# “Context” vs. “your work” redux

Recently, we (once again) discussed the practices of requiring context and asking for someone's work on a question.

It has been quite an established principle these days that people ought to include some form of "context", the definition of which is best taken from the relevant answer to the entry "How to ask a good question?".

Traditionally, "your work" has taken a prominent and elaborate place in the definition of "context". However, as the top-voted (+21/-4) answer by arjafi puts it:

[...] I would recommend that we seriously de-emphasize (if not eliminate outright) "work"/"effort" in our discussions of context. Other forms of context are, in my opinion, much better suited for giving precise questions which can be unambiguously answered, and also for future searchability. These two facets should be, I think, central to our understanding of "useful and clear" questions.

Because this post was well-received I felt this point deserved a separate discussion to determine if and how the Provide Context FAQ entry should be adjusted.

As a spin-off of any changes, also the "missing context" close-reason will need attention.

• Uh... What's your question? What do you want to discuss? I mean, what's the purpose of this post? I'm not being dense on purpose, I honestly cannot tell. – Najib Idrissi May 19 '16 at 20:01
• @NajibIdrissi "[...]discussion to determine if and how the Provide Context FAQ entry should be adjusted." seems like the purpose. – quid May 19 '16 at 20:06
• I think the policiy's fine, not that I'd dare say so if I didn't. But I often wish people would distinguish between trivial exercises, exercises, problems, and hard problems. When there's an obvious approach based on the material that the OP is obviously studying then "what have you done so far" seems right. But it bugs me sometimes when I see people comment on actual problems that way, more or less automatically - some problems are hard, and what makes them hard is that there simply is no obvious place to start. – David C. Ullrich May 20 '16 at 1:26
• Me personally, I'm satisfied by anything that shows someone didn't just put his homework up on here, go party for the weekend and then expect to see someone has done it all for him on Sunday night. – Robert Soupe May 20 '16 at 1:54
• @DavidC.Ullrich This kind of distinction is exactly why it was proposed to shift focus a little. People have trouble exercising such nuance, apparently. – Lord_Farin May 20 '16 at 6:33
• @DavidC.Ullrich Trivial and hard for whom? – user223391 May 20 '16 at 19:27
• @ZacharySelk For the OP. If the question is how to show that $\sum_{j=1}^nj=n(n-1)/2$ that's a trivial exercise for us, but it's clear the OP is studying induction, so it's a not-quite-trivial-maybe exercise, but still an exercise, for the OP. So ask what he's done so far. If the problem is showing that if a rectangle $R$ is decomposed into finitely many rectangles, each of which has height or width an integer, then $R$ has height or width an integer, that's not an exercise, it's a problem, and asking what he's done so far strikes me as silly. – David C. Ullrich May 20 '16 at 19:37
• @ZacharySelk Of course we can't always know. In the first case, could be the OP is not studying induction and never has, in which case it might be a problem. In the second case, if the OP happens to be Terence Tao then maybe it's just an exercise. But people could try harder to figure out which category it is and respond appropriately. – David C. Ullrich May 20 '16 at 19:39
• @DavidC.Ullrich: I agree with your first comment. But I disagree with your second-to-last comment. The rectangle decomposition problem you state is a widely known problem (and simple enough for first-year mathematics) that in most cases it is just a homework problem! Can you even point to a single question about that problem that you are certain is not a homework/exercise/textbook problem? – user21820 Aug 5 '16 at 8:23

After giving it some thought, I think the basic principles governing the discussion on context are:

1. Determine where the OP stands. Have they tried anything? Are they trying to get their homework done for free? What level of answer will they understand?
2. Value for later readers. Is the question of universal interest? Will different viewpoints yield fundamentally different answers? Is the question from some book or other source?

One of the main objections against including OP's work in questions is that it only serves part 1. On the other hand, it is tremendously effective there.

Another point of relevance from a quality perspective is that the length of the question should be minimised while maximal useful context is included. ("No context" is an explicit possibility here.) Additionally, in the light of generality, the amount of context specific to OP's situation ought to be just enough to make answering the question to their needs feasible.

Taking the above into consideration, I propose to start valuing context according to the following hierarchy:

1. Meta-context: Why is this question asked? Where does it come from?
2. Literature context: Is this a question from a book which you're studying? What are similar results or other relevant links?
3. Personal context: What have you tried? Are you taking a course?
4. Definitional context: What does $X$ mean in your post?

The reason I put 4. at the bottom is because in the unusual case that it's not obvious, the confusion is easily resolved by one or two comments and a subsequent edit.

