The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. — George Polya Copy Share Image
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:… — George Polya Copy Share Image
Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in… — George Polya Copy Share Image
A GREAT discovery solves a great problem but there is a grain of discovery in any problem. — George Polya Copy Share Image
Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as a whole as clearly… — George Polya Copy Share Image
In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we… — George Polya Copy Share Image
Look around when you have got your first mushroom or made your first discovery: they grow in clusters. — George Polya Copy Share Image
I am too good for philosophy and not good enough for physics. Mathematics is in between. — George Polya Copy Share Image
Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice. — George Polya Copy Share Image
An idea which can be used only once is a trick. If one can use it more than once it becomes a method. — George Polya Copy Share Image
To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not… — George Polya Copy Share Image
The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it… — George Polya Copy Share Image
The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till… — George Polya Copy Share Image
![“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 where it does not fit, is pedantry. [...] To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever…” quote by George Polya](https://sms4smile.com/quotes/img-quotes/927/george-polya-10766_action_pedantry-and-mastery-are-opposite-attitu_112396.jpg)
