The closure of the question https://math.stackexchange.com/questions/958420/about-a-particular-class-of-finite-groups surprises me quite a bit, and I believe it illustrates something that is wrong with the approach being taken on MSE to closing questions.

It is clear that, in mathematical terms, the question is not missing "context" or "details." Everything is there that would be needed in order to give a good answer. (This is not a case where the question is trivially easy, and one is simply looking to see "where the OP got stuck" to target a particular point in the proof. Rather, this is a question where many people with good mathematical maturity might not know where to begin.)

My questions are:

1) In light of current practices on MSE, does the prevalence of this kind of closure enhance or reduce the usefulness of MSE as a resource?

I won't define the words "this kind" because I think it should be left open to people replying to my question to determine what features of a question are significant in this respect.

2) Should there be an expectation that, where a person votes to close a clearly formulated math question as being "homework-like" or as lacking information about the OP's "thoughts," the voter should at minimum have entirely thought through what an answer to the question would be? (Trivial calculations are not included.)

I have answered these questions below.

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    The overall goal of the site, in my opinion, is to have excellent answers and excellent questions. This means that, unlike in the first years of this site, it is no longer reasonable to just ask a question, with no motivation or other discussion. Unlike other math sites, this site does not discriminate between "basic" and "advanced" questions - all questions need to be well written. On the other hand, our sister site MathOverflow only accepts research-level questions, so they can get by without requiring as much motivation. – Carl Mummert Oct 6 '14 at 0:15
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    I also think questions should be well written. I do not believe the objection to that question was that it was not well written, in the way that this notion would be commonly understood by mathematicians. – user180040 Oct 6 '14 at 0:18
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    But it is not "well written" in the sense that it has no motivation, no explanation of the context of the question, no description of what the asker has thought about already. We are inundated with these poorly-composed questions at the moment! For truly advanced questions, the asker may want to try MathOverflow instead, where the level of the question can speak for itself. But the only way that I see to maintain the quality of this site is to apply the same standards to all new questions. – Carl Mummert Oct 6 '14 at 0:21
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    I think those are the way people relate to discussing math. If I walk up to someone at tea and say "here is a problem I can't answer", I will usually tell them where I encountered the problem, and what I have thought about already. I would not walk up to someone at tea and ask them a random question as if it was a quiz! That, in my mind, would differ from the social norms of the wider world. But, yes, it also has the desired goal of discouraging homework questions that people haven't thought about, which many people here think is an important goal, even if we can't tell which are homework. – Carl Mummert Oct 6 '14 at 0:34
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    Let me add that I might not want to add my attempts at solving the problem because I didn't want to reveal my ignorance. – user180040 Oct 6 '14 at 0:43
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    Indeed, but this is not the site for that. The way that I view this site is like asking someone a question at tea: I will explain to them the question and the way I am thinking about it, and they will give me an explanation (if they can). The asker has already revealed, by asking the question, that they can't answer it. But who walks up to someone else at tea and just says "Answer this: ...." as if they are posing an examination question? – Carl Mummert Oct 6 '14 at 0:44
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    I can tell a lot more about a person's ignorance in some cases by their attempt to answer a question than by the mere fact of their asking it. And you sometimes don't know if what you write, beyond the minimum, is going to show that. I agree with what you said that in many cases, people do relate that way. However, people would generally not expect that it would be compulsory on a Q&A site like this one, particularly in situations where it doesn't assist in providing an answer. At most, they might think that fewer people would try to answer their question. – user180040 Oct 6 '14 at 0:50
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    "I might not want to add my attempts at solving the problem because I didn't want to reveal my ignorance." I am stunned by this statement. Revealing one's lack of knowledge is one of the most effective ways to learn. – Did Oct 6 '14 at 7:19
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    If you're asking the question here, it's already assumed that you can't answer it. How much "worse" can it get in terms of ignorance? There's no reason to be ashamed when you don't know the answer, but nobody would be fooled if you don't include your attempts. In fact, it's probably even worse. – Najib Idrissi Oct 6 '14 at 8:52
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    Obviously, the analogy can only go so far. I am not swamped at tea with scores of students, and students can't ask me questions anonymously. On this site, a key challenge we face is a large number of poorly-composed questions, and the ease of account creation. The easiness of creating an account and asking a question has real benefits. So the only even-handed way I see to maintain some sort of quality standards is to require all users to meet the same quality goals. These goals are not very high: a question with almost any sort of background or context is unlikely to be closed. @user180040 – Carl Mummert Oct 6 '14 at 19:33
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    As an aside, it would be good to take a look at how Physics.SE handles homework questions, and how EE.SE handles questions by people who are over their heads. While I don't recommend/condone going this far, the EE.SE site maintains a professional-level of questions (for the most part) while still keeping a strong user-base. – apnorton Oct 7 '14 at 4:38
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    You seem to forget that MSE and MO are different websites applying different quality standards. On MO the quality is maintained by asking questions to be of research level; this prevents them from being flooded by dozens of almost identical questions with almost identical answers by people looking for homework solutions. Questions are "hard" enough that people able to answer them have already a good idea of the context behind them. Here we don't discriminate on the level of questions, so there needs to be another kind of filter. – Najib Idrissi Oct 7 '14 at 6:13
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    I don't think anyone is claiming that these questions are rude or disrespectful, merely that they bring down the quality of the website. – Najib Idrissi Oct 7 '14 at 7:11
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    @NajibIdrissi: I'm sorry, I claim this, and similar questions, are rude; in fact, extremely so.This is not an "answer this for me, robot, site;" it is an online forum where you can ask for help from or pose questions to another human being. Where and the way I grew up, in and outside of math, asking a friendly question involves minimal humanizing context - for math, "here is where I am stuck", for directions in a city, "I am lost." This site is no text book, and self-appointed crusaders condoning and encouraging rude behavior seem a recent nuisance I wish would go away. – gnometorule Oct 7 '14 at 16:19
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    @user180040 A full week later... the OP who asked the question you wished to discuss the closure of, is fully active on the site and they still did not post a single word, either as a comment or to modify their question. In view of this observation, do you still maintain that this specific closure "illustrates something that is wrong with the approach being taken on MSE to closing questions"? – Did Oct 13 '14 at 16:41

