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This problem is one of the "unsolved" Millennium Prize Problems named by Clay Mathematics Institute (CMI)
It is very beneficial for fresh gradute student to be able to connect to a senior personel who has ample experience, and who at the same time still can relate to situations fresh gradute face. A mentor is the most often go-to person when dealing with personal issues, in case of unexpected events, or even in the aftermath of a calamity when seeking aftercare. However, what makes the task of mentor a difficult one in general is that the role of a mentor is ambiguous. As a mentor, you have to simultaneously connect on a personal level and relate to the organisational structure of the institution on a professional level.
So knowing who is who, which protocols are in place, and where your responsibilities as a mentor lie within an organisation, is crucial in understanding your role as a mentor, and knowing the boundaries of your responsibility. Also, having communicated all this to the fresh gradute student at the start, can help you deal with such situations later on.
All in all setting the right tone and sharing the expectations with fresh gradute student can help.
Explaining to the graduate what they can expect goes a long way toward preventing issues later on in the organization.
