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The term "handwaving" is used in mathematics and physics to describe arguments that are not mathematically rigorous.

Such arguments often include order-of-magnitude estimates and appeals to symmetry or dimensional consistency.

The term derives from the use of gestures to add emphasis when stating arguments, and the tendency to continue or increase the gesturing as a substitute for mathematics, when an argument is hard to put across or the proponent is tired of deploying words and/or symbols.

The expression "vigorous handwaving" is meant to suggest at least that the proponent should be aware of failing to convince; it may suggest the proponent lacks confidence in the validity of their own argument.