I started my second year as PhD student this Fall and I was wondering how often do PhD supervisor suggests research problem to their PhD student? Does it happen only during the initial years of PhD? If the supervisor gives the research problem, will it affect the student's progress in becoming an independent researcher?
I asked my supervisor this question once at the beginning of my PhD and he told me that it's difficult for me to come up with research problem at this stage.
I'm particularly interested in the answer to this question in the context of Pure Mathematics, but I would be happy to know the answer to this question in other fields, like computer science, engineering, biology, etc.