Here are examples of two questions which I would like to ask. I am afraid to ask them, because they might be closed. The question about 3-manifolds might survive. The question about sporadic groups would probably be closed as "not research level" question. This is my experience of asker in these two areas. My guess is that topologists are more flexible than algebraists. I might be wrong.

In area of 3-manifolds what are the possibilities of classifying them. I am interested in topological properties of manifolds. I see that there is focus on "geometrization" and hyperbolic manifolds. I am a bit skeptical about it. I admit it is interesting on one hand. On the other hand when we take one manifold, how do we see the geometry ? I think we first see the topology which is shape of the manifold. Of course this is just intuition or my brain preference. Maybe other person would see it in different way.

EDIT 2018-09-28

On this question I received answer from Bruno Martelli that nobody knows how to classify closed irreducible atoroidal orientable 3-manifolds. From this answer I conclude that "geometrization" didn't solve the problem for classification of 3-manifolds. I am stil in process of understanding the Haken manifolds and "virtual Haken conjecture". Can atoroidal manifold contain incompressible surface ? This is maybe "pub level" - as Gerhard suggests - my view is that there might be another path for 3-manifold classification. Since basic blocks left from JSJ decomposition - atoroidal ones - are not yet understood, then maybe we should look for another basic blocks.

END OF EDIT 2018-09-28

In area of finite groups I would like to ask how can we understand sporadic groups. They contain some symmetry - what symmetry it is ? I have read opinion that there is no one symmetry for all sporadic groups. It is rather different kind of symmetries which we can see. If we compare to exceptional Lie groups - these objects are connected to octonions. There is no similar one object which could explain existence of sporadic groups.

Regards,

  • 4
    I don’t think either question is at an appropriate level for MO. – Andy Putman Sep 26 at 13:22
  • @Andy, can you expand on this? What aspect of these questions is not right for MathOverflow? Gerhard "Can Misunderstand On Many Levels" Paseman, 2018.09.26. – Gerhard Paseman Sep 26 at 15:06
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    They're both extremely vague, and basically asking someone to write a survey of an entire huge area. In addition, the question about 3-manifolds is completely unreasonable -- geometrization is the main tool that people have used to study the 3-manifold classification problem for the past 30-40 years. Rather than complain that he doesn't like it, the OP should learn it if he wants to have any understanding of modern 3-manifold topology. – Andy Putman Sep 26 at 15:40
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    Good MO questions are specific questions, and not general ones about entire areas of research -- basically regardless of "how" the latter are asked. – Stefan Kohl Sep 26 at 22:24
  • @StefanKohl That feature of MO I do not like, that only specific questions can be asked. So I can ask technical question, that I encounter problem X in my reasoning, or I do not know how to get from point A to point B. But I cannot ask general question about which way should I go. Or "why most of the people go this way and not that" ? Exactly, I would like to go some other way than most people are going. Why I cannot do that ? And why I cannot discuss possible ways on MO ? Who decided that questions should be specific ? I am also co-owner of MO, as I found out on another topic. Therefore – Marek Mitros Sep 27 at 7:28
  • ... Therefore my voice matters here as well. Regards, Here is response from Francois, where he is saying that I can feel co-owner MO: meta.mathoverflow.net/questions/3454/… – Marek Mitros Sep 27 at 7:29
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    @MarekMitros: You may not like it, but the long-standing consensus here is that allowing free-flowing discussion and vague, open-ended questions would damage MO. Our goal is not to meet all mathematical needs; if one of yours is not being met, then there are many other websites/blogs on the internet. – Andy Putman Sep 27 at 14:06

That feature of MO I do not like, that only specific questions can be asked ... Why I cannot [ask other types of questions]? And why I cannot discuss possible ways on MO? Who decided that questions should be specific? I am also co-owner of MO ... Therefore my voice matters here as well.

You're taking Francois' comment too literally. MO is "community-owned" in a sense, and every individual's voice is important, but there can still be community-set guidelines which individual users should follow even if they personally disagree. (Every vote counts in a democracy, but some people get outvoted.)

The fact is that MO is not entirely what you want it to be. Ultimately, you need to respect that. Conversely, the MO community of course needs to respect you, but that doesn't mean deferring to your judgment.

  • I can accept that democracy is sometimes wrong :) On the other hand questions like this: mathoverflow.net/questions/115735/groups-that-do-not-exist or this: mathoverflow.net/questions/99736/… are accepted here !? Do you have explanation for this ? – Marek Mitros Sep 28 at 5:15
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    Those two questions were posted in 2012, which is several generations ago, in MO-years. They might not fare so well, @Marek, were they posted today. – Gerry Myerson Sep 28 at 6:10
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    @MarekMitros "I can accept that democracy is sometimes wrong :)" Can you accept that you may be wrong? At some point you need to acknowledge that it is reasonable to have a site whose focus is rather more limited than you want it to be. (There is a separate question of consistency - and there is an undeniable and problematic point that (i) standards at MO change over time and more unfortunately (ii) these standards are not uniformly enforced - but that's separate from the general issue that you need to recognize that the MO community will sometimes diverge from you and that that's fine.) – Noah Schweber Sep 28 at 14:33
  • @NoahSchweber I am sorry if I am expressing my feelings too strong here. The thing is that down-voting of my question here has unpleasant psychological impact. I feel like I am attacked here, so I try to defend. I think it is not a matter who is right and who is wrong. Meta MO is forum is the place to discuss issues like "why some questions are closed" here. Note there are three upvotings on my question here. Besides you are answering what I have written in comments and not what I have asked in the question. Is your answer: "There is no way to ask general questions about research on MO" ? – Marek Mitros Oct 1 at 9:30

I have a sense that the questions are rather broad. (Thanks to Andy Putman for confirming this sense.) Further, even if you did not intend this, a proper answer to the question would involve more effort than we expect a member of this forum to produce.

