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I get the feeling that the MSE community is being much more harsh and dogmatic than it used to be and that that is detrimental to its use to help people who are trying to learn mathematics and have identified specific questions that they do not know how to answer. We seem to be applying rules that were intended (IMHO) to stop MSE being used as a homework answering service without considering the possibility that a poster has come up with a valid question of their own, with a mathematically interesting answer, that they are unlikely to be able to begin to answer for themselves.

An example in point is Can we derive a norm and an inner product from a metric?. There is real mathematical interest here: the question of whether a normed space is actually an inner product space is non-trivial. Even coming up with a counter-example to the conjecture that normed spaces are all inner product spaces will not be obvious to someone who has not gone much further than learning the definitions. Yes, the poster in this case asks a few simpler questions as well, but it seems to me to be highly unlikely that this is a homework problem: so it merits either an answer, or closure as a duplicate. It does not merit closure on the basis of community guidelines: if it does, then the guidelines should be qualified to allow questions like this. Note that closure as a duplicate is giving an answer indirectly and that is useful and helpful.

[This question could arguably be closed as a duplicate of https://math.meta.stackexchange.com/questions/26659/a-criterion-for-distinguishing-between-two-kinds-of-questions. However, that post is 7 years old and things seem to have got a lot worse since then.]

In case the question I took as an example does disappear here is the text:

Given an inner product on a vector space I can always define a norm and a metric (and a topology using that metric). Is the converse true? Given a distance on a vector space, can I define a norm and an inner product? And what about a metric space that is not a vector space? Thanks

