Hermann Weyl Quotes About Math

• 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

  Math, Numbers, Violence

  "Philosophy of Mathematics and Natural Science".

• 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

  Teaching, Math, Creative

  Hermann Weyl (1968). “Gesammelte Abhandlungen”

• Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind.

  Hermann Weyl

  Math, Creative, Mind

  Hermann Weyl (1968). “Gesammelte Abhandlungen”

• Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.

  Hermann Weyl

  Strong, Math, Practice

• 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

  Math, Thinking, Essence

• 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

  Math, Imagination, Effort

  Hermann Weyl (1968). “Gesammelte Abhandlungen”

• 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

  Math, Science, Men

  Hermann Weyl (2015). “Symmetry”, p.5, Princeton University Press

• 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

  Truth, Math, Ideas

  Hermann Weyl (2013). “Levels of Infinity: Selected Writings on Mathematics and Philosophy”, p.33, Courier Corporation

• 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

  Couple, Book, Math

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