Two very different attitudes toward the technical workings of mathematics are found in the literature. Already in 1761, Leonhard Euler complained about isolated results which "are not based on a systematic method" and therefore whose "inner grounds seem to be hidden." Yet in the 20'th Century, writers as diverse in viewpoint as Feller and de Finetti are agreed in considering computation of a result by direct application of the systematic rules of probability theory as dull and unimaginative, and revel in the finding of some isolated clever trick by which one can see the answer to a problem without any calculation.

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Feller's perception was so keen that in virtually every problem he was able to see a clever trick; and then gave only the clever trick. So his readers get the impression that:

• Probability theory has no systematic methods; it is a collection of isolated, unrelated clever tricks, each of which works on one problem but not on the next one.
• Feller was possessed of superhuman cleverness.
• Only a person with such cleverness can hope to find new useful results in probability theory.

Indeed, clever tricks do have an aesthetic quality that we all appreciate at once. But we doubt whether Feller, or anyone else, was able to see those tricks on first looking at the problem. We solve a problem for the first time by that (perhaps dull to some) direct calculation applying our systematic rules. After seeing the solution, we may contemplate it and see a clever trick that would have led us to the answer much more quickly. Then, of course, we have the opportunity for gamesmanship by showing others only the clever trick, scorning to mention the base means by which we first found.

E. T. Jaynes "Probability Theory, The Logic of Science"