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Community: Should one attack hard problems - closing/reopening

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    This question got closed and now has 3 votes to reopen:
    http://mathoverflow.net/questions/123081/should-one-attack-hard-problems-closed

    Thought it might be nice to have a meta thread for discussion so the comments don't get out of hand. It managed to get 4 answers before being closed, as well as a comment which is more highly voted than any answer:

    "I'm not sure this is an ideal MO question because it doesn't have a unique answer, it just has people's opinion. But here's my opinion. I've supervised over 10 PhD students to completion and one thing I know is that if you give a PhD student a problem for which there is a non-zero chance that after 4 years they have done nothing worth publishing (e.g. because the problem has been studied for so long by so many people that 4 years isn't enough), then you have just ruined that person's math career. On the other hand, at least once a month I try to work on a famous unsolved problem for a bit. – wccanard"

    I agree with this comment and don't know why anyone would want to reopen the question.
    • CommentAuthorbsteinberg
    • CommentTimeFeb 27th 2013
     
    The comment says it all and the answers are variations on the comment. This type of question was popular in 2010. Normally such questions no longer garner so many answers and upvotes, but since this one has I am not sure it is worth having an open/close war about it. There are worse soft questions. I think the best thing is to leave it open unless really bad answers start to come in. If this happens then it is best to close as no longer relevant.
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    I have both voted to reopen and upvoted the comment (for its latter part, there is an identification problem in why people upvoted it). It is clear that is not a perfect fit for MO, but it is also clear that it is an important issue. Dissertation choices can obviously have a huge impact on a career. While there is no unique right answer (a property which is certainly shared by several "pure" MO questions), there are certainly interesting considerations one can collect and the weigh using ones own judgement. While one could rephrase the question to bring out that aspect more ("What are adavantages and disadvantages in attempting to tackle a big unsolved problem in ones dissertation?"), I think one can give a benevolent interpretation.
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    As is well-known, "advice questions" are generally subject to greater scrutiny as regarding appropriateness for MO.

    I certainly think the question is highly subjective. What sorts of problems one tackles, and especially whether one "should" tackle the hard open questions, is very much related to the individual personality. There are some who love to tackle the big ones (Paul Cohen, John Nash, and de Branges all come to mind), with varying degrees of success, and I think that's a personality thing. But there is no way of giving a one-size-fits-all answer.

    The answers that have appeared so far are good, but good in a very general piece-of-wisdom way, and absolutely the types of answers one would expect. I don't think there is much chance of improving on them, as general wisdom goes.

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