Quotes by Hermann Weyl - Page 1

You can not apply mathematics as long as words still becloud reality.
Hermann Weyl / Mathematician
Long
Mathematics
Reality
Words
Apply
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Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.
Hermann Weyl / Mathematician
Quality
Brilliant
Cold
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Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
Hermann Weyl / Mathematician
Math
Practice
Strong
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Our mathematics of the last few decades has wallowed in generalities and formalizations.
Hermann Weyl / Mathematician
Decades
Lasts
Mathematics
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God exists because arithmetic is consistent - the Devil exists because we can't prove it!
Hermann Weyl / Mathematician
God
Faith
Hope
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Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.
Hermann Weyl / Mathematician
Mathematical
Mathematics
Substance
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For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.
Hermann Weyl / Mathematician
Moving
Natural
Numbers
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Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind.
Hermann Weyl / Mathematician
Creative
Math
Mind
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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.
Hermann Weyl / Mathematician
Work Beautiful Always
Choose
Tried
Unite
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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.
Hermann Weyl / Mathematician
Geometry
Order
Physics
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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.
Hermann Weyl / Mathematician
Men
Science
Math
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... 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 / Mathematician
Numbers
Simple
Simplicity
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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 / Mathematician
Principles
Simple
Simplicity
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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 / Mathematician
Men
Matter
Mind
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Mathematics is not the rigid and rigidity-producing 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 / Mathematician
Essence
Math
Thinking
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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 / Mathematician
Construction
Glory
Infinite
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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 / Mathematician
Achievement
Greek
Years
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No mathematician of equal stature has risen from our generation... Hilbert was singularly free from national and racial prejudices; in all public questions, be they political, social or spiritual, he stood forever on the side of freedom.
Hermann Weyl / Mathematician
Forever
Our Generation
Spiritual
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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 / Mathematician
Doctrine
Physics
Support
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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 / Mathematician
Quality
Men
Numbers
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We must learn a new modesty. We have stormed the heavens, but succeeded only in building fog upon fog, a mist which will not support anybody who earnestly desires to stand upon it. What is valid seems so insignificant that it may be seriously doubted whether anlaysis is at all possible.
Hermann Weyl / Mathematician
Fog
Heaven
Support
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The introduction of numbers as coordinates by reference to the particular division scheme of the open one-dimensional continuum is an act of violence whose only practical vindication is the special calculatory manageability of the ordinary number continuum with its four basic operations.
Hermann Weyl / Mathematician
Math
Numbers
Violence
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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 / Mathematician
Truth
Ideas
Math
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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 / Mathematician
Attitude
Drawing
Foundation
Real
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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 / Mathematician
Creative
Math
Teaching
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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 / Mathematician
Men
Decision
Discovery
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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 / Mathematician
Art
Beauty
Reality
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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 / Mathematician
Book
Couple
Math
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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 / Mathematician
Imagination
Effort
Math
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