The Rice University Neologisms Database

Unexplained, unfounded; almost magical in origin. The adjective "hand-wavy" comes from a reference to a magician's act where he waves his hands and makes something (a bird, bouquet, handkerchief, etc.) appear as if out of thin air. The words 'hand' and 'wave' are compounded (from the phrase "I'll wave my hands and (something) will appear" or something similar) and then an adjective suffix "-y" is affixed to change the inflection to create "hand-wavy". It is generally used to describe an idea or concept that doesn't seem to have any foundation, that seems to appear "out of thin air". It is typically used by professors, TA's and students (anyone involved in the learning process) since they have the most contact with these novel ideas. It probably first came about due to its rather "magical" connotation to describe how "magically" some of these laws or concepts first appear.