George Polya Quotes - Page 2

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

  George Polya

  Overcoming, Method, Difficulty

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

  13 Copy quote

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

  George Polya

  Hurt, Acceptance, Ideas

  George Pólya (1957). “How to solve it: a new aspect of mathematical method”

  5 Copy quote

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

  George Polya

  Wise, Knowledge, Science

  6 Copy quote

• 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.

  George Polya

  Two, Style, Firsts

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

  4 Copy quote

• 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 the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.

  George Polya

  Education, Math, Two

  George Pólya (1945). “How to Solve it: A New Aspect of Mathematical Method”

  6 Copy quote

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

  George Polya

  Philosophy, Math, Not Good Enough

  8 Copy quote

• 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 like a monkey who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise.

  George Polya

  Real, Math, Tree

  8 Copy quote

• There exist a lot of questions that the fools can ask, and the intelligent cannot answer.

  George Polya

  Intelligent, Answers, Fool

  7 Copy quote

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

  George Polya

  Education, Knowledge, Math

  George Pólya (1957). “How to solve it: a new aspect of mathematical method”

  9 Copy quote

• What is the difference between method and device? A method is a device which you use twice.

  George Polya

  Math, Differences, Use

  8 Copy quote

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

  George Polya

  Knowledge, Math, Principles

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

  9 Copy quote

• 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 of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.

  George Polya

  Education, Teacher, Teaching

  22 Copy quote

• A mathematics teacher is a midwife to ideas.

  George Polya

  Teacher, Ideas, Mathematics

  13 Copy quote

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

  George Polya

  Motivational, Trying, Firsts

  8 Copy quote

• John von Neumann was the only student I was ever afraid of.

  George Polya

  Students, Von Neumann

  14 Copy quote

• In order to solve this differential equation you look at it until a solution occurs to you.

  George Polya

  Math, Order, Looks

  73 Copy quote

• 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 letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery.

  George Polya

  Attitude, Opportunity, Opposites

  George Pólya (1945). “How to Solve it: A New Aspect of Mathematical Method”

  23 Copy quote

• 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 he had enough imagination to be a mathematician.'

  George Polya

  Creativity, Men, Imagination

  18 Copy quote

• 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.

  George Polya

  Independent, Ideas, Numbers

  14 Copy quote

• 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 to make his first important discovery: he should discover his likes and dislikes, his taste, his own line.

  George Polya

  Mean, Science, Discovery

  5 Copy quote

• 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 to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.

  George Polya

  Expression, Order, Two

  George Pólya (1957). “How to solve it: a new aspect of mathematical method”

  8 Copy quote

• 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 what he has and uses it better.

  George Polya

  Appreciation, Ideas, Appreciate

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

  5 Copy quote

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

  George Polya

  Teaching, Math, Science

  6 Copy quote

• 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.

  George Polya

  Science, Anxiety, World

  7 Copy 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

  Teacher, Science, Opportunity

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

  7 Copy quote

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