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Yesterday I posted a question about a problem that appeared on a differential geometry book, and it happened to be written by an active member of this community.

I showed my work and another user wrote a comprehensive answer pointing out what I did wrong along with the correct solution of the problem.

The author of the book complained about the other user giving a detailed solution to a problem which was posted in his book and which he gives as graded homework in his classes.

While the answer the other user provided was very useful, I can understand the point of view of the author and the fact that posting detailed solutions in this site can make it easy for his student to cheat on this graded homework he assigns to them, so I don't know how to proceed here. Would deleting the question be a good idea?

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    $\begingroup$ I do not think that deleting the question is the appropriate course of action here. $\endgroup$ – Andrés E. Caicedo Sep 20 '18 at 16:27
  • $\begingroup$ Note, you do have the option of not accepting the complete solution to your question. I would not delete your question, but, given the answer of the author of the question you asked, I would pay closer attention to that answer. In one respect, the author of the text from which you are asking about an exercise is likely the go to source for hints, directions, to help you answer the question. $\endgroup$ – Namaste Sep 20 '18 at 17:16
  • $\begingroup$ @amWhy what made me open this post is that, since I took the question from the author's book, which he uses in his classes and whose exercises are given to his students as homework, the detailed answer will still be there and the author's students will still be able to copy their homework from it. I wouldn't hesitate that much if the question I posted was from some famous book like Do Carmo, but I find this case more delicate. $\endgroup$ – Yagger Sep 20 '18 at 17:44
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    $\begingroup$ I do not believe that you have done anything inappropriate or unethical. When one assigns homework, one has to accept that there are likely to be solutions on the interwebs somewhere, or that a student is going to get outside help. It does not "ruin" a book to have complete solutions running around, and it might be better to have those solutions in the public forum than hidden behind a paywall. I don't think that we should go out of our way to create a solutions manual, but I also don't see there being a great deal of damage being done here. $\endgroup$ – Xander Henderson Sep 20 '18 at 18:40
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    $\begingroup$ I think, especially in this day and age, that authors and professors have to realize that solutions to textbook problems at virtually any level are readily available online. Regardless of any ethics or morality, this is the reality of a modern course. I don't believe that having solutions available will "ruin" a textbook, because it doesn't deny any learning opportunities to students. It's up to students to make sure that they understand the material (without just reading solutions) and it's up to homework/exam writers to write evaluations that can't be easily cheated on. $\endgroup$ – user296602 Sep 20 '18 at 18:49
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    $\begingroup$ Of course, my comment in no way endorses people who make no-effort do-my-work-for-me posts. I'm really focusing on the students who are making a good faith effort to learn something. $\endgroup$ – user296602 Sep 20 '18 at 18:49
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    $\begingroup$ Since I am the heinous author in question, let me comment that I was in no way critizing @Yagger's original post. Indeed, I replied to it, trying to critique the partial solution he had posted and to indicate what he should do to finish it up. I complain because the other solution was a polished solution that didn't address in any way the strengths or weaknesses of Yagger's partial solution. And because I philosophically am on the side of NOT having MSE be a repository of complete homework solutions; I'm fully aware that there's another viewpoint there. $\endgroup$ – Ted Shifrin Sep 20 '18 at 19:03
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    $\begingroup$ Indeed, the other answerer has answered the same question at least one other place. I suppose it's OK to post answers to the same question multiple times to get more rep points? That is the game, I suppose. (Actually, I have answered the same question in some form several other places, too. So my approach here was to address Yagger's particular partial solution specifically.) But perhaps Yagger should have done a search before posting his question and seen several duplicates. $\endgroup$ – Ted Shifrin Sep 20 '18 at 19:10
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    $\begingroup$ @TedShifrin I'm certainly someone who gets offended by the rep farmers (which I guess is the more polite term...) which proliferate the site, but I don't think it's a fair accusation to bring up towards this particular user. I'll admit that I've answered duplicates simply out of a lack of remembering my answers over so many years on the site. $\endgroup$ – user296602 Sep 20 '18 at 19:17
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    $\begingroup$ The ideal situation is that there should be a lot of interaction and positive feedback between the university world and this site. Maybe a solution for this situation can be to edit a new answer with hints or adding what is the way to solve the problem (if it is acceptable for who posted the detailed answer, and also if it is acceptable by the author of the book), and after that the author of the detailed answer can delete the old one. Obviously I think in the good intentions of all previous users; and this comment is just my opinion about how solve it. $\endgroup$ – user243301 Sep 20 '18 at 19:30
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    $\begingroup$ @TedShifrin Hardly the heinous author! I thought you brought up good poinst in the linked post, and in this meta post. But to be certain, this is not a problem of the asker's (Yagger's) doing (save for perhaps not having searched the site effectively, though effective searches on this site can be tricky), just as you've said. It is a good time to revisit how much of an answer is too much, and in which circumstances. $\endgroup$ – Namaste Sep 20 '18 at 20:02
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    $\begingroup$ "Indeed, the other answerer has answered the same question at least one other place." @Ted, if that "other place" was another question here at math.se, then it would be useful to have a link, so we could close one of the questions as a duplicate of the other. $\endgroup$ – Gerry Myerson Sep 20 '18 at 23:45
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    $\begingroup$ @Gerry: Here are some of the previous occurrences. (math.stackexchange.com/questions/1645406/…) (math.stackexchange.com/questions/1132553/…) Robert's answer ... and there are more I'm too lazy to dig up. :) $\endgroup$ – Ted Shifrin Sep 20 '18 at 23:59
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    $\begingroup$ @TedShifrin While I understand your situation, like very much the way you answered the question, take into account your information about duplicates, etc., etc. - do you have any suggestion about what to do in this situation? $\endgroup$ – მამუკა ჯიბლაძე Sep 30 '18 at 13:10
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Having a full, detailed answer to a good question makes us all richer. I'd rather have the answer than not have it. And, if the question is worth answering, then it should be answered. (To Prof. Shifrin's comment, I don't think at all that solutions to problems in his textbook "ruin" it. On the contrary, it enhances its value because it's an(other) indication that people are engaging the material as he's presented it.)

