This is also a term in

mathematics, a sort of informal technical term, like "

obvious" or "

trivial" or "

intuitive". For all I know it may be used in other disciplines this way as well.

A hand-waving argument is one used to fill a gap in a proof. If it would be too tediously technical to actually explain the proof, given the time available in a lecture, but it is fairly obvious what line the proof would take, the detail may be skipped by waving a hand and saying in effect, Trust me, it does work if you do it in detail.

It is not an aspersion against the audience, nor an admission of failure by the lecturer, nor need the point being evaded be especially difficult, only long-winded or niggly.

It is slightly different from a section being obvious (in the mathematician's peculiar sense) or an exercise for the student, in that it might not be obviously true beforehand. The lecturer does explain it, just doesn't do so rigorously.

Of course, at times the hand waving *might* be used because the lecturer sees a problem they can't solve to their own satisfaction on the spot, but doesn't want to admit it, or even because they've seen that what they were saying was wrong but doesn't want to get sidetracked into working out the correct solution. But in general, the point is that a hand-waving proof in mathematics need not contain any such flaw. It is often legitimate.