Hermann Weyl Quotes About Mathematics

• 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”

• You can not apply mathematics as long as words still becloud reality.

  Hermann Weyl

  Reality, Long, Mathematics

  Hermann Weyl (2013). “Levels of Infinity: Selected Writings on Mathematics and Philosophy”, p.70, Courier Corporation

• 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

  Years, Achievement, Greek

• 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

• 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

  Men, Numbers, Quality

• 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

• 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

  Men, Discovery, Decision

  Hermann Weyl (2013). “Levels of Infinity: Selected Writings on Mathematics and Philosophy”, p.88, Courier Corporation

• Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

  Hermann Weyl

  Substance, Mathematics, Mathematical

  "Mind and Nature: Selected Writings on Philosophy, Mathematics, and Physics".

• Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.

  Hermann Weyl

  Quality, Brilliant, Cold

  Hermann Weyl (2013). “Levels of Infinity: Selected Writings on Mathematics and Philosophy”, p.192, Courier Corporation

• For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.

  Hermann Weyl

  Moving, Numbers, Natural

• 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

  Attitude, Real, Drawing

  Hermann Weyl, Frank Wilczek (2009). “Philosophy of Mathematics and Natural Science”, p.235, Princeton University Press

• Our mathematics of the last few decades has wallowed in generalities and formalizations.

  Hermann Weyl

  Lasts, Mathematics, Decades

• 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

  Infinite, Glory, Construction

  Hermann Weyl (1968). “Gesammelte Abhandlungen”

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