What's being discussed is the circumstances under which the answer is being used. (As such, it's not really a math question but a math education question.)

The Internet is a tool, but just like a real tool, it can be used to create something beautiful or it can be used to chop your hand off.

If someone is studying differential geometry on their own, then a full answer can be a great guide to learning how to apply the material. The quality of that person's learning is directly related to how much they struggle with the question before soliciting hints from Prof. Google.

The same is true of someone taking differential geometry for a grade, except there's an evaluation of how much that person has learned, possibly based on whether or not they can answer this particular question.

There will always be people looking for an easy way out. The easy way out is usually available if one knows where to look, and it's far easier now than when I was in college.

I don't remember a whole lot of my junior English class, but I do remember my English teacher saying, "If your essay even smells like CliffsNotes, you will fail." She was saying, "Don't take the easy way out. I know where the easy ways are."

What she didn't do was call up our local bookstore and ask them to take the CliffsNotes to Hamlet off the shelf.

It should be up to instructors to (a) set guidelines and restrictions as to what independent work is expected in solving problems, (b) to be diligent in knowing where there are answers "in the wild," and (c) to monitor students' answers accordingly against the known answers if their correctness has any bearing on their grade.

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    $\begingroup$ Huh -- does that instruction mean something appreciably different than "it is part of this assignment to read everything CliffsNotes has ever published on this matter and actively make sure you avoid saying anything they have also said; if you don't to this you risk failing because you notice something in the text that it is forbidden to say because it smells like CliffNotes"? $\endgroup$ – Henning Makholm Sep 22 '18 at 13:51
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    $\begingroup$ @HenningMakholm Yes. Our English teacher was nearing retirement and had more than ample judgment to tell which essays were the output of a student thinking and which weren't. She had a keen sense of smell. $\endgroup$ – John Sep 24 '18 at 3:51
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My take on the issue is:

We (MSE, and SE in general) have a policy that whenever a question gets asked here, it belongs here in a sense, and it is subject to the standards we have here. This sort of ownership is behind the principle of frowning upon self-deletion of useful content, for example.

There is some controversy regarding hint-like answers (this has been discussed relatively recently, and comes back from times to times), but it seems that it is widely accepted (here and elsewhere, corroborated by how the system of Q&A is itself envisioned) that detailed answers should always be on-topic (this is not saying that they are necessarily useful; more on this later). The point being: questions should be answered. This is the backbone of the concept of a Q&A site.

But... if we take that literally, to the extreme, quality (and even ethics) suffers. In order to prevent this, we have some barriers to prevent people who come ill-intentioned and/or low-quality questions. This puts some restriction to the previous "point", it now being: genuine, on-topic questions should be answered. What, exactly, those barriers should be is a little controversial. But I think it is not controversial to say that your question passes through these barriers.

Being a detailed answer to an on-topic question, that answer has its place here as well.$^{(1)}$ As far as how the system works go, there seems to be no issue at all.

The problem seems to be the concern regarding other people, not involved with the question or the answer, to grab an answer for their own use while skipping important processes of learning, circumventing the "genuine" part of the process on their end.

This is a valid concern, but one that is ultimately impossible to have anything practical and enforceable upon in my opinion. The only solutions which I can think of that would work on a large scale would be things like discouraging detailed answers to textbook problems, banning textbook problems etc, which seem to be all problematic.

One solution that could work in general and that may be fair is to let an author explicitly say that they do not want their questions in this site, and that the community respect this. But once one agrees to have their questions in this site, those questions (and their answers) should be addressed as per the procedures of the site itself.

Now, having addressed the general issue in those last three paragraphs, one is of course still free to think that some answers being complete, detailed solutions in certain cases are not useful. In those cases (and the particular situation alluded to by OP could be one of those), I think we can rely in the voting system. If you see an answer to a question which you think ends up being not useful due to the whole context of the question (or for some other reason), then downvote it. This is really not specific to this situation: recall that when hovering over a downvote of an answer, it says "This answer is not useful"!

$^{(1)}$ The community can discuss possible barriers regarding complete answers to textbook problems, but I personally think that this is a bad idea to be done systematically.

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    $\begingroup$ Aloizio, even if I were to say (which I won't quite) that I don't want questions from my textbooks to be allowed here, most times students and questioners don't cite their sources. As I think you probably know, I have written some very complete answers, but I really think the strength of this place is to start where the OP is and work with it — not just take the easy way out of posting a canned, polished answer — sometimes engaging the questioner so that that person derives the maximum learning. I realize I'm more willing to do this than most people, and it annoys some people when I do. $\endgroup$ – Ted Shifrin Sep 20 '18 at 23:53
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    $\begingroup$ @TedShifrin I can certainly agree with the fact that a lot of questions, by the context which they provide, admit as most useful answers those which are not a complete treatise on a given subject. I hope that my answer does not seem dismissive of that idea. It is intended to address that, as far as enforceable actions go (for example, deletions of those kind of answers or something like that), it is best and consistent in the grand scheme of things to leave those answers to be judged as per the votes criteria alone (which directly judges usefulness, or not, of an answer). $\endgroup$ – Aloizio Macedo Sep 21 '18 at 8:03

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