Of all the words in English that refer to the making of magic, this is perhaps the most resonant. It doesn’t have the negative associations of words such as sorcery or necromancy because it referred originally to the production of wonders for positive ends rather than any intent to cause someone harm.
The origin is the Greek word thaumatourgos, miracle working (from thauma, marvel, plus ergos, work). Though it’s not that common a word, it seems to have generated a surprisingly large set of derivatives since it first appeared in English in 1727. There are several words for a practitioner of thaumaturgy, including thaumaturge and thaumaturgist; another is thaumaturgus, which has been given to a number of Christian saints and others who are said to have performed wonders. The verb is thaumaturgise.
The thaumatrope was a Victorian toy, a card with two different pictures on its back and front that magically combined into one when the card was rapidly spun. And aficionados of Terry Pratchett’s Discworld novels will know that the wizards of Unseen University invented a device with which to measure the intensity of a magic field — what would you call that but a thaumometer?