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    $\begingroup$ The question (presented as an example in your post) is closed for lack of context. As of now it is just written as a series of a few problem statements. This may not be a homework problem, but it does lack context. $\endgroup$
    – Paramanand Singh Mod
    Commented Feb 15 at 23:51
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    $\begingroup$ I share the sentiment of this post. One problem I see is that many users push the idea (rightly or wrongly) that the primary purpose of this site is to create questions of lasting value to the community, not necessarily the original poster. But if this is the case, then surely a homework question with "context" is still far inferior to a conceptual question where the poster doesn't bother to give the motivation behind it. $\endgroup$
    – Joe
    Commented Feb 16 at 0:14
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    $\begingroup$ We don't care of a question came from homework or from stoned pondering or anywhere else. We care that the question is focused, clear, relevant, and includes context for why we specifically here on Stack Exchange should be the ones hosting, curating and answering it. If you just want "to communicate interesting mathematics to interested parties" go to Reddit, Quota, Discord, or any of the other thousands of platforms that actually do this. $\endgroup$
    – Nij
    Commented Feb 16 at 0:15
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    $\begingroup$ Recently, this very natural question about lie groups was closed for being an "isolated problem" lacking context. Mariano's comment there seemed to be very apt: "The question is so isolated that Dieudonné wrote a whole book about it." $\endgroup$
    – Joe
    Commented Feb 16 at 0:17
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    $\begingroup$ I don't think the question lacks context, because no context is needed. $\endgroup$
    – user1125430
    Commented Feb 16 at 4:22
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    $\begingroup$ It's not about homework problems, it's "has the poster made the effort to make their question attractive to us". Nothing the OP has done, beyond one sentence of "the converse is known" is even given. It doesn't matter that it's hard to attract people, one should still make demonstrable effort of research. Post your google search results. Post a proof of the converse. Post an example where it is true that inner product spaces are normed spaces, with a proof you can understand from some PDF. $\endgroup$
    – Sarvesh Ravichandran Iyer
    Commented Feb 16 at 5:34
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    $\begingroup$ @SarveshRavichandranIyer I don't think those extra pieces of information make a succinct question more attractive. They are not necessary to understand or answer the question. If they were written, I would skip over them. $\endgroup$
    – user1125430
    Commented Feb 16 at 8:38
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    $\begingroup$ @Hayatsu Completely disagree. What attracts you to the question is then your personal opinion of the topic itself, or your inherent interest in that question. You're interested in metric spaces or inner products or whatever, hence you like the question. I'm not interested in that topic, I don't like that question, period. That doesn't increase quality of the repository, it only divides it further into restricted cabals where questions are visited only by those that understand them and not by other visitors, and promotes people to not write their questions for a general audience. $\endgroup$
    – Sarvesh Ravichandran Iyer
    Commented Feb 16 at 8:41
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    $\begingroup$ While disagreeing quite strongly with a blanket comment no context is needed, I actually think the context of the question at issue is just fine. One of the more important contextual motivations for any mathematical question is something like this: We know $P$ implies $Q$. Is the converse true? Yes, one can improve the question by giving still more context such as one's own attempts; and yes, if there's a duplicate then close it. $\endgroup$
    – Lee Mosher
    Commented Feb 16 at 13:41
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    $\begingroup$ This meta post cuts very close to what I see as the source of the rot, but just misses it. The post suggests the issue is we sometimes misidentify a homework problem, thus our poor treatment of the question or its asker is unjustified. I would say the issue is that we are profiling askers and their questions in the first place. It's really not our business why they are asking their questions, and it's not our place to lay judgement on them. We have our standards for questions (not people), for better or worse, and we should be applying universally and non-judgmentally. $\endgroup$
    – Theo Bendit
    Commented Feb 16 at 14:11
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    $\begingroup$ @ParamanandSingh: what context do you need for this example? $\endgroup$
    – Rob Arthan
    Commented Feb 16 at 20:12
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    $\begingroup$ @SarveshRavichandranIyer: I don't see any reason why MSE questions should be phrased to attract a general audience. Mathematics is full of topics that are both very important and very recondite - so it takes an expert to explain the importance. It is an impossible ask to expect a beginner exploring one of those topics to phrase a question in a way that appeals to the masses. $\endgroup$
    – Rob Arthan
    Commented Feb 16 at 20:23
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    $\begingroup$ "why we specifically here on Stack Exchange should be the ones hosting, curating and answering it" Math.stackexchange doesn't try to avoid duplicating knowledge that can be found elsewhere on the internet. The great thing about math.stackexchange is that, due to stackexchange's good design, one tends to find better, more clear explanations here than elsewhere. Every fundamental math question, if it is not a duplicate of an existing question, should be welcomed and answered on this site. I think some people go overboard with demanding "context" for questions which are clearly fundamental. $\endgroup$
    – littleO
    Commented Feb 22 at 12:05
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    $\begingroup$ @Nij: I strongly disagree with what you say. You are making the utterly erroneous an assumption that the whole of mathematics is known and that all someone who cannot tackle a problem has to do is to learn more known mathematics. I said nothing about giving answers: my concern is that good questions are being shut out of MSE because of formulaic applications of site guidelines. $\endgroup$
    – Rob Arthan
    Commented Feb 22 at 20:11
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    $\begingroup$ ...which I guess is why "include more context" comments tend to rub me the wrong way in general. Sure, if a question doesn't include definitions of obscure terms then ask for that, or if the OP is asking for something a bit strange that smells like an XY problem then ask for clarification. But if a question already includes all the relevant mathematical context, even if that context can be expressed in a sentence or less, then nothing can possibly be gained by asking for more. There is no value in asking for additional irrelevant context just because a question is short. $\endgroup$
    – N. Virgo
    Commented Feb 25 at 5:25

3 Answers 3

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Thank you for your post and your concern, and for backing it up with some concrete evidence that we can look at! I admire and appreciate your desire for a healthy site, and I think you raise some good points.

On the general concern: Taking into account all the pluses and minuses, I don't think the site is being too harsh, by and large. No policy is perfect; any decision rule will have false positives and false negatives. The current policy is one that was able to gain community consensus, and my impression is the number of questions that are wrongly closed is vastly outweighed by the number of questions that are properly closed. The question is, if not the current policy, then what else, and will it be any better? I think anything else is also likely to make errors, too. So showing one example error is not, to me, a fully persuasive argument for changing a general policy.

This specific question: I think it is debatable what should be done with this particular question, and there are reasonable arguments on both sides. My personal opinion is that it was right to close the question, but the wrong close reason was used.

I believe this question should not be closed as a problem statement question.

I do think it should be closed as "too broad", as it basically asks four questions: (a) given a distance metric in a vector space, can I define a norm? (b) given a distance metric in a vector space, can I define an inner product? (c) given a distance in a metric space (not necessarily a vector space), can I define a norm? (d) given a distance in a metric space (not necessarily a vector space), can I define an inner product? It's usually not a good practice to ask four questions in one post.

