# How good is an answer without any explanation? And how far should an explanation go?

Often times I will see hints posted as answers to a question get up voted a lot and sometimes marked as the best answer, but sometimes the answer is not so intuitive, especially to someone inexperienced in the subject.

Other times there will be hard to understand answers, though they usually correspond in difficulty of the question, marked as the best answer.

And sometimes, a question that is deep and in depth may not be general enough and open to argument.

So how should hints be provided, answers be explained, and specificity considered?

Especially when multiple answers are considerably acceptable and completely different.

How should I consider my audience when posting an answer? Direct it towards the OP or the general (math or not) public?

How do I consider my answer if it is down voted and in my own defense correct? Should I be persistent in my view point or change? (assuming I do give a correct answer)

• It appears there are strong feelings going around here. – Simply Beautiful Art Dec 26 '15 at 16:22
• Bad hints piss me off. They represent everything wrong with this site in terms of perverse incentives and just outright laziness. – Ron Gordon Dec 26 '15 at 16:31
• @RonGordon I agree, by my feelings aren't so strong. I love the answers that seem to have taken an hour to write, showing true conviction, meaning at least some people here try hard. – Simply Beautiful Art Dec 26 '15 at 16:33
• I think it's good form to post hints as comments, then you can always say "I posted it first." – Robert Soupe Dec 27 '15 at 21:12
• And maybe some of the people who post hints as answers have good intentions. But maybe they are also making assumptions: "As soon as they see my hint, they should immediately think of this one concept that is so basic to me yet I don't list that concept in my hint, but they should still be immediately led to the full answer." – Robert Soupe Dec 27 '15 at 21:14
• @RonGordon: Answers with not even a whiff of a hint as to the method used are infinitely more annoying. (Ring any bells?) – user21820 Nov 28 '16 at 9:45
• @user21820: no, not really. – Ron Gordon Nov 28 '16 at 10:15
• @RonGordon: Haha you forgot about the integral calculator who said he/she will only post answers and nothing more? – user21820 Nov 28 '16 at 10:22
• @user21820: Oh, that. No, didn't forget, just answering questions too early. Funny thing about that: that poster has fans in Reddit that just love that type of answer because it is like giving the finger to all of us stodgy types that demand facts and reasoning. And if you are a U.S. citizen, that might ring a few bells. – Ron Gordon Nov 28 '16 at 10:27
• @RonGordon: Then I like stodgy types. =) I'm not too sure what you're referring to, but I infer it has to do with the recent events, whose future consequences I can hardly guess, except that it probably will affect many more than 4 years... – user21820 Nov 28 '16 at 10:34

1) Good hints belong here. Bad hints do not. If you want to make a good contribution to the site as an answerer, do the problem out always. It does not matter whether you plan to post a full, novella-like solution that details every step as far as $1+1=2$ or just enough to give a taste of the path one needs to take to realize your solution. But when you provide a good hint, it should sparkle with the authority you earned from solving the problem. That is good for everyone. As Asaf said, when written out well, a good hint serves a beautiful pedagogical purpose, even better than a full result.

In contrast, a bad hint is put up by someone who thinks they know what they are talking about (usually they do not) and is trying to answer first. Anyone here can tell from such a "hint" that little thought and zero work was carried out. Many times, they will send the OP down a terrible path and frustrate rather than inform. There is absolutely no place for such garbage on this site and they should be down voted with fury.

2) Some hints may go in the comments. I do this sometimes when what I have to say is less than insightful and I feel will easily be overshadowed by someone else's answer. (Let them get the glory.) If what is said is significant, however, then we should encourage the commenter to change the comment to an answer.

3) Your audience is the community, but the question you answer is the OP's.

4) If your correct answer is down voted, you may wish to post a comment asking where your answer is less than useful. You actually may wish to ponder the possibility yourself, but if you cannot think of any place, then just leave it alone. If it is part of a patter of personal downvotes, then they should be reversed anyway.

