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[ G.Polya ] Pedantry and mastery are opposite attitudes towards rules. 1. To apply a rule to the letter, rigidly, unquestion- ingly, in cases where it fits and in cases where it does not fit, is pedantry. Some pedants are poor fools; they never did understand the rule which they apply so conscientiously and so indiscriminately. Some pedants are quite successful; they understood their rule, at least in the beginning(Before they became pedants), and chose a good one that fits in many cases and fails only occasion- ally. To apply a rule with natural ease, with judgement, noticing the cases where it fits, and without ever letting the words of the rule where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery. 2. The questions and suggestions of our list may be helpful both to problem-solvers and to teachers. But first, they must be understood, their proper use must be learned, and learned by trial and error, by failure and success, by experience in aplying them. Second, their use should never become pedantic. You should ask no question, make no suggestion, indiscriminately, follow following some rigid habit. Be prepared for various question and suggestions and use your judgement. You are doing a hard and exciting problem; the step you are going to try next should be prompted by an attentive and open- minded consideration of the problem before you. You wish to help a student; what you say to your student should proceed from a sympathetic understanding of his difficulties. And if you are inclined to be a pedant and must rely upon some rule learn this one: Always use your own brains first.