A thaumaturge is a magician or mystic. If you impress your friend by pulling coins out of her ear or turning her homework into a bouquet of flowers, she may call you a thaumaturge.
The original definition of thaumaturge, dating from 1715, is "worker of wonders." Most early thaumaturges were practitioners of nonreligious magic, particularly magic that was based in science or mathematics. Occasionally, the word has also been used in a religious sense, to mean "saint" or "miracle worker." This word is rooted in the Greek thaûma, "wonder or astonishment."