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Is it a good idea to attend seminars and then try to generate new research problems? Once I attended a panel and a senior mathematician said, "That's like asking how a composer makes music." Not very helpful.

One tip I read was to ask for variations, e.g. modify hypotheses. The issue I've run into is that it sometimes leads to almost identical results with no new ideas or techniques. In other woeds, slight variations on known results. Those almost never get published in good journals.

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  • This seems like a duplicate of your past question (linked above), and very very similar to How do I know what the important problems to work on are? I realize you may still be stuck on this point, but duplicate and near-duplicate posts are not allowed; consider adding a bounty instead.
    – cag51
    Commented May 5, 2023 at 3:05
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    FWIW, I agree with the "senior mathematician" -- if you have reached the post-doc level, I suspect you should be able to generate research topics (though I'm no mathematician). From a distance, I can't tell whether you just didn't learn this as a grad student (did you have an unusually bad experience in grad school?), or if you have learned it and are experiencing the normal difficulties in a hyper-competitive field. But there is no simple answer; this is a skill that takes years (usually under supervision) to develop).
    – cag51
    Commented May 5, 2023 at 3:07
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    In the entire 50-60 year history of our low-ranked, small PhD program, as far as I can tell there have been zero pure math PhDs who have gotten a postdoc or indeed done any significant research after graduating. Most 40-ish ranked PhD programs have maybe one pure math graduate a decade who goes on to do a postdoc or write more than a couple papers not in a write-only journal in their career. It's a difficult and competitive field where all the interesting and easy problems were solved a century or more ago. Commented May 5, 2023 at 4:08
  • [deleted my intemperate+unhelpful comment]
    – Yemon Choi
    Commented May 6, 2023 at 2:11
  • @AlexanderWoo sorry for the random tag, but can I ask you what all those math PhDs do after graduating if they are not able to go further in the academic path? Does your institution have some statistics in that regard?
    – Amelian
    Commented Aug 23, 2023 at 5:47

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