Why would a professor doing pure math/ theoretical computer science want to take PhD students?

I understand that in computational and experimental sciences taking students is at least beneficial to them. However, in subjects like pure math, it is not obvious to me that there are any significant advantages to take some PhD students. It is probably expected from the department that you will take some students, and it is nice to have someone who can type things up for you. But other than that, I don’t see any reasons.

So, why would they want to do that? What are they expecting from their (prospective) students?

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