It is better to solve one problem five different ways, than to solve five problems one way.
George PolyaThe result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing.
George PolyaIf 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 PolyaThe world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is feasible.
George PolyaWhat is the difference between method and device? A method is a device which you use twice.
George PolyaSolving 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