As for 1. and 2., I think they're the most important types of context, because nobody can supply them but OP while they are important for both of the context considerations mentioned at the top. Moreover, I contend that when these two types of context are present, the added value of someone's work is limited.

I think the schema outlined above goes some way to optimise for pearls. For questions of intrinsic interest, one or two lines addressing the first one or two points would usually suffice. (e.g. "I found result $X$ in book $Y$, which made me think of $X'$.")

As the percentage of information only applicable to the situation of the OP (aka "work") increases, I conjecture the average number of votes, views, and answers to go down, in accord with the reduced usefulness of future viewers. I guess the discussion on how to deal with the ever-growing lake of past questions of this type is something for another thread. The same goes for the fate of proof-verification questions.

TL;DR I think we ought to migrate from "what have you tried" to "why are you asking this and where does it come from". This should at least take the burden off of the posts with intrinsic interest.

• The key distinction is "mathematical vs nonmathematical information about the question". Literature context in the form of a reference to a mathematical book, journal, web site, or competition is mathematical context. Meta-context such as "this is a variant of conjecture C" is mathematical context. Personal context "I proved the special case $n \leq 5$" is mathematical context; "I worked 5 hours on this" is personal but useless context. With some limited exceptions this is pretty much the dividing line between added material that improves a post and junk context that makes it worse. – zyx May 23 '16 at 7:12
• @zyx I agree to a large extent, particularly that what goes for nonmathematical context is usually dead weight. However, it seems to me artificial to not make some distinction between these types of what can be argued to be mathematical context. I still contend that meta- and literature context are the most useful types of context, well above "I proved it for $n\le5$" or the definition of a topological space. Moreover we should acknowledge that more context isn't always an improvement. In summary I think we're very much on the same page. – Lord_Farin May 23 '16 at 16:34

I have a simple proposal. I consider a good question one that tells you, explicitly or implicitly, why the asker is interested in the question, and that this reason has mathematical content. What do I mean? A lot of the problematic questions we get are from people who are not actually interested in the mathematics but in getting their homework done. Here are some possible reasons and some ways to fulfill my criterion for a good question:

1. It was inspired by something else. Name it! Link to it if it's online. The worst questions are those that just ask to solve some ugly equation or evaluate some ugly expression with no clue as to why anyone should be interested in it.

2. It is some kind of exercise that you want to solve, but you are stuck. State the source! I see no reason it should be kept a secret! References not only make it easy for people who have access to the original to see the full context and background of the exercise, but also make it easy for other readers to find the question. Also, briefly describe why you are stuck.

• If you are not sure what the question or some terminology in it means, rephrase it in your own words and ask whether you got it right.

• If you tried something, outline what you think is the most promising approach at a minimal level of detail. The goal is to minimize the effort needed for an expert to grasp what you are trying to do and to help you, so you should leave out unnecessary details. But do not omit steps that you are not absolutely sure are valid.

• If you understand the question but didn't try anything, why should anyone else try?

3. It is about the intuition behind or technical details of some theorem or proof (including proof verification). Such questions are almost always okay because it is clear that the asker is seeking understanding of the mathematics involved. But anyway, make sure that variables and unusual notation or terminology are defined to save people the time spent writing a comment asking about it.

I phrased my proposal this way to emphasize what I think "context" ought to be interpreted to mean, and that it does not necessarily include "what you have tried" but in many cases might.

Of course there are always exceptions to any criteria, but I think this is a good starting point.

• In response to 2, perhaps some users would be uncomfortable if we become a Q+A database including the book and exercise number for problems. It would make plagiarizing one's homework (on exercise from those books) even easier. On the other hand, instructors and graders looking for plagiarism could more easily locate the likely source of the cheating. – 6005 Aug 11 '16 at 10:00
• @6005: If questions really adhere to my criteria, it should be sufficient to make them specific enough to give the correct level of help to the asker, which in my opinion never includes a complete solution unless the asker built it on his/her own. This is the goal of Math SE after all! Plagiarism is indeed mitigated by asking for the source of the problem; as you say instructors can find the source of cheating more easily by searching. Cheaters who lie about the source can still cheat but those will cheat by hook or by crook anyway. – user21820 Aug 11 '16 at 11:31
• @6005: And if instructors do not want any plagiarism, it is completely their responsibility not to take exercises from a textbook, unless they want to trust their students or prowl the whole internet looking for obscure question answering services like Yahoo Answers (there are some people there who actually give full solutions to undergraduate math problems). – user21820 Aug 11 '16 at 11:33