Hermann Weyl quotes

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 
Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.
 Hermann Weyl 
Before you generalize, formalize, and axiomatize there must be mathematical substance.
 Hermann Weyl 
Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind.
 Hermann Weyl 

You can not apply mathematics as long as words still becloud reality.
 Hermann Weyl 
Our mathematics of the last few decades has wallowed in generalities and formalizations.
 Hermann Weyl 
God exists because arithmetic is consistent  the Devil exists because we can't prove it!
 Hermann Weyl 
Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
 Hermann Weyl 

Mathematics is not the rigid and rigidityproducing 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 
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 
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 
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 

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

... 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 
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 
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 
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 

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 
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 
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
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