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 math" was the premature introduction of technical terms. — 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
A GREAT discovery solves a great problem but there is a grain of discovery in any problem. — George Polya Copy Share
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
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
Look around when you have got your first mushroom or made your first discovery: they grow in clusters. — George Polya Copy Share
I am too good for philosophy and not good enough for physics. Mathematics is in between. — George Polya Copy Share
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
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
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
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
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
Hilbert once had a student in mathematics who stopped coming to his lectures, and he was finally told the young man had gone off… — George Polya Copy Share
An idea which can be used once is a trick. If it can be used more than once it becomes a method. — George Polya Copy Share
