Richard P. Feynman taught an undergraduate class that I sporadically sat in on circa 1975-76. Maybe the subject was advanced quantum mechanics; I don't really remember. I do remember the teacher.
Dick Feynman was an extraordinary physicist, and his passion for science was contagious --- but he was also an extraordinary entertainer. He loved to perform before an audience of Caltech kids as much as the students loved to learn from him. His Brooklyn accent was so pure and undiluted that we speculated he must listen to language tapes, to keep it fresh.
Once during a lecture Feynman appeared to get stuck during a derivation. He excused himself, moved over to one corner of the blackboard, and drew some small mysterious diagrams. After looking at them for a few moments he smiled, winked at us, erased his scribbles, and went back to continue solving the main equations. Did he really reinvent the math on the fly, in real time? Or was it a planned stage trick, a visual play on the Feynman Diagrams that were part of his Nobel prize-winning research many years before? No matter --- we all laughed together with him at the physical comedy. (pun intended!)
FourPiFeedback (27 Jan 2003) brought to mind another Feynmanesque moment. Dick was in the process of doing some surface integrals for the crowd, and as often happened he paused to reminisce. "You know the circumference of a circle and the surface area of a sphere," he said. Then he quickly demonstrated the general case, the formula for the boundary of a hypersphere in N dimensions. "See that factorial there? If you write it as a gamma function you get the surface area of a sphere in X dimensions. Notice that X doesn't have to be an integer. I did that a long time ago, and then I worked out a few other properties of objects in fractional dimensions. What the hell good are they? I have no idea!"