Full disclosure: I voted to close the question referenced in the OP.

1) In light of current practices on MSE, does the prevalence of this kind of closure enhance or reduce the usefulness of MSE as a resource?

Enhance. Hovering over the "upvote" arrow on a question says "This question shows research effort; it is clear and useful." Hovering over the "downvote" arrow says "this question does not show any research effort; it is unclear or not useful." PSQs (problem-statement-questions) do not, by nature, show research effort. They usually happen to be unclear and not useful to future users, but that's another story.

I believe that this closure enhances Math.SE's usefulness because it increases the signal-to-noise ratio. If someone really wants their question answered after it's been closed, they can edit the question into a good question, not a lazy question.

We close questions as "lacking context" not because we can't understand the question, but because the OP has lazily asked the question. A good "how do I do this type of calculation/proof" question shows effort.

2) Should there be an expectation that, where a person votes to close a clearly formulated math question as being "homework-like" or as lacking information about the OP's "thoughts," the voter should at minimum have entirely thought through what an answer to the question would be? (Trivial calculations are not included.)

I don't think this is necessary, or even something reasonable to implement. No one knows why people vote the way they do, and attempts to standardize people's voting processes don't end well. I don't need to solve a problem to determine it lacks context, I just need to look at it and realize: "Hey. This question doesn't tell me anything about what's been done on this problem."

To clarify, we don't close "homework-like" questions. We close questions that lack context; for examples of what I mean by context: Where did you encounter this problem? What are related problems? What attempts have you (or others) made to solve this problem? Basically, treat it like a research paper: tell me everything that's been done to solve this problem by anyone in the past, before I go and duplicate a bunch of work.

