George PolyaIt is better to solve one problem five different ways, than to solve five problems one way.371Life
George PolyaWhere should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as a whole as clearly and as vividly as you can. ... What can I gain by doi… ▶361PoliticsThought
George PolyaThe 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 … ▶362Reflection
George PolyaHilbert 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 rema… ▶363Thought
George PolyaEpitaph 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 H… ▶352Politics
George PolyaThe 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, no… ▶342Time
George PolyaGeometry is the science of correct reasoning on incorrect figures.331Thought
George PolyaMy method to overcome a difficulty is to go round it. ✨ George Pólya (1948). How to solve it: a new aspect of mathematical method364Humor
George PolyaBeauty in mathematics is seeing the truth without effort.365Truth
George PolyaIf you cannot solve the proposed problem try to solve first some related problem.345Philosophy
George PolyaWhen introduced at the wrong time or place, good logic may be the worst enemy of good teaching.313Time
George PolyaMathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself346Hope
George PolyaIf 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 (1981). Mathematical Discov… ▶314Humor
George PolyaThe 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 oth… ▶3710HopeTime
George PolyaOne 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… ▶292Death
George PolyaMathematics consists in proving the most obvious thing in the least obvious way. ✨ George Pólya (1968). Mathematical discovery: on understanding, learning, and teaching prob… ▶336Hope
George PolyaThe 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 … ▶348Thought
George PolyaIf the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in … ▶285Reading
George PolyaI am too good for philosophy and not good enough for physics. Mathematics is in between.297Philosophy
George PolyaA great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and bri… ▶242Life
George PolyaMathematics 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. ✨ Speakin… ▶275Humanity
George PolyaThe 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 student… ▶221HopeTime
George PolyaSolving 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 t… ▶277Humanity
George PolyaEven 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 m… ▶277Reading
George PolyaA GREAT discovery solves a great problem but there is a grain of discovery in any problem. ✨ George Pólya (1957). How to solve it: a new aspect of mathematical method278Reflection
George PolyaAn idea which can be used only once is a trick. If one can use it more than once it becomes a method. ✨ Problems and Theorems in Analysis I: Series. Integral Calculus. Theor… ▶246Thought
George PolyaThere 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 di… ▶2710Reading
George PolyaThe 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 Pólya (1948). How to … ▶214HopeThought
George PolyaIf there is a problem you can't solve, then there is an easier problem you can't solve: find it.192Humanity
George PolyaLook around when you have got your first mushroom or made your first discovery: they grow in clusters. ✨ George Pólya (1948). How to solve it: a new aspect of mathematical m… ▶237Life
