Hermann Weyl quotes

Hermann Weyl was a German mathematician and theoretical physicist who made important contributions to mathematics, physics, and philosophy. Renowned for his work in group theory, quantum mechanics, and differential geometry, his influence extends across multiple scientific fields. He helped shape modern scientific thought through his pioneering ideas and prolific writing. Here are 34 of his quotes:

A new development began for relativity theory after 1925 with its absorption into quantum physics. The first great success was scored by Dirac's quantum mechanical equations of the electron, which introduced a new sort of quantities, the spinors, besides the vectors and tensors into our physical theories. ...But difficulties of the gravest kind turned up when one passed from one electron or photon to the interaction among an indeterminate number of such particles. In spite of several advances a final solution of this problem is not yet in sight and may well require a deep modification of the foundation of quantum mechanics, such as would account in the same basic manner for the elementary electric charge e as relativity theory and our present quantum mechanics account for c and h. (Hermann Weyl)
A new theory by the author has been added, which draws the physical inferences consequent on the extension of the foundations of geometry beyond Reimann... and represents an attempt to derive from world-geometry not only gravitational but also electromagnetic phenomena. Even if this theory is still only in its infant stage, I feel convinced that it contains no less truth than Einstein's Theory of Gravitation-whether this amount of truth is unlimited or, what is more probable, is bounded by the Quantum Theory. View quote
Hermann Weyl
We cannot hope to give here a final clarification of the essence of fact, judgement, object, property; this task leads into metaphysical abysses; about these one has to seek advice from men whose name cannot be stated without earning a compassionate smile-e. g. Fichte. View quote
Hermann Weyl
You can not apply mathematics as long as words still becloud reality. View quote
Hermann Weyl
Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect. View quote
Hermann Weyl
In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain. View quote
Hermann Weyl
It seems clear that [set theory] violates against the essence of the continuum, which, by its very nature, cannot at all be battered into a single set of elements. Not the relationship of an element to a set, but of a part to a whole ought to be taken as a basis for the analysis of a continuum. View quote
Hermann Weyl
All characteristics of material things as they are presented to us in the acts of external perception (e. g. colour) are endowed with the separateness of spatial extension, but it is only when we build up a single connected real world out of all our experiences that the spatial extension, which is a constituent of every perception, becomes a part of one and the same all-inclusive space. ... every material thing can, without changing content, equally well occupy a position in Space different from its present one. This immediately gives us the property of the homogeneity of space which is the root of the conception, Congruence. View quote
Hermann Weyl
Consciousness spreads out its web, in the form of time, over reality. View quote
Hermann Weyl
This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind. View quote
Hermann Weyl
[Physicists and philosophers] stick stubbornly to the principles of a mechanistic interpretation of the world after physics has, in its factual structure, already outgrown the latter. They have the same excuse as the inhabitant of the mainland who for the first time travels on the open sea: he will desperately try to stay in sight of the vanishing coast line, as long as there is no other coast in sight, towards which he steers. (Hermann Weyl)
To gaze up from the ruins of the oppressive present towards the stars is to recognise the indestructible world of laws, to strengthen faith in reason, to realise the "harmonia mundi" that transfuses all phenomena, and that never has been, nor will be, disturbed. View quote
Hermann Weyl
We now come to a decisive step of mathematical abstraction: we forget about what the symbols stand for... [The mathematician] need not be idle; there are many operations which he may carry out with these symbols, without ever having to look at the things they stand for. View quote
Hermann Weyl
Recognition of the subjectivity of the qualities of sense is found in Galilei (and also in Descartes and Hobbes) in a form closely related to the principle underlying the constructive mathematical method of our modern physics which repudiates" qualities." View quote
Hermann Weyl
In the realm of physics it is perhaps only the theory of relativity which has made it quite clear that the two essences, space and time, entering into our intuition, have no place in the world constructed by mathematical physics. Colours are thus "really" not even æther-vibrations, but merely a series of values of mathematical functions in which occur four independent parameters corresponding to the three dimensions of space, and the one of time. View quote
Hermann Weyl
First, the physicists in the persons of Faraday and Maxwell, proposed the "electromagnetic field" in contradistinction to matter, as a reality of a different category. Then, during the last century, the mathematicians, ... secretly undermined belief in the evidence of Euclidean Geometry. And now, in our time, there has been unloosed a cataclysm which has swept away space, time, and matter hitherto regarded as the firmest pillars of natural science, but only to make place for a view of things of wider scope and entailing a deeper vision. This revolution was promoted essentially by the thought of one man, Albert Einstein. View quote
Hermann Weyl
The rapid development of science... has, as it were, burst its old shell, now become too narrow. View quote
Hermann Weyl
After Riemann had made known his discoveries, mathematicians busied themselves with working out his system of geometrical ideas formally; chief among these were Christoffel, Ricci, and Levi-Civita. Riemann... clearly left the real development of his ideas in the hands of some subsequent scientist whose genius as a physicist could rise to equal flights with his own as a mathematician. After a lapse of seventy years this mission has been fulfilled by Einstein. View quote
Hermann Weyl
Cartan developed a general scheme of infinitesimal geometry in which Klein's notions were applied to the tangent plane and not to the n-dimensional manifold M itself. View quote
Hermann Weyl
Above all, the ominous clouds of those phenomena that we are with varying success seeking to explain by means of the quantum of action, are throwing their shadows over the sphere of physical knowledge, threatening no one knows what new revolution. View quote
Hermann Weyl
With Mie's view of matter there is contrasted another, according to which matter is a limiting singularity of the field, but charges and masses are force-fluxes in the field. This entails a new and more cautious attitude towards the whole problem of matter. (Hermann Weyl)
Einstein's theory of relativity. View quote
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. View quote
Hermann Weyl
It was my wish to present this great subject as an illustration of the itermingling of philosophical, mathematical, and physical thought. View quote
Hermann Weyl
It is in the composite idea of motion that these three fundamental conceptions enter into intimate relationship. View quote
Hermann Weyl