Hermann Weyl: Quotes about mathematics

“It was my wish to present this great subject as an illustration of the itermingling of philosophical, mathematical, and physical thought”

Hermann Weyl

From the Author's Preface to First Edition (1918)
Space—Time—Matter (1952)
Context: 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.

Mathematics

“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

The Mathematical Way of Thinking (1941)

Mathematics , Decision , Forgetting

“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

Introduction
Space—Time—Matter (1952)

Mathematics , Sense

“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

Introduction
Space—Time—Matter (1952)

World , Mathematics , Time

“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

Symmetry (1952)

Art , Mathematics , Nature

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

Hermann Weyl Invariants

Weyl, Hermann. Invariants. Duke Math. J. 5 (1939), no. 3, 489--502. doi:10.1215/S0012-7094-39-00540-5. http://projecteuclid.org/euclid.dmj/1077491405.

Angels , Soul , Mathematics , Fight