George Polya Quotes

47 quotes in 789 categories

• If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to…
• Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases…
• A GREAT discovery solves a great problem but there is a grain of discovery in any problem.
• The best of ideas is hurt by uncritical acceptance and thrives on critical examination.
• An idea which can be used once is a trick. If it can be used more than once it becomes a method.
• Success in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side.
• Mathematics consists in proving the most obvious thing in the least obvious way.
• Mathematics is not a spectator sport!
• I am too good for philosophy and not good enough for physics. Mathematics is in between.
• It is better to solve one problem five different ways, than to solve five problems one way.
• Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as…
• Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice. Trying to swim, you imitate…
• The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who wishes to serve…
• Epitaph on Newton: Nature and Nature's law lay hid in night: God said, "Let Newton be!," and all was light. [added by Sir John Collings…
• The principle is so perfectly general that no particular application of it is possible.
• Hilbert once had a student in mathematics who stopped coming to his lectures, and he was finally told the young man had gone off to…
• A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is…
• I am intentionally avoiding the standard term which, by the way, did not exist in Euler's time. One of the ugliest outgrowths of the "new…
• 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…
• In order to solve this differential equation you look at it until a solution occurs to you.

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