On the other hand, well posed reference requests are acceptable. If you were asking for an existing survey (warning: I am inventing the following because I do not know the field) about geometrization, that itself would also be a poor question because it too is a bit broad, but if you added that in Thurston's survey you found that aspect X seemed opaque to you and Arthur's popular article did not mention these three topics that you felt should be covered, and was there another existing survey to be recommended, THAT would be a better question because it showed some effort you had involved in trying to answer it yourself. Further, the answerer might be sympathetic and share with you something that you had not asked directly but might find valuable. So I suggest spending some time answering your question yourself, and then make it a reference request along with a brief summary of why what you tried did not work. This might be the best way to have the forum help you with your quest.

Gerhard "MathOverflow Helps Those Helping Themselves" Paseman, 2018.09.26.

  • Thank you for this answer - it is nice try. Note that I do not want to ask for existing survey. This might be mentioned in the question or in the answer. I do not want to criticize existing progress or achievements in these areas. I want to ask for possible other ways to go forward. The requirement that I should first do my own effort before I can ask the question is sometimes comic in my opinion. Surely I can survive without asking the question. If however I have asked the quesion, it means that I would like to hear opinion or answer of other persons. I regret that it is not possible here... – Marek Mitros Sep 27 at 8:29
  • Some surveys include directions for further research and lists for open problems. However, if you are indeed looking for someone to create a post summarizing research directions, that is close to writing a survey. Still more than intended for this forum. Gerhard "We Do Brief Answers Here" Paseman, 2018.09.27. – Gerhard Paseman Sep 27 at 14:36
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    @Marek, I am now getting that you are asking for/about conjectural approaches to broad areas of research. (Sorry for not understanding that before.) That is definitely not MathOverflow. Again, if you have a specific idea and want to phrase it as a reference request, that might work. If you want a digital version of sitting at a pub with experts and spitballing ideas, well, go pub hopping. Gerhard "Or You Start A Blog" Paseman, 2018.09.27. – Gerhard Paseman Sep 27 at 18:46
  • Do you know pub in Warsaw where mathematicians meet ? – Marek Mitros Sep 28 at 10:07
  • Sorry. I've heard of cafe Skoca (or Scottish Cafe) in Lwow, which was famous for that sort of thing. You might ask at a local university for places where the lecturers lift a mug. Forgive my omission of accent marks. Gerhard "Has Never Been To Poland" Paseman, 2018.09.28. – Gerhard Paseman Sep 28 at 14:21
  • Yes, I heard legends about notes made directly on the table with pencil. Participants asked the personnel not to remove them in order not to loose some important proof of theorem. As a result Łucja Banach - wife of the mathematician - bought thick notebook - now known as Scottish Book. Regards. Marek "Has Been in Pub Few Times" Mitros – Marek Mitros Oct 1 at 12:49
up vote 1 down vote accepted

I would like to summarize what has been said in comments above.

It is not acceptable on MO to ask general questions about research in given area of mathematics. Most MO users see the value in fact that only specific questions about mathematics can be asked.

It is acceptable to ask for a reference to an existing survey.

Note: Survey - is general description of research in given area of mathematics. Good survey should also contain directions in which research should continue. It should also contain open issues to be solved.

If given MO user do not know which way to go then he/she should read the survey in order to find out. Ultimately he/she can start journey in some direction on his/her own risk without bothering MO.

  • In general, I think that requests for surveys of topics will be poorly received and closed as "too broad" unless they are extremely tightly focused (and probably not phrased as a request for a survey). – Andy Putman Oct 2 at 14:54
  • It is possible he means ask for references to existing surveys. However, to me this does not quite fit as a comment summary, and as an interpretation I find it a little wide of the mark. Gerhard "Hopefully Mark Will Clarify Further" Paseman, 2018.10.02. – Gerhard Paseman Oct 2 at 15:09
  • I corrected the answer and I accepted it, because I like it the most from existing three answers. I hope it is OK, to accept my own answer according to MO rules. If I understand idiom "wide of the mark", it means that I am not accurate, right ? – Marek Mitros Oct 2 at 19:01
  • Indeed, it does mean not accurate (like shooting an arrow). Sorry for the idiom. Your first version seemed (to me) less accurate than this version. And really, accuracy is not as important as capturing the intent. This version (at the moment ) does a better job at getting the intent of the comments right. Don't worry about accepting your own answer; that is your right as question proposer. Gerhard "Thank You For Contributing Here" Paseman, 2018.10.02. – Gerhard Paseman Oct 2 at 19:16

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