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On more than one occasion, always with an explicit disclaimer, I have posted a comment of more than 600 characters as an "answer". I have done this because I have quite often seen other people do it, and I have never once, in 5 years in Maths.SE, seen anyone object to the practice. But a comment I posted in this way last night has been deleted. The reason given was "low quality". (I have undeleted it, but I have no idea if that action will remain in effect for long.)

Has there been a change in policy?

Or is there some other reason why this comment in particular was singled out for deletion? Is it perhaps connected with there having been a truly extraordinary comment thread on the question? The thread - including the first comment, which had nothing to do with the very strange dispute that suddenly erupted - was deleted in its entirety, not even moved to chat (as I had requested, in order to mitigate the extreme distraction from the question that had been asked). That is something else that I have never seen happen in my 5 years in Maths.SE, and this coincidence seems highly unlikely to be accidental.

Timeline for answer to Is the sequence $(B_n)_{n \in \Bbb{N}}$ unbounded, where $B_n := \sum_{k=1}^n\mathrm{sgn}(\sin(k))$? by Calum Gilhooley - Mathematics Stack Exchange.

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    $\begingroup$ I mean, if the long comment is full of profanity, definitely not. If the long comment is relevant, and helpful, then maybe. It's more of a case-by-case situation. I don't think we want a "catch all" policy here. $\endgroup$
    – Asaf Karagila Mod
    Jun 30, 2020 at 7:44
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    $\begingroup$ Personal I find those data very confusing. We are asking if $B_n$ is unbounded, but your data seems to be arguing that there are sub-sequence $B_{n_k}$ so that $B_{n_k}$ is bounded? Sorry but I don't see how your data could help answer the question. At least there is no explanations. $\endgroup$
    – Arctic Char
    Jun 30, 2020 at 10:09
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    $\begingroup$ To those upvoting @ArcticChar's comment: I have already answered it in a stopgap comment on my disputed answer-cum-comment. [No, that was not a profanity, that was Latin. $\ \ddot\smile\ $ . Although on second thoughts it should probably have been qua.] That is the proper place for discussing it. It seems odd that no-one who cares so much about the proper answering of a mathematical question that they want to delete my improper answer has bothered to comment on either the question or my "answer". Curiouser and curiouser. $\endgroup$
    – Calum Gilhooley
    Jun 30, 2020 at 13:14
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    $\begingroup$ @Calum If you want to comment in an answer field, due to the length of the comment, and you straight-out say, "Not an answer", then please mark your comment "community wiki", so you don't get rep for any upvotes, just like any comment does not earn rep for comment upvotes. $\endgroup$
    – amWhy
    Jun 30, 2020 at 13:17
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    $\begingroup$ I don't think the practice of commenting in an answer field was every strictly okay. Just like answering PSQ's is controversial. Just because you've seen others do it, and did it yourself, doesn't make it always okay to do. So your premise "Is it no longer okay to ...", leads me to say "it hasn't been entirely okay for a long, long time". Just because people do X, doesn't make doing X right. All you see is what remains. You don't see the tons of answers already deleted for doing what you misread as "okay". $\endgroup$
    – amWhy
    Jun 30, 2020 at 15:31
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    $\begingroup$ This seems to be a case that somehow got out of control (one user even got suspended). My own take is that the joy of math should be able to offset other emotions which have come into play here. People involved here are far more mature (in terms of experience and academic knowledge) than me and they should be able to observe that the question on main site and its answers were posted in good faith. IMHO the question is one which has a fairly simple statement but no easy answer (maybe an open problem). A cross posting on MO should help. $\endgroup$
    – Paramanand Singh Mod
    Jul 2, 2020 at 3:12
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    $\begingroup$ @ParamanandSingh It was heartening to read your comment, but I think it would be only fair to wait until after mathworker21 has returned from his suspension before considering cross-posting to MO. $\endgroup$
    – Calum Gilhooley
    Jul 2, 2020 at 7:25
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    $\begingroup$ Yeah we should definitely wait before cross posting on MO. Mathworker21 answer is already a great start and who knows the bounty placed may motivate others to attack the problem. But I do feel saddened by whatever happened in this case. Much worse than what happened in recent past in meta thread dealing with my actions (vote to close and answer a question simultaneously). $\endgroup$
    – Paramanand Singh Mod
    Jul 2, 2020 at 9:35
  • $\begingroup$ Is this post the reason this account is suspended temporarily? Stack Exchange strikes again! $\endgroup$
    – user307169
    Jul 6, 2020 at 21:14
  • $\begingroup$ @tilper It is generally not safe to make assumptions about the reasons that moderators have suspended accounts, particularly when you do not have access to the full record. By the way, there are, by my count, three accounts which were temporarily suspended in relation to this post. $\endgroup$
    – Xander Henderson Mod
    Jul 7, 2020 at 0:43
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    $\begingroup$ @tilper: I don't think suspensions are due to this post, but they are perhaps due to some heated discussions in comments (which may have been deleted as well so I can't confirm). $\endgroup$
    – Paramanand Singh Mod
    Jul 7, 2020 at 1:53
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    $\begingroup$ @XanderHenderson: This also shows the gravity of the problem here. Discussions related to this post seem to have to gone to such a level where mods were forced to suspend 3 users to let them cool down. I don't know how mods might be feeling in such a situation. $\endgroup$
    – Paramanand Singh Mod
    Jul 7, 2020 at 1:58

