An idea which can be used only once is a trick. If one can use it more than once it becomes a method.
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 PolyaA 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 PolyaSolving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice.
George PolyaIf you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.
George Polya