George Pólya - Cases Quotes

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Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry. … To apply a rule with natural ease, with judgment, noticing the cases 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.

George Pólya

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 Pólya

If we deal with our problem not knowing, or pretending not to know the general theory encompassing the concrete case before us, if we tackle the problem "with bare hands", we have a better chance to understand the scientist's attitude in general, and especially the task of the applied mathematician.

George Pólya