April 15, 2011

« Yes, the solution seems to work, it appears to be correct; but how is it possible to invent such a solution? Yes, this experiment seems to work, this appears to be a fact; but how can people discover such facts? And how could I invent or discover such things by myself? »

« Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself. »

« The feeling that harmonious simple order cannot be deceitful guides the discoverer both in the mathematical and in the other sciences, and is expressed by the Latin saying: simplex sigillum veri. »

« Good problems and mushrooms of certain kinds have something in common; they grow in clusters. Having found one, you should look around; there is a good chance that there are some more quite near. »

« Leibnitz, great mathematician and philosopher, planned to write an “Art of invention” but he never carried through his plan. Numerous fragments dispersed in his work show, however, that he entertained interesting ideas about the subject whose importance he often emphasized. Thus, he wrote: “Nothing is more important than to see the sources of invention which are, in my opinion, more interesting than the inventions themselves”. »

~ “How to solve it”. G. Polya.

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