Is it a good question? Some of those questions are not great ones. It looks to me like question (a) is answered by Not every metric is induced from a norm, and thus I would vote to close it as a duplicate of that question, if it were posted separately. Also, Wikipedia gives some hints about question (a). I think it's reasonable to expect people to have done enough research that they find information that already exists in standard resources like Wikipedia, other questions on this site, basic textbooks, etc., before asking. I don't think we're doing the world any great service by repeating material that already exists. Once (a) is answered, the same counterexample is going to help a lot with the other questions as well.

So in this case, I think the proper remedy would be vote-to-close as too broad; if the question had asked only (a), I would vote-to-close as a duplicate; and I think the best thing would be for the original poster to go through that material and determine if there is still an interesting question that hasn't already been answered on this site or in standard resources.

About homework and PSQs: The current policy doesn't care whether a question is from a homework or not; that is irrelevant. What matters is whether it is a "problem statement question". The policy applies to all PSQs, regardless of whether they come from homework or not. These questions cause more or less the same harms to the site, regardless of whether the question came from a homework assignment or not.

To avoid becoming rigid and dogmatic, I think it's helpful to recall why we have a policy about PSQs, and then in specific cases, query whether those reasons apply to that specific case. Some common elements of PSQs are: They are often super-specific and unlikely to be helpful to anyone else in the future (unless someone else happens to be facing exactly the same exercise); it's debatable whether they are helpful to the question-asker (if we are robbing them of the opportunity to practice, we may not actually be helping them); there is a massive supply people wanting to post PSQs, more than we can keep up with; a very large percentage of PSQs are bad for the health of the site; they often don't contribute to the mission of the site, to build an archive of knowledge that will be helpful to others in the future; they risk driving away some important contributors to the site. So that gives some alternate criteria you can use to evaluate a question to determine whether any particular question should be treated as an exceptional case.

If/when you see a PSQ that avoids all of those common flaws, I think it's great to edit it to improve it, vote to re-open it, and/or advocate for re-opening it. I don't think policies should be treated as rigid rules that can never be overruled. There probably will be exceptions, and I agree with you that dogmatism is unhelpful.

About valuable questions that you see as wrongly closed: When you see a question that was closed but you think should not be closed, I encourage you to edit the question to improve it. Almost always, there are opportunities to improve the question. I think editing is a constructive path that benefits the site, and is a show of good faith towards improving the site and advancing the mission. Debating policy doesn't always lead somewhere good. In this case, I perceive a lot of debate about whether this question should be closed or not but I haven't noticed anyone stepping up to edit the post to address its limitations and improve it.

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  • $\begingroup$ At least this point matches one perceived purpose of this site: "it's debatable whether [homework and PSQs] are helpful to the question-asker (if we are robbing them of the opportunity to practice, we may not actually be helping them)". But also, from a comment under this Q, 'We are not here either to "help people who are trying to learn mathematics and have identified specific questions that they do not know how to answer"'. $\endgroup$
    – peterwhy
    Commented Feb 17 at 0:47
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    $\begingroup$ Incidentally, beyond the specific counterexample to (a) helping with the others, some of the questions are ill posed: (c) and (d) make no sense, because norms and inner products are things imposed on vector spaces, not on general metric spaces. (It would make sense to ask "is there any analogue of a norm or an inner product for a general metric space?", which may be what was meant, but that's a question where the answer may be a flat "no", or lots of subtly related structures, depending on where the user is coming from. Hence the need for context!) $\endgroup$
    – LSpice
    Commented Feb 19 at 20:09
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    $\begingroup$ @LSpice: If a question does not make sense, clearing up the misconceptions which led to the question would IMHO be a helpful answer for future readers (who might fall into the same or related misconceptions), and so I do not like the idea of closing questions as "making no sense" unless they are well and truly nonsensical (i.e. they are so incoherent that no useful explanation can be provided). $\endgroup$
    – Kevin
    Commented Feb 20 at 20:36
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    $\begingroup$ "When you see a question that was closed but you think should not be closed, I encourage you to edit the question to improve it." There is a school of thought that says we should not do this; that we should add nothing to a posted question that wasn't already there, that we should not try to speak for the user who posted the question. Any outside improvement beyond fixing typos and formatting leaves you open to heated criticism. (This has been discussed before, though I don't have a link handy.) $\endgroup$
    – Gerry Myerson
    Commented Feb 22 at 11:52
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    $\begingroup$ @GerryMyerson, Good point. Thank you for raising that. Yeah, I've seen that school of thought on Math.SE before. Personally I think it is a harmful view and one that just hasn't yet fully absorbed the Stack Exchange mindset of building an archive of knowledge (maybe it's a left-over attitude from those familiar with forums or other contexts?) so I didn't want to get into that. But thanks for warning people that there is a risk of getting negative feedback if one tries to edit a question to improve it. $\endgroup$
    – D.W.
    Commented Feb 22 at 18:57
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    $\begingroup$ I think the above-stated opinion on edits is based on the fear that someone could go overboard and make the question their own with their edits. We have a page for guidelines on editing, and it needs to be enforced the same way that we enforce the rules for good questions. That is, if questions that pass the guidelines can be well-received, then edits passing the guidelines should also be well-received. $\endgroup$
    – Sarvesh Ravichandran Iyer
    Commented Feb 23 at 6:31
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I would put this in a comment, but I don't have enough reputation. How it makes sense that I'm allowed to "answer" but not comment is beyond me.

