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Are there problems posed with any frequency on MSE that are known to be unsolvable in a strong formal sense, such as being independent, undecidable, or blocked by Goedel's theorem? Requests for solution of NP-hard problems or graph isomorphism recur, but has there been any stream of questions like:

prove mathematics is consistent
solve the Continuum Hypothesis
test if two groups are isomorphic from their presentations
algorithm to solve arbitrary Diophantine equations

?

Clarification (edit). This is not intended as a question about policy, allowed questions, or what to close, but about the content of the traffic on MSE. I am requesting links or memories of examples, and briefly had added the [big-list] tag to the original posting, but dropped it when a list of questions in that tag looked like it is being used for different things. Adding the tag again.

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    $\begingroup$ Rolling back the edit : this is not asking about "allowed-questions" or suggesting these questions not be allowed. Of course they are on-topic and the askers probably do not know that they are requesting the impossible. $\endgroup$ – zyx Jun 7 '13 at 15:57
  • $\begingroup$ Also the problem arises with problems that are conjectured intractable, e.g. a recent example is this question on a problem related to the $\,3x+1\,$ Collatz conjecture. It may be that some classes of this problem are tractable, but probably only experts would be able to decide in the half-hour it took to quickly close it (which probably was not the optimal way to welcome a relatively new user who spend much time composing the question). It's not clear if it was closed for being conjectured intractable, or for other reasons (e.g. not focused). $\endgroup$ – Key Ideas Jun 7 '13 at 16:06
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    $\begingroup$ In any case, if we wish to attract further experts, it certainly helps to leave difficult questions open, so that they will find some things of interest when they stumble upon MSE. $\endgroup$ – Key Ideas Jun 7 '13 at 16:07
  • $\begingroup$ @KeyIdeas : amazing, not in a good way, that the Collatz variant was closed. The OP raised an interesting matter of whether the rule he proposes for assigning a multiplicative constant is a valid way to gauge difficulty. I cannot see how any objection to random posting of unsolved problems should block a discussion of that. $\endgroup$ – zyx Jun 9 '13 at 21:23
  • $\begingroup$ So this question is not about the recent rise in Beal conjecture related questions? $\endgroup$ – Hagen von Eitzen Jun 15 '13 at 22:22
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For comparison, the policy on MathOverflow is roughly the following. I am not arguing that M.SE adopt the same policy, merely bringing it up for informational purposes.

  1. Questions which are well-known to be open are off-topic and are closed
  2. If a question turns out to be a not-famous but nonetheless known to be open to experts, then someone will leave an answer saying "This is equivalent to a well-known open problem in subfield X, see paper Y."

By "open problem" I mean an old question that experts have thought about and everyone is stuck on. This is different from a new question which hasn't been answered yet. The latter is appealing to experts, the former is off-putting to experts.

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    $\begingroup$ Thanks. I have added an edit to the question. Which is not to say that it would not be interesting to have a thread with discussion of policy on these questions, but the (policy) and (allowed-question) tags were excluded for a reason. $\endgroup$ – zyx Jun 7 '13 at 17:03
  • $\begingroup$ Sorry, I should read more carefully. $\endgroup$ – Noah Snyder Jun 7 '13 at 17:18
  • $\begingroup$ I believe MO actually moves constructive questions about open problems (questions about particular approaches, for example) to CW. $\endgroup$ – dfeuer Jun 15 '13 at 18:26
  • $\begingroup$ I second the second motion. $\endgroup$ – yiyi Jun 20 '13 at 6:09
  • $\begingroup$ For updates, see here. $\endgroup$ – Andrés E. Caicedo Jul 6 '13 at 20:57

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