Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements.
George PolyaMathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself
George PolyaQuite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so inconspicuous. The expert has, perhaps, no more ideas than the inexperienced, but appreciates more what he has and uses it better.
George PolyaLook around when you have got your first mushroom or made your first discovery: they grow in clusters.
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 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