# George-Polya Quotes

Enjoy the top 19 famous quotes, sayings and quotations by George-Polya.

“It is generally useless to carry out details without having seen the main connection, or having made a sort of plan.”

— George-Polya —

Mathematics 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.

— George-Polya

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

If you can't solve a problem, then there is an easier problem you can solve: find it.

— George-Polya

Beauty in mathematics is seeing the truth without effort.

— 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

I started studying law, but this I could stand just for one semester. I couldn't stand more. Then I studied languages and literature for two years. After two years I passed an examination with the result I have a teaching certificate for Latin and Hungarian for the lower classes of the gymnasium, for kids from 10 to 14. I never made use of this teaching certificate. And then I came to philosophy, physics, and mathematics. In fact, I came to mathematics indirectly. I was really more interested in physics and philosophy and thought about those. It is a little shortened but not quite wrong to say: I thought I am not good enough for physics and I am too good for philosophy. Mathematics is in between.

— George-Polya

The 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 see them.

— George-Polya

It is generally useless to carry out details without having seen the main connection, or having made a sort of plan.

— George-Polya

Nothing is more important than to see the sources of invention which are, in my opinion, more interesting than the inventions themselves.

— George-Polya

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

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

— George-Polya

A 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 brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.

— George-Polya

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

Good problems and mushrooms of certain kinds have something in common; they grow in clusters.

— George-Polya

Analogy pervades all our thinking,

— George-Polya

Mathematics, you see, is not a spectator sport. To understand mathematics means to be able to do mathematics. And what does it mean [to be] doing mathematics? In the first place, it means to be able to solve mathematical problems.

— George-Polya

You should be grateful for all new ideas, also for the lesser ones, also for the hazy ones, also for the supplementary ideas adding some precision to a hazy one, or attempting the correction of a less fortunate one.

— George-Polya

There is nothing to learn about reasoning and invention if the motive and purpose of the most conspicuous step remain incomprehensible.

— George-Polya

Even 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 miss an important and instructive phase of the work ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.

— George-Polya

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