For mathematics education and the world of problem solving it marked a line of demarcation between two eras, problem solving before and after Polya.
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A. H. Schoenfeld, in "Polya, Problem Solving, and Education" in Mathematics Magazine (1987)George Polya
Design is really a special case of problem solving. One wants to bring about a desired state of affairs. Occasionally one wants to remedy some fault but more usually one wants to bring about something new. For that reason design is more open ended than problem solving. It requires more creativity. It is not so much a matter of linking up a clearly defined objective with a clearly defined starting position (as in problem solving) but more a matter of starting out from a general position in the direction of a general objective
Edward de Bono
I honestly don't believe we will be solving the greater human conflict with our efforts. The problem is not a certain type of legislation or even a certain politician; the problem is the same that it has always been. I am the problem.
Don Miller
The problem of thermonuclear reactions is not a usual physics problem. This is a problem that must transform society and the world. Our generation, which gave to mankind atomic energy and thermonuclear energy in the form of explosions, is responsible to humanity for solving the main problem of energy – obtaining energy from water. People are waiting for the solution of this problem. Our duty is to solve it within the lifetime of our generation, and therefore we must set out on this path.
Gersh Budker
I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.
Andrew Wiles
The Feynman Problem-Solving Algorithm:
(1) write down the problem;
(2) think very hard;
(3) write down the answer.Murray Gell-Mann
Polya, George
Polybius
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