Is it a "rule" of Math Stack Exchange that when asking a question, it's **never** good just to state the question?

Question

I recently asked the following question, and within 3 minutes it got 2 downvotes:

Is there a set $A \subset [0,1]$ such that both $A$ and $[0,1] \setminus A$ intersect every positive-measure set?

(Some minutes later it then received an upvote, but then it received another downvote.)

Also, someone else shortly afterwards posted a question asking whether equivalence of two norms on the same vector space can be determined just from whether they share the same collection of compact sets. Again, this question almost immediately received several downvotes. After one person (of very high reputation) posted a comment to say that they didn't understand the downvotes, someone else responded that the text over the downvote button says "This question does not show any research effort...".

(Similarly also, in my question, the first comment posted was "what are your thoughts?")

So my question:

It seems to me that there are essentially three types of question that one can ask on MathSE:

1. I'm a student (or researcher in a different field who is "functionally" a maths student here), and as part of my learning I would like help trying to work out the answer to this problem...
2. I'm a researcher, and I would like help trying to solve this particular problem that's relevant for my research... [although this is probably more appropriate for MathOverflow]
3. I'm a researcher, and I have the following interesting/useful question that is simple enough that there is clearly a known answer somewhere, but it's difficult to find the answer using Google...

Obviously in category 1, the student should give an indication of what they've tried, as this will best help the person answering to benefit the student effectively. Obviously in category 2, the researcher should offer his thoughts or commentary.

But in category 3, is it not an active waste of everyone's time to have to read your "initial thoughts" on how to answer the question? Isn't the most important thing that if the question gets answered, then vast numbers of people who might in the future be interested in the question (or just find it cool) are much more likely to see the answer to the question (whether by a Google search or by just browsing interesting questions on MathSE)?

And in category 3, isn't the statement "This question does not show any research effort" only true if the answer (or information that immediately yields the answer) is fairly easy to search and find on Google?

Now I understand that MathOverflow is often the place to ask questions of category 3, but I think the attitude of many professional mathematicians is that if the question is sufficiently basic - but not directly within the researcher's particular field of expertise - then the question is well-suited for Math Stack Exchange.

---

As for my own "initial thoughts" on this question:

MathOverflow also has exactly the same text over the downvote button as MathSE, and one of the central purposes of MathOverflow is that professional mathematicians can ask questions of category 3.

Answer 1

In my opinion it is virtually always better to have some context provided for the question. In the cases you mentioned, a reasonable form of context can be a short explanation why the question is relevant and interesting, or also just how it came up.

Formatting the question well will allow those readers that do not care for it to skip it. Moreover, skimming a few lines of text does take a pretty minimal amount of time, especially for somebody well-versed in the subject. Conversely, if somebody would appreciate some context and none is provided, the situation is not all that easy to solve.

Therefore, even if (hypothetically) there was a relatively large majority of readers that do not appreciate the context, it would in my opinion still be beneficial to provide it for the minority that will appreciate it.

Thus, indeed, it is basically never good just to state the question.

However note this does not mean that we must crush-down hard on each and every question that does not provide context. If the post is otherwise very good, one might accept it being lacking in this one category (it still remains a lack of the post).

Since you mention MathOverflow the main difference as I see it is not that context is considered as not relevant on MO, but rather that more leeway is given regarding this aspect if the question is otherwise good (the fact that it is never good persists though).

Finally regarding the "research effort," if you checked a standard reference and did not find the result there, then you having done that is pertinent information that should be included in the question (as it might save prospective answerers the effort to do the very same check).

If however you did not check any standard reference, then I would say the criticism "no research effort" seems spot on (in a way, regardless to the fact being in a standard reference or not).

Answer 2

This is a controversial topic in the math.SE internal politics, and on the meta site many words were minced on the subject of "context" or "problem statement questions" (PSQs) in the distant and less distant past.

The importance of context is that I, as someone wanting to answer and engage with the OP (in this case, you), don't know what knowledge you have at your disposition.

Are you familiar with Bernstein sets? Do you know that every Borel set is countable or has a perfect subset? What other knowledge you may or may not have? Even worse, it is sometimes very easy to ask a fairly simple and intuitive question, whose only known solutions are extremely technical. This can lead to a lot of frustration.

I have felt that frustration many times, as an answerer, when I wrote a technical answer which shot way above the OP's head—through absolutely no fault of my own—and received absolutely no comments from the OP. Now imagine, that you pour a good hour into researching the details of an answer (which you knew vaguely, otherwise it's well more than a good hour), sat down to type a long answer, and received no comment. Whereas a "simpler" answer received immediate thank you comments from the OP. How is this not frustrating? How is this not something that would cause you to feel that the OP was frustrated with you as well?

And this is not uncommon. If I experienced it more than a handful of times, I am sure that the aggregate collective of users who put a lot of effort into their answers have felt it collectively many times. Both the people who asked the questions, and both for those who answer them on an "inappropriate level".

And that feeling sucks. Like a super-massive black hole.

Now you could argue that this site is more of an archival website for people to find answers to their questions. But you get that sense of frustration from other people to, who came with a "simple question" and only find "complicated answers". If you ask a question in a manner that indicates what is the context of you as the one posing the question, then future readers will also be able to judge whether or not the answers even have a chance of being clear.

An easy example would be the many generalizations we have from freshman calculus through general topology, measure theory and otherwise advanced topics. So a simple question, phrased in a general-enough way could invariably find its way to receiving mainly incompatible answers.

