The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.
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- An idea which can be used only once is a trick. If one can use it more than once it becomes a method. β¨ Problems and Theorems in Analysis I: Series. Integral Calculus. Theory of Functions.
- The teacher can seldom afford to miss the questions: What is the unknown? What are the data? What is the condition? The student should consider the principal parts of the problem attentively, repeate β¦ βΆ
- The principle is so perfectly general that no particular application of it is possible. β¨ George PΓ³lya (1948). How to solve it: a new aspect of mathematical method
- Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as a whole as clearly and as vividly as you can. ... What can I gain by doing so? You should un β¦ βΆ
- 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 app β¦ βΆ
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