I was all excited when it looked like my AP Physics class had (initially by accident) discovered and then proven a new theorem:
If a physical pendulum with pivot at point A has its center of oscillation at point B, then when the same pendulum has its pivot at B, its center of oscillation will be at A.
But it turns out that Christiaan Huygens had beaten us to it by about 350 years. See this paper and scroll down to Proposition XX. And he did it with his hands tied behind his back -- he didn't even have Newton's Laws at his disposal, let alone the Parallel Axis Theorem. Huygens was certainly no slouch, so if we're going to lose to someone, it might as well be to him.