Abracadabra! Thaumaturgy is a fancy way to say magic. If you're interested in thaumaturgy, you might want to apprentice with a renowned magician.
While it's most common to use this word to mean "magic" or "mystical powers," thaumaturgy has had a variety of meanings since its appearance in the 18th century. It comes from the Greek roots thaûma ("miracle") and érgon ("work"), and it's frequently used to refer to the scientific principles behind magic or the "magic" of science and mathematics. Other definitions include "the work of Christian saints" and simply "philosophy."