even or odd

The character Dupin and his supernatural abilities are nicely exhibited in 'the purloined letter.' with the contrasting paris police working opposite, we see the height of these extraordinary abilities. his reference to the child's game, 'even and odd' shows how his state of mind and the police's differ. Dupin has this cognitive psychological perception where rationality isnt always going to take you toward the answer fastest.
Poe interjects also this issue of mathematics vs poetry. Where the prefect sees a poet as a fool, Dupin, one who has been 'guity' of taking personal interest in poetry, does not make the prefect's mistake. because the prefect judges Minister D's intellect, he assumes that D would hide it like any normal person (like himself) would-- merely hidden in a minuscule spot in the apartment. already he has eliminated the option that it could have been so obvious as on the desk.
poe writes: "The mathematics are the science of form and quantity; mathematical reasoning is merely logic applied to observation upon form and quantity...Mathematical axioms are not axioms of general truth. What is true of relation--of form and quantity--is often grossly false in regard to morals, for example."

I think this is a nice example, like sonnet--to science, of an acknowledgment for the logical mind, though perhaps poe finds it completely useless to 'general truth' without moral, emotional, and certainly the INTUITION, which not surprisingly, poe often seems to hold very close throughout his writings. thoughts?