As a newcomer whose first question was deleted for "lacking context," I wholeheartedly agree that MSE moderation is (currently?) Draconian.

Here is some context: I am a professor of computer science. I have a relatively strong and broad mathematical background for a computer scientist, but I am not a mathematician. So, when I run into a problem that neither my background, my personal library, nor the internet allows me to solve, I turn to experts for help.

Of course, I know from decades of experience what happens if I walk across campus to talk to a math colleague and explain in detail what I'm working on. The first part of the conversation is inevitably the process of dispensing with the unnecessary details of my research to get to the mathematical question at its heart. On the other hand, if I present my question in purely mathematical terms, we begin to make useful progress right away.

Well, despite many hours of searching for the necessary insights, I recently found myself stuck on a theorem I am trying to prove related to my research. At the same time, it seemed very plausible that an entire community of mathematicians knew the answer to my question off the top of their heads. It still would amaze me if no one at least knew an approach I'm unaware of that would make my problem imminently solvable.

So, I posted my mathematical question on MSE, with nothing more or less than what I thought was possibly mathematically relevant. However, the only feedback I got was that my question "lacked context." There was no apparent effort to help me write a "better" question, despite my attempts to engage with the moderators in the comments on my question. It was just a metaphorical big red F on my paper with a big circle around it. The message I got from the MSE moderators was loud and clear: "Go away. You're not part of the club. You don't belong here."

Postscript: Shortly after I posted the above "answer," my question was reopened and I now have a very thorough answer that I am currently digesting. Thank you to everybody involved!

