Humans tend to be better at physics than at mathematics.  After all, when an apple falls from a tree, there are more people who can catch it—they know physically how the apple moves—than people who can compute its trajectory from a differential equation.  Applying physical ideas to discover and understand mathematical results is therefore natural, even if it has not been tried so often in the history of science.  (The exceptions include Archimedes, some old Russian sources, a recent book of Levi’s, as well as articles and lectures by yours truly.)  A variety of elementary yet surprising examples will be presented.