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    It is also important, in my mind, to consider the volume of questions that this site currently receives. We do not have the problem that we have too many well-written questions to answer. – Carl Mummert Oct 6 '14 at 0:24
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    How would any of the "context" you mention have helped answer the question better in this instance? – user180040 Oct 6 '14 at 0:24
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    @user180040 In the comments to the referenced question, you say "This is a difficult problem that a person wouldn't reasonably be expected to have any ideas about, particularly if they are starting out in group theory." I am just starting out in group theory, and could easily see this problem and think "Oh! I'll try this!" ...only to waste a bunch of time because it's over my head. If I know the approximate level of a problem before approaching, it helps filter which users attempt to answer. Also, if someone researches a question, they may find some source (e.g. the book you listed)... – apnorton Oct 6 '14 at 0:28
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    (cont)... that answers their question. If someone can answer their own question, all the better! Showing attempts can also help avoid the XY problem--someone may ask about "how do I prove this theorem?" when their real confusion is on "why does $(n-1)\mid (n-1)!\implies\text{ n is prime}$? (or something similar) – apnorton Oct 6 '14 at 0:28
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    Yes, someone may find a book, but if someone hasn't found a book, and they don't describe their fruitless attempts to find one, that is not a deficiency in the question. Also, including pointless attempts at solving a problem is not the way all people relate when talking about math; many people would think that was counterproductive. – user180040 Oct 6 '14 at 0:32
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    @user180040: even if the OP cannot approach the question, they can at least say where they encountered it and what they have already thought about. These things do often help answer the question: they tell the rough level of sophistication that the OP is working at, and the methods that are on the mind of the OP. You wrote that someone would not have an idea how to start the question if they are "starting out in group theory" - but that leads immediately to the problem: where did they find the question in the first place if they are just starting out in group theory? – Carl Mummert Oct 6 '14 at 0:32
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    Saying what textbook they found it in would not reasonably be expected to assist in a solution in this instance. In any case, why not ask that in the comments? Then if you don't hear back, you don't have to answer the question. But why close it? Maybe someone else doesn't need that information to answer the question. I didn't need it to provide the reference with the solution. – user180040 Oct 6 '14 at 0:38
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    @CarlMummert I think that if a person who intends to answer the question needs the information, they can ask for it in the comments. There are cases where the level of sophistication of the answer will change, others where it won't. Whether an answerer wishes to invest time in an answer without that information is best left up to him. And often, the best questions have answers at different levels of sophistication. – user180040 Oct 6 '14 at 0:57
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    @user180040: I agree that would be a reasonable approach in an ideal world. But we are currently overrun with ill-motivated problem-statement-only questions. That is not the sort of site I want this to become, and the main tool that I have to influence the site are upvotes/downvotes and close votes. On the other hand, someone with genuinely interesting, advanced questions can always ask on MathOverflow, which is more amenable to problem-statement-only questions. – Carl Mummert Oct 6 '14 at 1:03
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    @Carl Mummert I am concerned about the effect this has on people coming to the site for the first time. I am afraid that the reaction they get comes across as unfriendly and unreasonable. If I had asked the question I linked to, I would have been quite upset at the reaction. I think this is a serious problem in its own right, and a different balance needs to be struck to handle the kinds of questions you said are a problem. I don't think Math Overflow would have been suitable in this case, for a number of reasons. – user180040 Oct 6 '14 at 1:10
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    I think it is a bit lazy to claim that the OP asked the question lazily. A person might have any number of reasons for only stating the problem. I think that a fairly common scenario might be this. A person who is minimally familiar with the site comes and asks a decent math question, which as far as he can tell is like the other ones asked here. He then receives a bizarre message saying that his question is "off-topic" for MSE. After concluding that the people at MSE are somewhat off their rocker, he walks away from the question and perhaps the site. Maybe he would have been a contributor. – user180040 Oct 7 '14 at 3:12
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    @user180040 You seem to forget the purpose of putting questions "on-hold" first instead of closing them as off topic. If the OP returned, he would see a message saying "your question is lacking context and details. Please edit your question to provide this." That's perfectly reasonable, and is no cause to abandon a site. If he was confused, he could have reached out and asked. If someone doesn't show any effort to understand, then what is the likelihood of being a good contributor? Also, you think too highly of people. I anticipate this will change after a few years. ;) – apnorton Oct 7 '14 at 3:19
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    You say that that's reasonable, but I am saying that it is a reasonable reaction for people to find it crazy. Why would I "reach out and ask" after being answered with that? I personally do find all of this very strange, yet I've provided several answers on the site that have been accepted. Perhaps I'm not a good contributor. Perhaps that's so of the author of the question, who has answered several questions on the site. I would appreciate it if you could acknowledge that some people can be put off by this, rather than concluding facilely that they must not be worth having anyway. – user180040 Oct 7 '14 at 3:30
  • @user180040 I just looked back over what I wrote, and I believe what I've said hasn't accurately reflected my thoughts. I willingly acknowledge that some people can be put off by this behavior. My natural response if someone closed my question is to say "why?" but I realize this may not be everyone's. My response to this concern is that I believe the risk of repulsing a prospective contributor is worth it, given the size of the site. With so many questions asked per day, we must close early and often to stem the tide of "junk" questions. Sure, there will be mistakes. Sure, some (cont...) – apnorton Oct 7 '14 at 3:38
  • ...questions will be unjustly closed. But the site's state renders it advantageous to err on closing too many, rather than too few, questions. The average asker of a closed question won't be a major contributor (anecdotal-statistically speaking ;)), so I feel OK with perhaps scaring off a couple of possible contributors to gain a cleaner site. – apnorton Oct 7 '14 at 3:38

