The best of ideas is hurt by uncritical acceptance and thrives on critical examination. — George Polya Copy Share Image
The principle is so perfectly general that no particular application of it is possible. — George Polya Copy Share Image
There are many questions which fools can ask that wise men cannot answer. — George Polya Copy Share Image
Mathematics consists in proving the most obvious thing in the least obvious way. — 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
A GREAT discovery solves a great problem but there is a grain of discovery in any problem. — George Polya Copy Share Image
It is better to solve one problem five different ways, than to solve five problems one way. — George Polya Copy Share Image
If there is a problem you can't solve, then there is an easier problem you can't solve: find it. — George Polya Copy Share Image
In order to solve this differential equation you look at it until a solution occurs to you. — 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… — George Polya Copy Share Image
Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean… — George Polya Copy Share Image
If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the… — George Polya Copy Share Image
The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who… — George Polya Copy Share Image
I am intentionally avoiding the standard term which, by the way, did not exist in Euler's time. One of the ugliest outgrowths… — George Polya Copy Share Image
The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and… — George Polya Copy Share Image
Hilbert once had a student in mathematics who stopped coming to his lectures, and he was finally told the young man had… — George Polya Copy Share Image
Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice. Trying to… — 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.… — George Polya Copy Share Image
The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the… — George Polya Copy Share Image
“I started studying law, but this I could stand just for one semester. I couldn't stand more. Then I studied languages and… — George Pólya Copy Share Image
What is the difference between method and device? A method is a device which you use twice. — George Polya Copy Share Image
Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do… — George Polya Copy Share Image
It may be more important in the mathematics class how you teach than what you teach. — George Polya Copy Share Image
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
A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can… — George Polya Copy Share Image
One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have… — 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… — 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)
