George Pólya Short Quotes

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My method to overcome a difficulty is to go round it.

George Pólya
Geometry is the art of correct reasoning on incorrect figures.

George Pólya
This principle is so perfectly general that no particular application is possible.

George Pólya
It may be more important in the mathematics class how you teach than what you teach.

George Pólya
If you cannot solve the proposed problem, try to solve first a simpler related problem.

George Pólya
In order to solve a differential equation you look at it till a solution occurs to you.

George Pólya
The best of ideas is hurt by uncritical acceptance and thrives on critical examination.

George Pólya
Simplicity is worth buying if we do not have to pay too great a loss of precision for it.

George Pólya
What is the difference between a method and device? A method is a device which you use twice.

George Pólya
A great discovery solves a great problem but there is a grain of discovery in the solution of any problem.

George Pólya
We need heuristic reasoning when we construct a strict proof as we need scaffolding when we erect a building.

George Pólya
In plausible reasoning the principal thing is to distinguish... a more reasonable guess from a less reasonable guess.

George Pólya
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 Pólya
Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work yourself.

George Pólya
Mathematics presented with rigor is a systematic deductive science but mathematics in the making is an experimental inductive science.

George Pólya
Mathematics succeeds in dealing with tangible reality by being conceptual. We cannot cope with the full physical complexity; we must idealize.

George Pólya
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 Pólya
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 Pólya
Facing any part of the observable reality, we are never in possession of complete knowledge, nor in a state of complete ignorance, although usually much closer to the latter state.

George Pólya
I... present also examples of historic interest, examples of real mathematical beauty, and examples illustrating the parallelism of the procedures in other sciences, or in everyday life.

George Pólya
The efficient use of plausible reasoning is a practical skill and it is learned... by imitation and practice.... what I can offer are only examples for imitation and opportunity for practice.

George Pólya
It is hard to have a good idea if we have little knowledge of the subject, and impossible to have it if we have no knowledge. Good ideas are based on past experience and formerly acquired knowledge.

George Pólya
The general or amateur student should also get a taste of demonstrative reasoning... he should acquire a standard with which he can compare alleged evidence of all sorts aimed at him in modern life.

George Pólya