I'm as annoyed as anyone about the preponderance of boring homework questions on MSE, I'm enthusiastic about downvoting and closing "solve this integral" or "compute this stabilizer", but I think this closure was inappropriate (and have voted to re-open). I claim that the question does not demand justification because it is mathematically interesting even without any further exploration.

When I choose whether or not to answer a question, there are basically two angles it might appeal to me on:

  • as a mathematician, I look for problems that I would enjoy thinking about and exploring further, and questions whose answer I would like to discover,
  • as an (amateur) teacher, I look for opportunities for exploring how people make mistakes, form misunderstandings, which concepts they find difficult, and what kind of exposition can make those concepts clear to them.

Only really in the second capacity do I care if the author has shown effort, because only then do I need to develop any insight into their thought processes. The linked question strikes me as something I would enjoy thinking about even if I could never tell the original asker what I came up with, and as such their particular attempt at the question is of no more interest to me than anyone else's.

Moreover, the question seems to me a natural enough problem (not the most natural, perhaps, but I would not be so surprised to see it as a theorem in a textbook) that it represents a positive contribution to the general library of quality mathematical results presented in the MSE format, and could well be useful to other visitors in the future.

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    While the question does not need justification, it needs context. This is not a question you come up with yourself (for several reasons), so at least the source should be indicated to give potential answerers an idea of what tools would be appropriate for it. – Tobias Kildetoft Oct 7 '14 at 10:54

1) I believe that MSE becomes less useful as a resource as soon as there becomes a significant possibility that an intelligent person who comes and asks a well-formulated question that he has thought about is told to clean up his question, particularly in the way it's being done.

Normal people coming here for the first time can perceive this response as hostile, and I don't blame them. I don't think that the procedure for having questions re-opened is really a complete solution for this, because once this has happened once, the damage is done; and in any case a person shouldn't have to run an obstacle course to get help with their question. They're much more likely just to leave.

Although this is subjective, I think well-formulated questions above a certain level of difficulty should never be closed for being too homework-like. I would propose the following categorization.

Type A Questions Questions which, if asked as a homework question, are likely to present difficulties primarily to students who have not mastered the background knowledge appropriate to people studying at that level. A student with appropriate background knowledge would not ordinarily have difficulty with the problem, or at least, most people with that knowledge would start the problem in the same correct way.

