When entering spaceship in order to leave Synnax for Trentor, Gaal is reaching her right arm to touch the palm recognition screen. When her hand is touching the screen, it's the left hand.
A sound mathematical proof can be judged correct by any competent mathematician who has learned the terminology, even if it required a genius to find it. A proof which can only be verified by two people in the galaxy is not mathematics but magic. (In the novel, the estimate of the probability of Trantor's destruction is a routine field-differentiation which Seldon expects Dornick to do in his head.)