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. Everybody who looks at the spectacle of modern algebra will be struck by this complementarity of freedom and necessity.
More Quotes from Hermann Weyl:
You can not apply mathematics as long as words still becloud reality.Hermann Weyl
Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
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
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
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
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Based on Topics: Accident Quotes, Birth Quotes, Emotions Quotes, Imagination & Visualization Quotes, Liberty & Freedom Quotes, Mind Quotes, Necessity QuotesBased on Keywords: axioms, complementarity, constructs
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