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In the spirit of the question: This started life as more of an extended comment than an answer. I think it has morphed into an answer now though.

Math.SE seems to be based around the idea that every problem is soluble by a single person. This is clearly not the case, as, for example, in research mathematics single-authored papers are the exception rather than the normal. Providing an incomplete answer, for example by proving that the result does not hold for a large number of cases, or verifying that it does hold in many cases, should therefore not be discouraged (especially for hard questions); it may lead someone else to solving the problem, which is how collaboration works. This all requires effort and thought, and readers should be allowed to decide, in the usual way, whether or not the author should receive reputation for this partial answer; therefore, such answers should not be automatically made community wikis.

I see no reason why providing data, found via computation and confirming the result for a sufficiently large number of cases, does not fall under the above paragraph, provided it comes with supporting explanations. Computational results of this nature can be useful. Indeed, the journal Experimental Mathematics is essentially devoted to computation-led research. The Ternary Goldbach Conjecture is a concrete result which relied on this sort of explicit computation. It's proof proceeded in two steps: 1) prove the result for all numbers bigger than a certain, known number $n$, and 2) use a computer to verify the result for all numbers less than $n$.

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    $\begingroup$ Math.se does not purport to be research level math. As you stated, you are aware that "Math.SE seems to be based around the idea that every problem is soluble by a single person. " $\endgroup$
    – amWhy
    Jun 30, 2020 at 14:18
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    $\begingroup$ @amWhy to be fair, I think MSE does not purport to not be research-level math either, as it is meant "for people studying math at any level". $\endgroup$
    – Theoretical Economist
    Jun 30, 2020 at 16:20
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    $\begingroup$ @TheoreticalEconomist I think the point amWhy wanted to convey is that not every type of question is a good fit for the format. One might phrase it as saying the site is not for engaging in mathematical research (on the site). $\endgroup$
    – quid Mod
    Jun 30, 2020 at 17:48
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    $\begingroup$ @user1720 SE is not "based around the idea that every problem is soluble by a single person"; what is true though is that SE does not pretend to be suitable for every type of mathematical inquiry, only those that fit into the format, which arguably can be paraphrased as can be answered by a single person in a few paragraphs. This is a healthy self-limitation. $\endgroup$
    – quid Mod
    Jun 30, 2020 at 17:50
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    $\begingroup$ @quid Thanks for the clarification. While I do agree that the site is designed with the expectation that answers have to have some sense of definitiveness to them (hence open-ended and opinion-based questions are off-topic), I do think there is value in partial answers that build towards a definitive one. Of course, as you say, just because it has value doesn’t mean it belongs here, but my feeling is that maybe it should. Admittedly, I don’t know how much room there is for opinion on this matter, so maybe my thoughts on this are moot. $\endgroup$
    – Theoretical Economist
    Jun 30, 2020 at 18:03
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    $\begingroup$ @TheoreticalEconomist partial answers are actually alright. $\endgroup$
    – quid Mod
    Jun 30, 2020 at 18:14
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    $\begingroup$ @quid I fear we might differ on what qualifies as a partial answer then :) $\endgroup$
    – Theoretical Economist
    Jun 30, 2020 at 18:16
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    $\begingroup$ You say that Math SE is "based around the idea that every problem is soluble by a single person." I don't think that is quite right. Rather, Math SE is built to answer only certain kinds of questions. The questions that are most appropriate for Math SE are those which have authoritative answers, which can typically be provided by a single user in a couple of paragraphs. There are tons of good questions in the world which would, nevertheless, be poor questions here, because they don't fit the format. $\endgroup$
    – Xander Henderson Mod
    Jun 30, 2020 at 19:06
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    $\begingroup$ @XanderHenderson I don't know if what you're saying is true, i.e. if MSE is only for those types of questions, but I really, really, really hope it isn't. I think collaborating with others on difficult questions is very fun, and this website is a great place to do it. $\endgroup$
    – mathworker21
    Jul 1, 2020 at 6:31
