Quotes by Math In mathematical analysis we call x the undetermined part of line a: the rest we don't call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language. Georg C. Lichtenberg linesmathlife I have often noticed that when people come to understand a mathematical proposition in some other way than that of the ordinary demonstration, they promptly say, "Oh, I see. That's how it must be." This is a sign that they explain it to themselves from within their own system. Georg C. Lichtenberg understandingmathpeople I've seen pretty clear, ever since I was a young un, as religion's something else besides notions. It isn't notions sets people doing the right things--it's feelings. It's the same with the notions in religion as it is with math'matics--a man may be able to work problems straight off in's head as he sits by the fire and smokes his pipe; but if he has to make a machine or a building, he must have a will and a resolution, and love something else better than his own ease. George Eliot firemathmen It is better to solve one problem five different ways, than to solve five problems one way. George Polya differenteducationmath 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 swimmingeducationmath If there is a problem you can't solve, then there is an easier problem you can't solve: find it. George Polya educationmathknowledge An idea which can be used only once is a trick. If one can use it more than once it becomes a method. George Polya methodmathideas In order to solve this differential equation you look at it until a solution occurs to you. George Polya mathorderlooks Beauty in mathematics is seeing the truth without effort. George Polya efforteducationmath Mathematics is not a spectator sport! George Polya mathematicsmathsports Mathematics consists in proving the most obvious thing in the least obvious way. George Polya obvious-thingsmathknowledge Geometry is the science of correct reasoning on incorrect figures. George Polya figureseducationmath A GREAT discovery solves a great problem but there is a grain of discovery in any problem. George Polya educationmathknowledge 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 realmathtree 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 educationmathtwo What is the difference between method and device? A method is a device which you use twice. George Polya differencesusemath 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 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«2425262728293031323334»
