Beauty in mathematics is seeing the truth without effort. George Polya More Quotes by George Polya More Quotes From George Polya My method to overcome a difficulty is to go round it. George Polya method difficulty overcoming The open secret of real success is to throw your whole personality into your problem. George Polya real success science Geometry is the science of correct reasoning on incorrect figures. George Polya figures education math There exist a lot of questions that the fools can ask, and the intelligent cannot answer. George Polya fool intelligent answers A GREAT discovery solves a great problem but there is a grain of discovery in any problem. George Polya education math knowledge The 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 other means, he should endeavor to make his first important discovery: he should discover his likes and dislikes, his taste, his own line. George Polya discovery science mean 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. George Polya opportunity teacher science 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 teaching writing science The best of ideas is hurt by uncritical acceptance and thrives on critical examination. George Polya acceptance hurt ideas If 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 proving the most obvious things in the least obvious way. George Polya obvious-things giving book 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 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 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 expression two order 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 inventory pudding giving The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. George Polya guessing creative science Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements. George Polya achievement expression thinking Quite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so inconspicuous. The expert has, perhaps, no more ideas than the inexperienced, but appreciates more what he has and uses it better. George Polya appreciate appreciation ideas What is the difference between method and device? A method is a device which you use twice. George Polya differences use math 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. George Polya light law night 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
