If you cannot solve the proposed problem try to solve first some related problem. George Polya More Quotes by George Polya More Quotes From 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. George Polya good-luckmathscience The principle is so perfectly general that no particular application of it is possible. George Polya principlesmathknowledge I am too good for philosophy and not good enough for physics. Mathematics is in between. George Polya not-good-enoughmathphilosophy 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 numbersdiscoverygiving 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 George Polya lazyhard-workscience 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 teachingmathteacher 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, and from from various sides. George Polya datateacherscience You should not put too much trust in any unproved conjecture, even if it has been propounded by a great authority, even if it has been propounded by yourself. You should try to prove it or disprove it. George Polya too-muchauthoritytrying There are many questions which fools can ask that wise men cannot answer. George Polya wisescienceknowledge 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 anxietyscienceworld To write and speak correctly is certainly necessary; but it is not sufficient. A derivation correctly presented in the book or on the blackboard may be inaccessible and uninstructive, if the purpose of the successive steps is incomprehensible, if the reader or listener cannot understand how it was humanly possible to find such an argument.... George Polya purposewritingbook Euclid 's manner of exposition, progressing relentlessly from the data to the unknown and from the hypothesis to the conclusion, is perfect for checking the argument in detail but far from being perfect for making understandable the main line of the argument. George Polya progressdataperfect When introduced at the wrong time or place, good logic may be the worst enemy of good teaching. George Polya teachingmathscience 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 truthmathmean 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 styletwofirsts 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. George Polya swimmingwishwater Success in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side. George Polya aspectproblemsides 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 mathdiscoveryway
