Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice.
George PolyaSuccess in solving the problem depends on choosing the right aspect, on attacking the fortress from its accessible side.
George PolyaA mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is like a monkey who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise.
George PolyaWhen introduced at the wrong time or place, good logic may be the worst enemy of good teaching.
George PolyaTo write and speak correctly is certainly necessary; but it is not sufficient. A derivation correctly presented in the book or on the blackboard may be inaccessible and uninstructive, if the purpose of the successive steps is incomprehensible, if the reader or listener cannot understand how it was humanly possible to find such an argument....
George Polya