A Professor Emeritus can be really ancient. Win a Nobel Prize and your courted well into your dotage. Gwyneth Paltrow in Prime suggests that it's never going to happen if you haven't developed your elegant mathematical theorum before 30. I'm not sure where John Nash and Stephen Hawkins fit - they are outside the box and in their own categories.
Does the brilliant brain stay nimble and is a nimble brain essential?
How physically demanding is thinking, reading, presenting? It was a real shock to me how much stamina it took just to audit CCK08 from my own home. It certainly ended any delusions that it was possible to pick up where you left off after raising a family.
What aspect of teaching finally does one in? I had a professor who said the key to teaching is enthusiasm. So maybe people reach a point where it just isn't exciting anymore. Perhaps it's when your style is no longer in vogue or your name is no longer a drawing card.
Here's a confession. When I'm paying tuition, I google the teacher's name. You'd be surprised how often nothing comes up. How can that even be possible? Even dead people have their obituaries online.