Often in the comments on questions involving challenging sums or integrals, I will see someone make a comment something to the effect of "Do you have any reason to believe this has a nice answer?" I'm curious as to what sort of assurance the user making such a comment is looking for. If the problem is something like a homework problem and the answer is already known, it would certainly be helpful to indicate that in the question.

In other cases where it is not already known that a "nice answer" exists, it is often not obvious (at least for me) that a problem has a "nice answer" until an approach to finding that nice answer has been found and the problem is basically already done. In a question like this, what other sort of a priori evidence of "niceness" is being requested?

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    $\begingroup$ In general, these users aren't necessarily being critical. They're asking if the problem came from somewhere, or if it just arose from the poster's curiosity (or from some other work). If it should have a good closed form solution, this changes how one approaches the problem, and if it doesn't necessarily have one, this allows an answerer to accept when he comes to a solution that isn't pretty rather than worrying he made a mistake. $\endgroup$ – Alexander Gruber Sep 18 '13 at 23:15
  • $\begingroup$ @AlexanderGruber This makes sense, thank you. $\endgroup$ – Bitrex Sep 18 '13 at 23:34
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    $\begingroup$ For indefinite integrals at least, one can have very good intuition about whether a nice answer is plausible. $\endgroup$ – André Nicolas Sep 19 '13 at 6:57
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    $\begingroup$ I think such users should make this clear though. Certainly some of them have not, as otherwise Bitrex would not be asking this question...(If they don't make it clear, it does come across as kind of accusatory, and also the OP isn't necessarily going to know that all they want to know is that it is a problem from somewhere...) $\endgroup$ – user1729 Sep 19 '13 at 10:27
  • $\begingroup$ If you don't know whether a nice answer exists, then it might make sense to state in the question what kinds of ugliness you are willing to accept. Would numerical approximations be fine? Would a sequence converging to the actual value be fine? Would a formula spanning hundreds of pages be fine? Or do you need a short but exact closed form, and everything else would be useless as an answer? In cases where you don't know whether a nice solution exists, you usually have some application in mind, and therefore can give specifics along these lines. $\endgroup$ – MvG Sep 28 '13 at 21:12

I think the person making such a comment simply wants to know what reason there might be to think there is a nice solution before investing a lot of time chasing down a rat hole. If the problem came from a list of questions, then there is a better possibility that it has a nice solution than if it is just a made up question.

  • $\begingroup$ Thanks for the answer. I was unclear as to whether, in the case of "rat hole" type made-up problems, there was some specific supplementary mathematical evidence related to the problem that was being requested, rather than just acknowledgement that it was unknown if it had a nice solution or not. $\endgroup$ – Bitrex Sep 18 '13 at 23:38

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