George Polya Quotes About Math

Quotes about: Math

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

  George Polya

  Education, Math, Different

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

  George Polya

  Education, Knowledge, Math

• 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 phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.

  George Polya

  Teacher, Book, Hard Work

• Beauty in mathematics is seeing the truth without effort.

  George Polya

  Education, Math, Effort

• Geometry is the science of correct reasoning on incorrect figures.

  George Polya

  Education, Math, Figures

• 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 keep their heads above water, and, finally, you learn to swim by practicing swimming. Trying to solve problems, you have to observe and to imitate what other people do when solving problems, and, finally, you learn to do problems by doing them.

  George Polya

  Education, Math, Swimming

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

  George Polya

  Math, Order, Looks

• 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 to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.

  George Polya

  Teacher, Teaching, Math

  George Pólya, Leon Bowden (1977). “Mathematical Methods in Science”, p.1, Cambridge University Press

• 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”

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

  George Polya

  Wise, Knowledge, Science

• 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.

  George Polya

  Good Luck, Math, Science

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

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

  George Polya

  Philosophy, Math, Not Good Enough

• 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”

• 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

• 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

• 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

  Math, Discovery, Way

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

  George Polya

  Math, Differences, Use

• 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”

• 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

  Math, Ideas, Method

  "Problems and Theorems in Analysis I: Series. Integral Calculus. Theory of Functions".

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

  George Polya

  Knowledge, Math, Obvious Things

  George Pólya (1968). “Mathematical discovery: on understanding, learning, and teaching problem solving”

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

  George Polya

  Teaching, Math, Science

• Mathematics is not a spectator sport!

  George Polya

  Sports, Math, Mathematics

• 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, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.

  George Polya

  Truth, Mean, Math

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