Type B Questions The difficulty of these problems is inherent in the problems themselves. A student with generally appropriate background knowledge could reasonably not know what facts or methods are applicable to solve the problem. Such a student might make some progress with the question, but be unable to say in advance whether those initial steps have the potential to lead to a correct solution.

The "background knowledge" I'm talking about can generally be inferred from the question. This means the facts and methods usually taught in the kind of course in which the OP's question might appear as homework.

I understand that there are a spectrum of problems ranging from Type A ones to Type B ones, and that this evaluation is subjective, but I think it's important to make some effort to distinguish between them. I feel emphatically that people asking Type B questions should not be pestered to "share their thoughts"; I really feel that this is being rude to them, as mathematically mature people do not normally communicate this way, at least not compulsorily. An unknown number of people are having a negative first experience with MSE and not coming back, and despite the fact that I haven't been here for long, I am convinced from what I've observed that that number is high.

I don't want to debate whether clear "Type A" questions should be closed. However, I think it might be more appropriate and friendlier to give these people hints than to close their questions. Indeed, hints may be more appropriate even for Type B questions in some cases.

2) Yes, this would be a significant safeguard against closures of Type B questions, including extreme Type B questions like the one given as an example.

EDIT: I would like to quote from the FAQ on homework. How to ask a homework question?

The following are some things that may help your question get better answers, or at least answer more tailored to your situation.[...] Show your work. You should definitely include any partial work you have done. This will help bolster your claim that you are not just coming here asking other people to do your homework for you, and it will help the answerers to give more clinical responses. Showing your work will help us gauge where you are having problems: if it is a technical thing near the end, a short to the point answer will suffice; if it is some fundamental problem with understanding the subject, we will then write a longer, more detailed response. It will also prevent people from spending a lot of time going over ground that you have already covered or understand well already.

First note that this advice is presented in the FAQ as assisting the asker in "getting better answers," not avoiding having their question closed. The advice is not described as compulsory, and a person reading the FAQ couldn't reasonably anticipate the kind of reaction that seems to happen frequently. (Not to mention that many questions that have been closed were clearly not homework.)

Also, this advice is of limited applicability for Type B questions in which a person is unsure of the value of what they've achieved so far, since the proof is still incomplete for them. Who would think that it would be beneficial for an answerer to see their meandering thoughts on a difficult problem?

EDIT: I'm adding the following to respond to some objections from Did and Najib.

Let's say I want to know why the group $(\mathbf{Z}/p\mathbf{Z})^{*}$ is cyclic when $p$ is prime. Here are two ways I could ask the question.

  1. Can anybody tell me how you prove that $(\mathbf{Z}/p\mathbf{Z})^{*}$ is cyclic when $p$ is prime? Thanks.

  2. Can anybody tell me how you prove that $(\mathbf{Z}/p\mathbf{Z})^{*}$ is cyclic when $p$ is prime? Here is my attempt. The element $1$ generates the group because every element is of the form $n \cdot 1$. Thanks.

Yes, Question 1 reveals a degree of ignorance. Question 2 suggests a good deal more, although it could sometimes be that a usually able person is simply having a bad day. (For example, I missed that $(1-x)(1+x) = 1 - x^2$ in a comment recently.)

As idealistic as we'd all like to be, can anybody tell me with a straight face that we will all think as highly, in terms of mathematical ability, of a person who asks Question 2 as we might of a person who asks Question 1? I think it is human nature that many people will feel ashamed after receiving a reply to #2, particularly if it was the case that they were simply having a bad day. In any event, a reply to #1 will quickly dispel their misunderstanding, in addition to providing the answer to their problem, without any likelihood of embarrassment.

