Hermann Weyl Quotes

22 quotes in 451 categories

• Before you generalize, formalize, and axiomatize there must be mathematical substance.
• 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…
• You can not apply mathematics as long as words still becloud reality.
• Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind.
• Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
• One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant,…
• 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…
• 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,…
• Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.
• 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,…
• 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…
• ... numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them…
• 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…
• 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…
• The introduction of numbers as coordinates is an act of violence.
• 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…
• 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…
• God exists because arithmetic is consistent - the Devil exists because we can't prove it!
• 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…
• Our mathematics of the last few decades has wallowed in generalities and formalizations.

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