The winged staff of Hermes (Mercury), which gave the god the power to fly.
Originally a simple olive branch, its stems were afterwards formed into
snakes, and several poetical tales devised by the mythologists to explain
this, as that Hermes having found two snakes fighting, divided them with
his rod, and thus they came to be used as an emblem of peace. It was the
staff or mace carried by heralds and ambassadors in time of war. It was
not used by the Romans. Many magical virtues were ascribed to the caduceus;
in Homer, Hermes touches with it the souls of the dead, and so lulls them
to sleep before carrying them to the underworld. It is also seen in the
hands of Ares (Mars), Dionysius, Hercules, Demeter, and Aphrodite.
in mathematics and medicine (Encyclopedia of Science)