Poe's Stories brief biography of edgar allan poe

Dupin then explains himself to the narrator of "The Purloined
Letter". He says that he had faith that the police would do a completely thorough search of the apartment, as far as their methods allowed. But this method is not suited to the criminal in question – the prefect has been both too shallow and too deep in his search. Dupin gives an example to illustrate his point. He reminds the narrator of a schoolboy game, where one boy conceals marbles in his hand, and the other must guess whether it is an even or odd number of marbles. One boy that
Dupin once knew was a master of this game because he knew how to predict the other boys behavior according to their intellect. The boy claimed that he mimicked the other boy’s expression and in doing so, found a natural kind of sympathy for the boy’s thoughts and intentions. Dupin compares the schoolboy to famous thinkers like Machiavelli.
One of the most unlikely and intimidating factors of Dupin’s
intelligence is his understanding of many different kinds of people,
to the extent that he seems to inhabit their minds. But his
sympathies also allow him to see genius in unlikely places, this child
on the school playground for example. This sensitivity to displays of
intelligence in many walks of life is significant in making Dupin seem
more human.
So, the accuracy of the guess depends on the accuracy with which the opponent is judged. Dupin says that the police only think about what they would have done in the situation, where
they would have hidden the letter, and this is only accurate of a kind of average, Prefect-like intelligence and not of the more unusual kind of the Minister. Their problem is they never adjust their approach, they only exaggerate it, as they did by searching the house over again. By assuming that the letter can be found by something as basic as searching, they are completely disregarding the acumen of the criminal.
There is something about the mind of a criminal and minds
themselves that fascinates Dupin. This passion and his unusual
sensitivity and sympathy for other minds makes him an intimidating
character, because he fills neither the role of detective nor the role of
criminal, but somewhere in between or both at once.
The Prefect’s shortsightedness is also down to his perception of the Minister as a fool, because he is a poet. All fools are poets, says Dupin, but it does not necessarily follow that all poets are fools. The narrator remembers that the minister is a renowned mathematician and wonders if Dupin has misattributed the title of poet, but Dupin claims he knows the man well, and he is both mathematician and poet. If he were only a mathematician, he wouldn’t have been able to reason so well, says Dupin. The narrator of "The Purloined Letter" thinks this is a strange theory. It is completely contrary to popular opinion about mathematics. But Dupin responds with a French phrase about how inconsequential an idea’s popularity is.

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