George Polya Quotes About Giving

Quotes about: Giving

• One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

  George Polya

  Teacher, Science, Opportunity

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

• In the "commentatio" (note presented to the Russian Academy) in which his theorem on polyhedra (on the number of faces, edges and vertices) was first published Euler gives no proof. In place of a proof, he offers an inductive argument: he verifies the relation in a variety of special cases. There is little doubt that he also discovered the theorem, as many of his other results, inductively.

  George Polya

  Numbers, Discovery, Giving

• If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.

  George Polya

  Book, Obvious Things, Giving

  George Pólya (1968). “Mathematical discovery: on understanding, learning, and teaching problem solving”

• The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. ... Mathematics cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information.

  George Polya

  Giving, Pudding, Inventory

  "How to Solve It" by George Polya, Expanded Princeton Science Library Edition, (p. 219), 2004.

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