• That third item is a concise, beautiful point of view of the answer-system which addresses many doubts I've had at some point when answering. Thanks for that. – Aloizio Macedo Dec 26 '15 at 18:10
• Another thanks for #3 (rest was also nice). But in what sense is the "the question ... the OP's"? It seems to me that the question-posters forfeit any notion of ownership or entitlement to direct the discussion once the query is let loose onto the wilds of the Internet. – zyx Dec 26 '15 at 21:18
• Regarding 3: what is "the community"? The (active) users of this site, or the prospective readers of the text? As far as I know around 90 percent of the readership come to the site via searches. Thus, this is not at all the same. – quid Dec 26 '15 at 21:54
• @zyx: I meant, answer the question that was asked. – Ron Gordon Dec 27 '15 at 1:02
• @quid: at that point, does it matter? Address your answer to those imaginary or real (or complex) people who may be interested in reading it. – Ron Gordon Dec 27 '15 at 1:03
• = "Your audience is all interested readers, but answer the question that was asked". Change the second part to "but keep replies plausibly relevant to the question" and we get (imo) a complete FAQ in one sentence. – zyx Dec 27 '15 at 1:14
• Yes it does matter, in that it shifts the balance. I am of the opinion that the question asked should be answered, like you, and that this should in general be done in a away useful for somebody that actually might have this question (and not so much for those that happen to read and to vote as usually a leisurely activity close to the time of writing). – quid Dec 27 '15 at 1:14
• Comments are not for extended discussion; this conversation has been moved to chat. (Sorry for yet another ping, Ron.) – Daniel Fischer Dec 28 '15 at 23:10
• I think it needs saying that posting a hint for an answer needn't imply that you don't intend to expand on it, eventually. True, most viewers will encounter the question long after the dust has settled; still, there's something to be said for guided discovery of the answer, and a temporary hint can serve a double function (help the OP the right way, and also let other people know that you've taken it upon yourself to answer the question. Not to discourage other answers, if someone has a better approach in mind, but to save them the effort if they don't). – Jonathan Y. Jan 2 '16 at 23:01

Hints should sometimes go to the comments, and sometimes to the answers.

First of all, hints are useful to future visitors, since they might be standing at the same shoes (or isomorphic shoes) as the person who asked the question. And therefore the same hints can be helpful to them as well.

Secondly, not all hints should immediately spark that fire in your brain. I recall when I took measure theory as an undergrad, the professor used Folland's book for pretty much everything. So when we got homework, we would go to check that he didn't introduce typos or what hints have been omitted. The hints would take about a good 30 minutes to figure out. They are hints, not "dehydrated answers".

Finally, when someone asks a question like "How do I solve X" the answer might depend on their previous knowledge. Sometimes the obvious approach would be through some advanced theorem or technique, whereas an elementary approach exists as well, but is the road less traveled (for obvious reasons). When asking a question without giving proper context, it is hard to aim the answers or the hints, or anything else, to the correct level. This also causes the opposite situation, that future visitors who come to the same X but with an entirely different context might not be able to decipher the hints or answers.

And let me add that giving good hints is as difficult, if not more difficult, than giving reasonable answers. And it can serve a pedagogical purpose, too.

• Yes, I have seen very valuable hints, but whether or not there are valuable is indeed up to do the viewer. – Simply Beautiful Art Dec 26 '15 at 15:32
• "... giving good hints is as difficult, if not more difficult, than giving reasonable answers." When done correctly, i.e., when the answerer has actually answered the question for his/her/themself and then takes the trouble to communicate the pathway to the answer in such a way as to teach the OP and future visitors something. The incorrect way to give a hint is to half-assedly say the first thing that comes to one's mind without any thought as to how to carry it out. That is actually far worse than doing nothing or even giving a wrong answer. – Ron Gordon Dec 26 '15 at 16:08
• @RonGordon I see what I believe to be bad hints all the time and it disappoints me. I see what I believe to be good hints rarely and it makes me smile. And yes, I agree that hints can be better than nothing. – Simply Beautiful Art Dec 26 '15 at 16:21
• @Ron: I don't disagree, in general, that thoughtless hints can be damaging. But there is something to gain even from wild goosechases in mathematics. – Asaf Karagila Dec 26 '15 at 16:22
• Those measure-theory hints you mention just would not belong on this site though, in any case not as answers. (This site is not for any type of content that is in some sense valuable.) The answers on this site in some sense should be ready to use. I am not against terse answers, they might still leave some work for some, but still an answer should be a complete outline to a solution, not a starting point or important idea only. Whether or not they are harder, easier, or the same to come up with is completely irrelevant in my mind. – quid Dec 26 '15 at 19:27

