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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.

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    My advisor's strategy was to point out a few interesting papers, that might inspire a direction, but it was my responsibility to propose a thesis topic. This was pretty common, though there were exceptions where a colleague's advisor actually handed him or her the core problem.
    – A rural reader
    Commented Nov 15, 2021 at 1:46
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    What do you mean "suggest"? Advisors throw out ideas all the time, that's practically what they're for. Or do you mean "set research problems" as in you can't choose something else?
    – Azor Ahai -him-
    Commented Nov 15, 2021 at 3:25
  • @AzorAhai-him- By "suggest", I mean suggest. Advisor suggesting a problem to his student, saying that this might be a good problem to work on. It's not that he's forcing the student to do that particular problem.
    – It'sMe
    Commented Nov 15, 2021 at 4:02
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    So, like, are you worried this prof is suggesting you more things than other people, and that might be some indicator of how skilled you are?
    – Azor Ahai -him-
    Commented Nov 15, 2021 at 4:56

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This varies widely, even within pure math. Some advisors will refuse to give students any very specific advice about problems to work on—for instance this was known to be the policy of Marshall Stone, and I think I recall Mandelbrot writing that in his generation it was only just becoming conceivable for a French mathematician to suggest a problem to an advisee. Noting that both these guys are from a few generations ago, it’s probably much rarer now to get almost no guidance from an advisor. Plenty of students get extremely specific guidance; in European PhDs, which are shorter than American ones, it seems to me that many students are given a problem to solve before they’re even selected to enroll. Perhaps the majority of students, at least in the US, fall somewhere in between: it’s a critical function of the advisor to stop students from pursuing unreasonable or unimportant directions, while ideally not forcing them away from their particular interests.

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