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Hermann Weyl Quotes

God exists because arithmetic is consistent - the Devil exists because we can’t prove it! Picture Quote #1

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 Picture Quote #1

Before you generalize, formalize, and axiomatize there must be mathematical substance Picture Quote #1

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong Picture Quote #1

Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold Picture Quote #1

You can not apply mathematics as long as words still becloud reality Picture Quote #1

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The introduction of numbers as coordinates is an act of violence Picture Quote #1

Our mathematics of the last few decades has wallowed in generalities and formalizations Picture Quote #1

... 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 Picture Quote #1

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 Picture Quote #1

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 Picture Quote #1

The whole is always more, is more capable of a much greater variety of wave states, than the combination of its parts.... In this very radical sense, quantum physics supports the doctrine that the whole is more than the combination of its parts Picture Quote #1

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In geometric and physical applications, it always turns out that a quantity is characterized not only by its tensor order, but also by symmetry Picture Quote #1

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 Picture Quote #1

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 Picture Quote #1

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 Picture Quote #1

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 Picture Quote #1

Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind Picture Quote #1

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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 Picture Quote #1

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God exists because arithmetic is consistent - the Devil exists because we can’t prove it! (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 Quotes) Before you generalize, formalize, and axiomatize there must be mathematical substance (Hermann Weyl Quotes) Logic is the hygiene the mathematician practices to keep his ideas healthy and strong (Hermann Weyl Quotes) Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold (Hermann Weyl Quotes) You can not apply mathematics as long as words still becloud reality (Hermann Weyl Quotes) The introduction of numbers as coordinates is an act of violence (Hermann Weyl Quotes) Our mathematics of the last few decades has wallowed in generalities and formalizations (Hermann Weyl Quotes) ... 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 Quotes) 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 Quotes) 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 Quotes) The whole is always more, is more capable of a much greater variety of wave states, than the combination of its parts.... In this very radical sense, quantum physics supports the doctrine that the whole is more than the combination of its parts (Hermann Weyl Quotes) 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 Quotes) 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 Quotes) 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 Quotes) 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 Quotes) 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 Quotes) Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind (Hermann Weyl Quotes) 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 Quotes)