Rules of discovery. 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.
It may be good to be reminded somewhat rudely that certain aspirations are hopeless. Infallible rules of discovery leading to the solution of all possible mathematical problems would be more desirable than the philosophers’ stone, vainly sought by the alchemists. Such rules would work magic; but there is no such thing as magic. To find unfailing rules applicable to all sorts of problems is an old philosophical dream; but this dream will never be more than a dream.
A reasonable sort of heuristic cannot aim at unfailing rules; but it may endeavor to study procedures (mental operations, moves, steps) which are typically useful in solving problems. Such procedures are practiced by every sane person sufficiently interested in his problem. They are hinted by certain stereotyped questions and suggestions which intelligent people put to themselves and intelligent teachers to their students. A collection of such questions and suggestions, stated with sufficient generality and neatly ordered, may be less desirable than the philosophers’ stone but can be provided. The list we study provides such a collection.