As a teaching assistant, when students came to me with questions, I ask them for context. Now, I am more suitable to judge the needed answer because I know what they should know on a certain topic, and I am able to judge what would be spoon feeding and what would be a teachable trail of hints via a more Socratic method. But nevertheless, I always insist they explain to me where they got stuck. This is the context I need to provide them with the best help that I can give them.

The same is true here. And of course, it's impossible and impractical for you to give me all your previous knowledge when you ask about what are effectively Bernstein sets. But some context can in fact go a very long way.

Once you've added some information as to what you know about this question (e.g., you are familiar with the notion of 'category' and that you are aware that Lebesgue measurable sets are not likely to work), it shows me that you have some understanding of the topic, and not that you're asking out of idle curiosity. It shows that you're more engaged with the topic, compared to an undergrad halfway through her first course in measure theory. And it shows to me, that the answer given to you (despite not being what I would write, as I would definitely bring up Bernstein sets), does hit the nail on the head.

Answer 3

I agree with the other two answers regarding the general importance of providing context for a question. However, my own reasons for that have not quite been captured by either of the other answers.

Other answerers and commenters (and the OP) have emphasized the importance of writing for a general audience. I don't really know how to do that, because I have a hard time imagining what a "general audience" is. Instead, in looking at any question, I take the person who posted that question as an example of a person who is interested in that question (yes, this is tautological, but please bear with me). But that person may have some mis-understandings. The trouble is, the questioner's understanding of their own question seems often to be limited. Furthermore, there can be many different ways to have limited understanding of the very same question.

A good question with lots of context sometimes contains enough information that one can see, or figure out, where the "real" question lies. If this is not always immediately apparent, the context gives hints which one can follow up in order to get to the gist of the real question. Here are two such examples which I answered recently:

1. Fundamental group of a Cayley Graph used to Calculate Kernels of Group Morphisms. In this question, the person really needed to understand a theorem about deck transformations of regular covering maps, and although that need was not immediately apparent, there was enough in the question that after some back-and-forth in the comments I could figure out the way to helpfully answer the question.
2. Prove that open half planes are open sets (again). This question appeared to be a duplicate and was fast on the way to being closed, but the question had quite a lot of context, and again I was able to probe the OP in the comments and to figure out what he really needed to know.

Because of this phenomenon of varying kinds of misunderstanding, when I see a question with no context I feel no urge to provide any answer except for possibly leaving a generic comment of the sort "Tell us what you've tried, where you failed, etc. Without that, it's very hard to answer your question."

One last thing, regarding the point made by the OP on the most important thing: Even in category 3 questions I think my comments above apply. I don't know how to write for the masses, I only know how to write for people, and in this situation the person (virtually) in front of me is the writer of the question. I want to answer that person's question, but it is very easy to miss the target unless that person gives me some context of their own understanding.

Answer 4

Sometimes the same question can be answered at very different levels of sophistication. Sometimes the answer can be a trivial consequence of a general theorem - can the theorem be assumed? Sometimes it is unclear whether the question is part of motivating an approach to proving a general theorem, or one of the early easy examples illustrating how the theorem works. Sometimes it is unclear whether calculus (or related forms of derivative) can be assumed (e.g. certain questions about polynomials). Many of the people who answer questions here are teachers by instinct, and want to help those who ask questions to get a good understanding of the mathematical ideas behind an answer - it helps to know the mathematical background and context of the asker.

These issues may be invisible to the person asking the question if they don't have the mathematical sophistication to see them, and they may get the kind of answer they don't want and can't understand. See the beginning of Bill Thurston's classic essay on proof and progress in mathematics for an example of the layered sophistication of an apparently simple idea.

So the need for context can be invisible to the person asking the question, but might be more significant than they realise for getting a good answer.

The basic rule when asking a question is to give the person answering it the best chance of giving a helpful answer. The request for context should generally be read as "help me to help you".

Answer 5

I'm going to add a separate issue here. Maybe your question is a homework question. In that case, there are two issues.

First (what the answerer cares about) - if you're just coming here to avoid thinking through your homework, then you deserve to be downvoted. At least show us that you're making a good faith effort to do the work and that the responses you get will actually stimulate thought in you rather than just being copied onto your paper mindlessly. I will gladly put in effort to help you understand something if I believe you will then understand it. If I'm worried I'll just help you get a better grade than someone else who is putting that effort in, then I don't want to do that.

Second (a warning for the asker) - you might get an answer that has nothing to do with what you've been taught in class. I've helped grading a project where a number of people did things very differently from the expected method. A quick google search on some keywords they used found the webpage that they had copied without attribution...

Answer 6

I think it kind of is a rule. Just now I tried to post a question with just the title and tags, and the system wouldn't let me post it.

Of course what some people do to get around that is to simply repeat the question title in the question body. Now, you did go a little beyond that, but still it was easy to assume (incorrectly) that you were just trying to get someone else to do your homework.

Well, maybe technically it's a norm rather than a rule, you know, like releasing your taxes when you run for president. Regardless, it's good form here to give some context rather than just state the question. I can't think of a case in which it would make sense here to only state the question.

Now, if you're concerned that your own efforts could be misleading to others, you can always put in phrases like "Am I on the right track?" or "Did I overlook something?" to give some idea to others as to your doubts.

Answer 7

If you are a researcher, it is really annoying (since contradicts the laconic spirit of math) to add extra context. But one has to take into account that who answers is a person who wants to be motivated before giving his or her answer.