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    $\begingroup$ Thanks for sharing your experience with us. It is an excellent example of what I was concerned about. $\endgroup$
    – Rob Arthan
    Commented Feb 29 at 0:23
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    $\begingroup$ I am sorry to hear that you had a bad experience. The thing is, we get bombarded with all sorts of Do-My-Homework-For-Me questions by lazy students, and so many of us--myself included--are quick to close brief questions by new users, even when they turn out to be good questions. I hope you are happy w the responses you got on your question on commutators $\endgroup$
    – Mike
    Commented Feb 29 at 23:18
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    $\begingroup$ Thank you for sharing this context. One thing that might not be obvious is that (at least for some members of the community) the primary mission of Stack Exchange is "a place where people can collaborate to build an archive of knowledge that will be useful to many people, in the form of questions and answers", rather than "a place where you can go and others will answer your question". Based on past experience, the community's judgement is that questions without context typically don't advance that mission. $\endgroup$
    – D.W.
    Commented Mar 3 at 1:01
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    $\begingroup$ I recognize that the experience feels like and sounds like "go away", and that there is a lack of helpful explanation of the norms and expectations here, to help people learn how to participate constructively here, which I think are shortcomings of the tools and practices we have to educate people and guide people towards that vision. Also, another phenomenom on this site in particular is that there is not uniform agreement about the mission. Some members of the community resonate more with the former mission statement, and some resonate with the second mission statement as well. $\endgroup$
    – D.W.
    Commented Mar 3 at 1:02
  • $\begingroup$ Obviously, it is for the community to decide on the appropriate mission, hopefully through some inclusive governance process. To oversimplify, it sounds like one end of the spectrum wants all examples while the other wants all theorems. $\endgroup$
    – xphileprof
    Commented Mar 4 at 17:00
  • $\begingroup$ My $0.02 is that if the mission is to build an archive of knowledge that will be useful "to many people," the community needs to recognize that "many people," almost by definition, have various needs. Some need more context than others for a question and its answers to be helpful. Regardless, my point was that the feedback on questions that don't meet the guidelines needs to be formative (i.e., helpful to the person trying to write a good question). Again, my thanks to those who reopened my question and to those who posted answers to it! $\endgroup$
    – xphileprof
    Commented Mar 4 at 17:00
  • $\begingroup$ @xphileprof please keep in mind that entropy is not on this site's side. There are a lot of people who struggle with their maths courses and who just want quick answers to their exercises. There are far fewer good interesting questions written by keen students or researchers. RE your last comment: We simply do not have the time to try to coach everyone on how to make their question better, so we do close rather hastily, and if a few potentially good questions get caught in the spam folder then it is what it is. It is probably better than this site being inundated [even more] w bad questions... $\endgroup$
    – Mike
    Commented Apr 11 at 19:16
  • $\begingroup$ ..which is what seems likely to happen if we don't close as quickly as we do. $\endgroup$
    – Mike
    Commented Apr 11 at 19:17
  • $\begingroup$ Meanwhile, it takes the better part of a day [often a couple of days] for MOST posts [that end up being closed] to be closed. And even then there are typically warnings as to why the post is being closed, so plenty of time to revise. So while I am happy to hear that your post got reopened, I don't agree that moderation on MSE is too draconian. $\endgroup$
    – Mike
    Commented Apr 11 at 19:31
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Well, I did not vote-to-close this question [believe me I would say if I did--I do downvote and vote-to-close many questions here on MSE!] but I can see why this question was closed and I don't disagree. D.W. breaks it down above on the specific question, and I pretty much agree with their take.

I will add my take on PSQ in general. I often vote-to-close banal homework questions and pick the "needs context" option, just to pick something. I am really thinking however, that this question is so straightforward or pedantic that it hardly adds value to the site--with the possible exception of the person asking [and even then the joy of helping someone is tempered, for me at least, with the concern that maybe we are doing their homework or even their take-home exam]. The more interesting a question is however [which this question on MSE that is the subject of this thread seems to qualify], the more I give a pass on the "context". Thing is, the question is interesting enough in its own right so that it needs the context thing a lot less. But even for the interesting questions, it is still not for me a full pass on "context". The two big problems with even the potentially interesting PSQ with no context is that

    1. It is needed to for someone attempting to answer to know whether this is a research problem or an exercise--contest or from a textbook. The Riemann Hypothesis is very interesting indeed, but having members of MSE to unwittingly work on that is very likely not very good. Just as importantly, if an answer to the question could be a publishable paper, then anyone who answers should be aware of that themselves too, beforehand.
    1. And this is more relevant--we need to know the level/background of the person asking, as this informs what a good solution would look like. A question may be solvable modulo a result taught in an upper-level math class, but what if the question is in fact from a math olympiad. Then the answer for the question really involves a more clever approach that needs only elementary methods. [Getting back to the specific question closed that is the topic of this thread, it is hard for me to tell the level of the person asking. So this may leave the prospective answerer spinning their wheels on how to answer.]

My 2 cents on this.

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  • $\begingroup$ The additional points you've made don't seem to apply much to the question being discussed, though: it is certainly not research level (and research level questions really belong on MO, not MSE, anyway), and it's pretty easy to tell from the question itself what level the OP is at: they've clearly encountered the concepts of "inner product", "norm", "metric" and "topology" and know that each one induces the next, but they have yet to see counterexamples to the converse. Thus, they're either taking a first year "intro to topology (in metric spaces)" course or self-studying at the same level. $\endgroup$
    – Ilmari Karonen
    Commented Feb 28 at 10:56
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    $\begingroup$ @Ilmari, research-level questions certainly do belong on math.stack, which is for math questions at all levels. $\endgroup$
    – Gerry Myerson
    Commented Mar 1 at 20:50

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