In "The Purloined Letter," Dupin is strongly asserting that to find the letter, the detective must think both like a poet and a mathematician. Dupin believes there is no other way to find the stolen letter.

Dupin continually preaches that logic (mathematics) alone is insufficient to solve crimes. By being a "poet," Dupin means that the detective must engage imaginatively with the thinking and psychology of the criminal. As he says of the police,

They consider only their own ideas of ingenuity; and, in searching for anything hidden, advert only to the modes in which they would have hidden it.

In the case of the political minister who stole the letter, this won't work, Dupin says, because the minister is both a poet and a mathematician. This means that the minister, being a poet, thinks imaginatively and in creative ways that outsmart normal people.

Dupin acknowledges that the police have done an excellent job of applying logic to the case. They have completely ripped apart the minister's apartment from top to bottom, searching in walls, in floors, and in every possible crevice to find the missing letter. And yet, they have failed. They have been utterly thorough about the details but have overlooked the big picture, because they have failed to engage with the personality of the criminal.

Because Dupin is able to think both logically and creatively—to use, as we would say today, both sides of his brain—he is able to see the answer to the puzzle of stolen letter. He is able to see what is hiding in plain sight.

Poe's insight that psychology ("poetry") and getting into the mind of the criminal is important to crime-solving has become a staple of the mystery genre, later used expertly by literary detectives such as Sherlock Holmes.