If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.
George PolyaThe best of ideas is hurt by uncritical acceptance and thrives on critical examination.
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 PolyaAnalogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements.
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 Polya