Please forgive me if I did not post this correctly. I'm writing following https://mathoverflow.net/help/reopen-questions. I would like to ask for my question to be reopened: https://mathoverflow.net/questions/135605/how-to-discover-counterexamples-and-required-objects. I do not understand why it would be deemed "off-topic." I am grateful for the comments there which support it. Here is some of the calculus:

  1. Before posting my question, I read When and how is it appropriate for an undergraduate to email a professor out of the blue?. This was a question which had been open and now answered, posed by an undergraduate asking for advice from professors. Moreover, that question could apply to professors of any subject and yet remains extremely helpful. My question concerns the study of math specifically.

  2. Similarly, my question seeks advice from professors and research mathematicians. Since it appears that research mathematicians encounter counterexamples and objects which must be created, they seem to be in the most apposite and reasonable position to answer and so I have posted on MathOverFlow.

  3. Also, professors would experience and be privy to more learning and studying styles from many diverse students. This bolsters and corroborates this question's fitness for MathOverFlow.

  4. I think that many other math students, and not just undergraduates, would benefit from this question.

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    $\begingroup$ The questions doesn't seem to require the expertise of a researcher in mathematics. You are essentially asking how should a student develop the skill for finding counterexamples generally. This seems more suitable for Mathematics. $\endgroup$ – Kaveh Jul 3 '13 at 8:12
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    $\begingroup$ I must say I have mixed feeling about this question. First I should point out that I would love to see what sort of answers it might attract, but I am still not sure I find it a good fit for MO. For one thing, it would have to focus on how to find examples and counter examples while doing research to truly fit into the scope, but that could be amended with a simple edit. But generally, the soft nature of the question puts it clearly into the "please don't ask these until you have a very good sense of the site, and even then, there is no telling how it will be received". $\endgroup$ – Tobias Kildetoft Jul 3 '13 at 9:03
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    $\begingroup$ In view of the question (on main) it is perhaps worth stressing that there are numerous research mathematicians and professors active on the site mentioned by @Kaveh. Overall it seems a much better fit for that site. (The email-question you link to was asked when this other site was non-existant or at least very recent and not yet that developped.) $\endgroup$ – user9072 Jul 3 '13 at 12:59
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    $\begingroup$ Clarification: I think a question by an instructor who wants to know how to teach something is different from a question from a student who wants to know how to learn something, they have different answers. I think questions by teachers about teaching can be on-topic while questions by undergraduate students are probably more suitable for Mathematics. $\endgroup$ – Kaveh Jul 3 '13 at 18:16
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    $\begingroup$ Three questions that I ask myself when deciding if a question I have is suitable for MO: 1. is there a good reason to think researchers in mathematics can answer the question in a satisfying way? 2. is there a good reason to think answering the question really requires the expertise and knowledge of a researcher in mathematics? 3. is there a good reason to believe the question is interesting for researchers in mathematics (as researchers in mathematics)? If all are answered positively, then the question is likely to be suitable for MO, otherwise it is probably not. $\endgroup$ – Kaveh Jul 3 '13 at 18:18
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    $\begingroup$ Your question was not put on hold for being "off-topic" but rather for being "too broad". With regard to the latter: Even asking about a particular area (e.g., How to discover counterexamples in topology) would probably still be too broad. (Though for that parenthetical area: You would probably just get comments about the book "Counterexamples in Topology".) If you wish to read a bit about finding counterexamples, Eric Knuth's work on conceptions of proof and Liping Ma's work on Chinese versus US teachers' understandings are both good places to look (in the Mathematics Education literature). $\endgroup$ – Benjamin Dickman Jul 3 '13 at 22:30
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    $\begingroup$ For more on student understandings of counterexamples (again, I cite from the Mathematics Education literature) search google scholar for work by Orit Zaslavsky: scholar.google.com/… I am not sure if this will help at all with your own ability to "discover" counterexamples, but perhaps it would be of interest. $\endgroup$ – Benjamin Dickman Jul 3 '13 at 22:34
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    $\begingroup$ @BenjaminDickman: please note the question got closed twice, the first time (after which this question was asked) indeed as "off-topic" only then as you say as "too broad". $\endgroup$ – user9072 Jul 4 '13 at 13:03
  • $\begingroup$ @BenjaminDickman: Thank you very much. I will look into that author. $\endgroup$ – NNOX Apps Jul 20 '13 at 2:32
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    $\begingroup$ It appears that my original question has now been deleted. There were numerous answers before its closure, many of which received many upvotes, so the answers proved very helpful and the deletion feels woeful. Thus, could my question please be reinstated? $\endgroup$ – NNOX Apps Jul 20 '13 at 2:52
  • $\begingroup$ I agreee the question should rather not be deleted (and voted to undelete; there is one undelete vote missing). [If it does not get undeleted soon, if I were you I would flag for moderators with the request; also I might do so if I do not forget.] $\endgroup$ – user9072 Jul 20 '13 at 13:44
  • $\begingroup$ @quid: Many thanks for your comment. I have flagged this question for the moderators. $\endgroup$ – NNOX Apps Jul 24 '13 at 2:40
  • $\begingroup$ The question has been undeleted. $\endgroup$ – Gerry Myerson May 1 '17 at 12:54

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