I think my stance on hints is a bit more extreme than some, but IMO hints do not belong on this site. I've already posted a rant in meta comments about this, and I think it's a good place to reiterate it.

For some context, I was replying to someone suggesting that hints was "helping/forcing OP to think for him/herself and in that process actually learn mathematics" and that "Spoon-feeding OP with full answers is often counter-productive to this goal":

If you want to "force the OP to think for himself", don't answer at all and ask for their thoughts in the comments. It seems that people who answer with hints "show a complete lack of understanding" of how this platform works too.

It's happened several times now that I can't prove some result, look it up and find the same question on this site, and then I'm greeted with some half-assed hint that I already thought of but couldn't make anything of. Now what? I can't ask a new question, it would be a duplicate. I can't offer a bounty every time that happens.

If the question is truly bad, close it and either force the OP to improve it or eventually delete it. No one is calling for spoon-feeding. If the OP improves the question, great, post a full answer and contribute to the knowledge repository that math.SE is. If the OP doesn't, please don't contribute to the pollution of this website by putting all the people that will have the same question in the future in a catch-22 situation.

And I'm not even talking about all the people who take advantage of the "hint" policy to post some one-line hint that they didn't think through and doesn't even work when you try to work out the details -- just two days ago someone posted a solution for some question in that worked in the one-dimensional case and then "HINT: use induction on dimension" or something like that. As you can guess, higher dimension was orders of magnitude more difficult than dimension 1 and the answerer eventually acknowledged that.

And to clarify a discussion that happened later in the thread, I'm not saying that every single detail should be written in the answer. I think there's a difference between "HINT: integration by parts" (horrible) and "Hint: do integration by parts twice. Let $$u = x^2$$ and $$dv = e^x$$. Then after let $$u = 2x$$ and $$dv = e^x$$". IMO the first one is completely unacceptable, I'm more reserved about the second (and I wouldn't downvote it), but I believe it would be better with more detail.

tl;dr I don't like hints, and I think they're actively harmful. Either answer the question completely or don't.

Don't answer in the comments either. I think that goes without saying. But don't answer with a hint in the comments, too. People will then be reluctant to actually answer the question because it's already "solved", and then the unanswered queue gets cluttered.

