# George Polya

## A Quote by George Polyá on argument, books, duty, good, opportunity, problems, solution, students, teachers, understanding, and work

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. 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.

Source: How to Solve It. Princeton: Princeton University Press. 1945.

Contributed by: Zaady

## A Quote by George Polyá on men and questions

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

Source: H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.

Contributed by: Zaady

## A Quote by George Polyá on enemies, good, logic, teaching, and time

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

Source: The American Mathematical Monthly, v. 100, no. 3.

Contributed by: Zaady

## A Quote by George Polyá on devil, god, laws, nature, and soul

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," restored the status quo] [Aaron Hill's version: O'er Nature's laws God cast the veil of night, Out blaz'd a Newton's soul and all was light.

Contributed by: Zaady

## A Quote by George Polyá on familiarity, language, order, understanding, and words

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.

Source: How to Solve It. Princeton: Princeton University Press. 1945.

Contributed by: Zaady

## A Quote by George Polyá on mathematics

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

Source: N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

Contributed by: Zaady

## A Quote by George Polyá on mathematics, needs, physics, and science

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.

Source: D. J. Albers and G. L. Alexanderson, Mathematical People, Boston: Birkhäuser, 1985.

Contributed by: Zaady

## A Quote by George Polyá on correction, difficulty, generations, legends, losing, mathematics, order, popularity, principles, science, and solution

The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face the blackboard and to turn his back to the class. He writes a, he says b, he means c; but it should be d. Some of his sayings are handed down from generation to generation. "In order to solve this differential equation you look at it till a solution occurs to you." "This principle is so perfectly general that no particular application of it is possible." "Geometry is the science of correct reasoning on incorrect figures." "My method to overcome a difficulty is to go round it." "What is the difference between method and device? A method is a device which you used twice."

Source: How to Solve It. Princeton: Princeton University Press. 1945.

Contributed by: Zaady