Top 32 Weyl Quotes
#2. 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
#3. 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
#4. You can not apply mathematics as long as words still becloud reality.
Hermann Weyl
#5. Two possibilities present themselves for the analytical treatment of metrical geometry.
Hermann Weyl
#6. 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
#7. Our mathematics of the last few decades has wallowed in generalities and formalizations.
Hermann Weyl
#8. God exists because arithmetic is consistent - the Devil exists because we can't prove it!
Hermann Weyl
#9. 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
#10. We must here follow the first course so as to be able to pass on later to generalisations which extend beyond the limits of Euclidean geometry.
Hermann Weyl
#11. Besides language and music mathematics is one of the primary manifestations of the free creative power of the human mind.
Hermann Weyl
#12. 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
#13. Before you generalize, formalize, and axiomatize there must be mathematical substance.
Hermann Weyl
#14. The objective world is, it does not happen. Only to the gaze of my consciousness, crawling along the lifeline of my body, does a section of this world come to life as a fleeting image in space which continuously changes in time.
Hermann Weyl
#15. Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.
Hermann Weyl
#16. 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
#17. 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
#18. 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
#19. the problem is then to develop a theory of invariance with respect to arbitrary linear transformations, in which, however, in contra-distinction to the case of affine geometry, we have a definite invariant quadratic form, viz. the metrical groundform once and for all as an absolute datum.
Hermann Weyl
#20. Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
Hermann Weyl
#21. The surplus of society overrides all our traditions and shapes all our philosophies.
Walter Weyl
#22. 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
#23. The introduction of numbers as coordinates is an act of violence.
Hermann Weyl
#24. For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.
Hermann Weyl
#25. With mathematics we stand precisely at that intersection of bondage and freedom that is the essence of the human itself.
Hermann Weyl
#26. We are developing new types of destitutes-the automobileless, the yachtless, the Newportcottageless. The subtlest luxuries of today reaches very high in the social scale ... The end of it all is vexation of spirit.
Walter Weyl
#27. 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
#28. Or, we may use Cartesian co-ordinate systems from the outset:
Hermann Weyl
#29. 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
#30. By refraining from reducing multiplication to addition we are enabled through these axioms to banish continuity, which is so difficult to fix precisely, from the logical structure of geometry.
Hermann Weyl
#31. 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
#32. 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
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