The real student is the teacher. Because teaching is, in essence, also studying; but studying in a depth that can only be achieved through teaching. Or rather: it is teaching itself that demands it, since it brings up a multitude of problems that lead to further research, unimaginable to the average student. So the teacher, if he is not a bad teacher, the more he teaches, the deeper he gets into the subject, the more he learns about its details, the more he crystallizes the theory in his mind and the more able he becomes to teach, because he discovers what the student needs to learn.