Hermann Weyl - Mathematical Quotes

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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.

Hermann Weyl
It was my wish to present this great subject as an illustration of the itermingling of philosophical, mathematical, and physical thought, a study which is dear to my heart. This could be done only by building up the theory systematically from the foundations, and by restricting attention throughout to the principles. But I have not been able to satisfy these self-imposed requirements: the mathematician predominates at the expense of the philosopher.

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
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.

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".

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.

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

Hermann Weyl