Some people might say that it is easier to teach a person who is frank about their level of ability and understanding. That is generally the case. However, imagine that that person is using their real name, that they are sensitive by nature, or that they are afraid of the kind of situation I mentioned. Even if you do not want to answer the person in these circumstances, how can you justify preventing others who want to from answering them? I think in these circumstances, it is not for a few people to decide that the person must conform to standards that they may have legitimate reasons for not wanting to meet, or else be unworthy of receiving help.

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    No, I really think 2 is better. At least the asker tried something. Okay, the attempt doesn't work, but at least there's some thought behind it, and it at least proves the asker knows what "cyclic" means. And anyway... Why should that matter? We all ask "dumb" (and I put that in quotes) sometimes. It shouldn't prevent you from asking questions, and it doesn't prevent people from answering them. I think I can speak on behalf of most people here if I say that I prefer questions that are "basic" but show some thought, however misguided, rather than PSQ where it feels like we're assigned homework. – Najib Idrissi Oct 6 '14 at 18:02
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    I don't disagree with you that those questions are often easier to handle. However, I think it is quite paternalistic to make it imperative rather than letting a person decide for themselves. Just because some people aren't bothered about asking a question like #2, doesn't mean nobody will be. In any case, what is the justification for preventing other people from answering if they want to? Why can't the penalty just be receiving fewer replies, as a natural consequence of the way the person interacts in the comments, etc.? – user180040 Oct 6 '14 at 18:08
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    2. is good, as soon as I read it, I start to see a pair of approaches, based on the mistake, that I could develop to dispel the confusion the mistake reveals and to solve the question in the same movement. Then I will probably ponder them a few minutes to gauge which of them is the most effective from what the OP told me. And then I will answer--and perhaps I will have missed the target but perhaps the OP will say so and I will be able to aim better by modifying my first try. 1. is opaque and makes me feel I should run away. – Did Oct 6 '14 at 19:32
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    The justification for preventing other people from answering (i.e., closing the question) is to keep the site at Stack Exchange level, as opposed to Yahoo/Quora/etc. "If you don't like it, don't answer it" is the conventional wisdom of internet forums, and the fruit of that wisdom is a conventional internet forum. Stack Exchange strives to be better than that. – user147263 Oct 6 '14 at 22:40
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    @CareBear One of the results of this approach is that MSE presents an unwelcoming and unfriendly face to many innocent first-time users. – user180040 Oct 7 '14 at 3:44
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    @user180040: It is unwelcoming only to those who just "crash the party". Those who spend time observing how the regulars behave will quickly enough learn what is ok, and what is not. This is normal courtesy. When you join in a new group of people (say, at a bar or at a work place), you play it safe first, and don't start picking fights or such right away. It's the same here: the advice is to observe first for a while. – Jyrki Lahtonen Oct 7 '14 at 11:15
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    @JyrkiLahtonen No, it is unwelcoming to many people who post their first question here, who do not do anything to deserve the response. – user180040 Oct 7 '14 at 17:20
  • @user180040: We disagree about some things, but agree about some others. I do recognize the difference between your types A and B. I posted a wall of text as an answer, but deleted it because it didn't add anything to what I have said before. A quick summary: 1) If it is part of HW dump, close it on sight. 2) Otherwise I will shamelessly apply different standards to questions at different levels or from different askers. 2A) I only vote to put on hold for this reason (no effort shown) those questions that I can solve myself right away. – Jyrki Lahtonen Oct 7 '14 at 18:32
  • (cont'd) 2B) If it is from a new poster ("first offense", if you like), and I cast the first close vote, then I strive to leave a suggestion on how to improve the question (see my comment to the question you linked to). BUT, my approach is not MSE main stream. Also, the flood of low quality questions is a serious problem for our site. Thus I also sympathize with those members who have lately become more aggressive. Higher level question (the linked one is borderline) are not much of a problem, because the volume of traffic is not there. But some members want to apply a uniform policy. – Jyrki Lahtonen Oct 7 '14 at 18:37
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    @JyrkiLahtonen Thanks for sharing your point of view. – user180040 Oct 7 '14 at 19:54

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