• To sort of repeat what I said in Asaf's post: hint or no, do the problem out if you really want to help. How you communicate your insight in a helpful way afterward is really up to you. But do it out and know what on earth you are talking about. – Ron Gordon Dec 26 '15 at 16:10
• There is a problem here: Reading what you say, you seem not to be against hints, but against non-detailed answers (which you are seemingly defining as hints). What defines a hint is not the "HINT" preceding the answer, but the structure of the answer itself. There is obviously a correlation between hints and lack of detail, but they are not equivalent concepts. Also, it is not clear what is to answer the question completely, and in what level of detail should one person stop. – Aloizio Macedo Dec 26 '15 at 18:47
• @AloizioMacedo in my mind a crucial difference between a hint and a terse answer is that an answer, terse or not, should come with the implicit promise that it is complete (even if initially only an outline) and works. However, I agree sometimes the prefix "HINT" seems there for no apparent reason. There is still a problem there as there is a (at least perceived) lack of commitment of the form described above by the answerer. – quid Dec 26 '15 at 19:35
• And I think it's very difficult to post an answer that will be understood by every single person that will ask themselves the same question. It also fosters the idea that hints are acceptable, and then other users will post their hints, of varying quality. If other users only see full answers, then they will only post full answers. Basically, I think the users who post subpar, not-thought-out-through hints have ruined hints for everyone. If no hint answers were posted ever again on this website, I believe this would result in a net increase in quality of content. – Najib Idrissi Dec 26 '15 at 19:46
• @AloizioMacedo I think quid's comment matches what I think. For a simplistic example, imagine a solution that has two steps.The typical hint will help solve the first step, and leave the second step to OP. Maybe OP will manage, and if they don't you're here to answer comments. But what if years later someone has the same question, manages the first step alone, but not the second? The hint will be useless. Now we have to deal with questions "I have this question, but don't understand the answer... Can someone explain it?" And future users need to sift through 2-3 answers to get the full answer. – Najib Idrissi Dec 26 '15 at 19:53
• @NajibIdrissi I understand your point of view, but I think you are being too extreme. However, I should note that your observations, particularly: "But consider the consequences too. If a question already has an answer, people will be much less likely to answer it.", are very pertinent. I've never thought about that in this way. – Aloizio Macedo Dec 26 '15 at 19:59
• "Hints" as a way of denying information to OP are ineffective, since others may give full answers, and may be encouraged to do so by the annoying-ness of dropping mere hints. But the negative aspects and inefficiencies created by hints should be distinguished from the positive contributions made by (correct) partial answers and suggestions from answer-writers who do not have the time or ability to post a complete analysis. – zyx Dec 26 '15 at 21:43
• @zyx In general I think "do not have the time" is a bad reason to post something incomplete. There's no rush, it's better for everyone to wait until you have the time to post something complete. It's not a race, unlike what some users seem to believe (the FGITW movement is the source of many, many bad answers). – Najib Idrissi Dec 27 '15 at 10:44
• The alternative is to posting something short and quick, but incomplete, is often to not post anything at all. It would be great to come back later but that is just not realistic where users check the site during short interludes from work. Not posting at all can be less good for OP and everyone else if the short quick thing would have advanced the state of "answeredness" of the question. – zyx Dec 27 '15 at 15:16
• @zyx it can be less good for OP, but it can also be better. An important factor, which you do not acknowledge at all, is that while this alternative may very well be accurate for one particular user viewed in isolation this one user's actions or non-actions have repercussions on future users' actions, and what is actually relevant is the final state of the question after a reasonable period of time not one particular user's contribution. The presence of a two-line answer may very well make the next user not write their five-lines answer. This is a very real phenomenon. – quid Dec 27 '15 at 17:47
• My view on this depends on the circumstances. If an expert goes through a week-old or even just a day-old or let it even be just a couple hours old question and add brief answers to not yet answered questions, then indeed this is likely to be useful. However, if we are talking about standard questions at the very front of the new-queue than this argument partial-is-better-than-none just does not hold water. @zyx – quid Dec 27 '15 at 17:47
• @zyx I know it is significant for me personally. And, I know others expressed a similar view. Anyway, do you want to actually deny it is a significant phenomenon or is this just some epistemological exercise? 'If what is relevant is final metastable state of the question then every correct nonredundant reply is positive progress toward "answered-ness".' If some specific temporary progress prevents bigger progress later having it is ultimately a net negative. – quid Dec 27 '15 at 21:27
• @zyx on the ps: It depends on your notion of expert. But I did not specifiy it is an expert at the top of the queue so this is moot. More to the point I'd say a relevant fraction of the highest point users "writ[e] partial lazy answers to standard questions at the very front of queue" as do any number of other users (including me at times). I never said they "stop all later answers." Please try to avoid distorting what I write. – quid Dec 27 '15 at 21:38
• @zyx "stop all later answers" is not the only-apparently-relevant sub-case. I do not see what issue you take with "epistemological exercise" given a situation where you engage in some discourse about how I can know and about not taken actions not being observable etc. rather than to state if you disagree or not with the claim I made. – quid Dec 27 '15 at 21:51

If an