The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea.
George PolyaThe best of ideas is hurt by uncritical acceptance and thrives on critical examination.
George PolyaThe cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. ... Mathematics cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information.
George Polya