George Polya quote

"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

Born: December 13, 1887

Die: September 7, 1985

Occupation: Mathematician

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More quotes of George Polya

George Polya

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 Squire: It did not last: the Devil shouting "Ho. Let Einstein be,"...

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George Polya

There are many questions which fools can ask that wise men cannot answer.

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George Polya

If you cannot solve the proposed problem try to solve first some related problem.

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George Polya

The principle is so perfectly general that no particular application of it is possible.

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George Polya

Geometry is the science of correct reasoning on incorrect figures.

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George Polya

My method to overcome a difficulty is to go round it.

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George Polya

The first rule of style is to have something to say. The second rule of style is to control yourself when, by chance, you have two things to say; say first one, then the other, not both at the same time.

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George Polya

Beauty in mathematics is seeing the truth without effort.

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George Polya

If there is a problem you can't solve, then there is an easier problem you can't solve: find it.

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George Polya

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 solve problems.

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George Polya

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...

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George Polya

A GREAT discovery solves a great problem but there is a grain of discovery in any problem.

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George Polya

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive...

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George Polya

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...

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George Polya

The teacher can seldom afford to miss the questions: What is the unknown? What are the data? What is the condition? The student should consider the principal parts of the problem attentively, repeatedly,...

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George Polya

To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm...

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George Polya

There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann...

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George Polya

Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself

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George Polya

The best of ideas is hurt by uncritical acceptance and thrives on critical examination.

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George Polya

An idea which can be used once is a trick. If it can be used more than once it becomes a method.

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George Polya

Success in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side.

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George Polya

Mathematics consists in proving the most obvious thing in the least obvious way.

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George Polya

Mathematics is not a spectator sport!

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George Polya

The open secret of real success is to throw your whole personality into your problem.

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George Polya

Quite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so inconspicuous. The expert has, perhaps, no more ideas than the inexperienced, but appreciates more...

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George Polya

I am too good for philosophy and not good enough for physics. Mathematics is in between.

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George Polya

It is better to solve one problem five different ways, than to solve five problems one way.

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George Polya

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 a systematic, deductive science; but mathematics in...

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George Polya

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 what other people do with their hands and feet to...

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George Polya

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 equally all his students, future users and nonusers...

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George Polya

The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is feasible.

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George Polya

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.

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George Polya

The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea.

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George Polya

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.

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George Polya

When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.

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George Polya

Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as a whole as clearly and as vividly as you can. ... What can I gain by doing so? You should understand...

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George Polya

If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences,...

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George Polya

A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive...

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George Polya

Look around when you have got your first mushroom or made your first discovery: they grow in clusters.

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George Polya

The future mathematician ... should solve problems, choose the problems which are in his line, meditate upon their solution, and invent new problems. By this means, and by all other means, he should endeavor...

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George Polya

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...

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George Polya

In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar...

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George Polya

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 become a poet. Hilbert is reported to have remarked: 'I never thought...

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Related quote

George Polya

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...

Read more


George Polya

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive...

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William James

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