw the lines firm.

Hermann Weyl
The states of affairs with which mathematics deals are, apart from the very simplest ones, so complicated that it is practically impossible to bring them into full givenness in consciousness and in this way to grasp them completely.

Hermann Weyl
As far as I can see, all a priori statements in physics have their origin in symmetry.

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
The scene of action of reality is not a three-dimensional Euclidean space but rather a four-dimensional world, in which space and time are linked together indissolubly. However deep the chasm may be that separates the intuitive nature of space from that of time in our experience, nothing of this qualitative difference enters into the objective world which physics endeavors to crystallize out of direct experience. It is a four-dimensional continuum, which is neither "time" nor "space". Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet it and passes behind it as history, that is, as a process that is going forward in time and takes place in space.

Hermann Weyl