Quotes by George Polya - Page 2

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 / Mathematician
Teacher
Book
Hard Work
Copy Quote
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 / Mathematician
Truth
Math
Mean
Copy Quote
The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. ... Mathematics cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information.
George Polya / Mathematician
Giving
Inventory
Pudding
Copy Quote
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 didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.
George Polya / Mathematician
Science
Teaching
Writing
Copy Quote
In the "commentatio" (note presented to the Russian Academy) in which his theorem on polyhedra (on the number of faces, edges and vertices) was first published Euler gives no proof. In place of a proof, he offers an inductive argument: he verifies the relation in a variety of special cases. There is little doubt that he also discovered the theorem, as many of his other results, inductively.
George Polya / Mathematician
Discovery
Giving
Numbers
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 / Mathematician
Opportunity
Attitude
Opposites
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 / Mathematician
Math
Real
Tree
Copy Quote
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 / Mathematician
Education
Math
Swimming
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 / Mathematician
Expression
Order
Two
Copy Quote

Related Mathematician Authors

Wolfgang Smith
Mathematician
William Thurston
Mathematician
Wednesday, Oct 30, 1946
Tuesday, Aug 21, 2012
William Mitchinson Hicks
Mathematician
Monday, Sep 23, 1850
Friday, Aug 17, 1934
William Kingdon Clifford
Mathematician
Sunday, May 04, 1845
Monday, Mar 03, 1879
William Fogg Osgood
Mathematician
Thursday, Mar 10, 1864
Thursday, Jul 22, 1943
William A. Dembski
Mathematician
Monday, Jul 18, 1960
W. W. Sawyer
Mathematician

Friday, Feb 15, 2008
W. W. Rouse Ball
Mathematician
Wednesday, Aug 14, 1850
Saturday, Apr 04, 1925
Vaclav Hlavaty
Mathematician
Saturday, Jan 27, 1894
Saturday, Jan 11, 1969
Urbain Le Verrier
Mathematician
Monday, Mar 11, 1811
Sunday, Sep 23, 1877
Tobias Dantzig
Mathematician
Tuesday, Feb 19, 1884
Thursday, Aug 09, 1956
Timothy Gowers
Mathematician
Wednesday, Nov 20, 1963
Thomas Little Heath
Mathematician

Saturday, Mar 16, 1940
Thomas Bradwardine
Mathematician

Tuesday, Aug 26, 1349
Thomas Banchoff
Mathematician
Thursday, Apr 07, 1938

View All Mathematician Quotes

Top Authors

Carrie Fisher
Actress
Sunday, Oct 21, 1956
Tuesday, Dec 27, 2016
W. Edwards Deming
Statistician
Sunday, Oct 14, 1900
Monday, Dec 20, 1993
Abraham Lincoln
16Th U.S. President
Sunday, Feb 12, 1809
Saturday, Apr 15, 1865
Ruth Bader Ginsburg
Associate Justice Of The Supreme Court Of The United States
Wednesday, Mar 15, 1933
William Blake
Poet
Monday, Nov 28, 1757
Sunday, Aug 12, 1827
George Bernard Shaw
Playwright
Saturday, Jul 26, 1856
Thursday, Nov 02, 1950
Steven Wright
Comedian
Tuesday, Dec 06, 1955
Winston Churchill
Former Prime Minister Of The United Kingdom
Monday, Nov 30, 1874
Sunday, Jan 24, 1965
Dwight D. Eisenhower
34Th U.s. President
Tuesday, Oct 14, 1890
Friday, Mar 28, 1969
Bob Marley
Singer
Tuesday, Feb 06, 1945
Monday, May 11, 1981
Ralph Waldo Emerson
Essayist
Wednesday, May 25, 1803
Thursday, Apr 27, 1882
Niccolo Machiavelli
Historian
Monday, May 03, 1469
Tuesday, Jun 21, 1527
Robert Frost
Poet
Thursday, Mar 26, 1874
Tuesday, Jan 29, 1963
Michael Jordan
Basketball Player
Sunday, Feb 17, 1963
Pope John Paul Ii
Priest
Tuesday, May 18, 1920
Saturday, Apr 02, 2005

View All Authors

George Polya Quotes - Page 2

App & Tools

Related Mathematician Authors

Popular Topic Tags

Top Authors

Share This Page

Stay Connected

App & Tools

Related Mathematician Authors

Popular Topic Tags

Top Authors

Share This Page