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    $\begingroup$ @XanderHenderson You have put your finger on the problem, as you also did in the GENTLE chatroom on my one visit there. (It's not very active, so no-one should have any difficulty in finding our discussion, but I'll try to work out how to post a reference.) I'll briefly state my own opposing view (but this should really be for a separate Meta question): the key is objectivity of questions, not prediction in advance of their answerability. (Of course, if it is evident in advance that a question is of research level, it does not fit.) That, or so I believe, is the consensus of the community. $\endgroup$
    – Calum Gilhooley
    Jul 2, 2020 at 7:00
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    $\begingroup$ For example, Jaeseop Ahn's first question, Alternating Harmonic Series Spin-off, might have been a research level question (like the convergence of the Flint Hills Series), for all that anybody knew at the time, but @mathworker21 provided a fully satisfactory answer to it. Must the status of a question's belonging or not belonging to this community be in a state of perpetual oscillation and suspension, according to the present state of work on it? Or can we have a bit more stability than that? $\endgroup$
    – Calum Gilhooley
    Jul 2, 2020 at 7:14
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    $\begingroup$ @CalumGilhooley : While we are discussing whether the questions are fit for MSE or MO, the MO people seem to be more lenient and often give good answers to well posed questions which are clearly not research level. But this is based on my far limited experience on MO. $\endgroup$
    – Paramanand Singh Mod
    Jul 2, 2020 at 9:49
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    $\begingroup$ @ParamanandSingh please don't encourage people to post non-research questions to MathOverflow. While some users there may post answers to such questions, I think more users are quick to vote to close, and really don't want to see such questions. $\endgroup$
    – Gerry Myerson
    Jul 2, 2020 at 22:26
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    $\begingroup$ @GerryMyerson: Well, I was not trying to do that. If my comment is being seen even as a slight endorsement for such behavior then I feel sorry for the same. The right way to decide whether questions are fit or not is through the democratic process of voting and in general one should avoid meta trials and heated arguments and instead use the vote and don't be so emotional about it. $\endgroup$
    – Paramanand Singh Mod
    Jul 2, 2020 at 23:59
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    $\begingroup$ @quid: the goal in such meta discussions should be reach out to the other faction and opt for a happy compromise rather than ugly skirmish. If a question / answer gets closed / deleted there is always a way out to rectify it (improve it, add more stuff, post new question/answer) or to convince the other side $\endgroup$
    – Paramanand Singh Mod
    Jul 3, 2020 at 16:08
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First I must point out that this question is somewhat unclear. What do you mean by "post a comment of more than 600 characters (...)"? (Emphasis mine.) If "comment" means that I would post it in the comments below the question, but there is no space, then obviously this has never been OK. It is even somewhat self-contradictory, considering the role that comments have.

By the development of the discussion, I take it you mean by "comment" just that it is not a complete answer, and I'll assume this to be the case for my answer.

This is somewhat tricky. The short answer is: it depends on how useful the answer is.

The long answer is that in general, the network allows (and wants) answers to be useful and relevant. It is the case that in Mathematics those two are heavily correlated with correctness and completeness. So the "safest" way to make a useful answer is just to make a complete and correct answer. Others which usually can also be OK can be summarized in "partial" and "incomplete", and I'll clarify the distinction I make. (The way I use the terms may be nonstandard, which is why I'm clarifying.)

By "partial answers" I mean answers that solve a problem considering some simplifying hypotheses. For example, a question which asks "Is every foo a bar?" can have a useful answer "If the foo is also a xyzzy, then this holds because of (...)". How useful that is obviously depends on the question, on the restriction and the context, and will be evaluated by the community. (E.g., if someone asks "Is every continuous real function $f$ on $[0,1]$ integrable", then responding it with "Yes if we assume it to be constant" is obviously not useful. )

By "incomplete answers" I mean answers which make significant progress towards a solution but do not quite manage to close it up. Again, how useful that is will depend on the question, the context and will be evaluated by the community.

Those kinds of answers can be OK. Again, it depends and will be evaluated by the community. As always, these evaluations can be contested by the community. Preferably, all this should happen in a reasonable way, no matter how outrageous one thinks something is.

If an "answer" is not any of those, then it will usually be the case that it is not even an answer. And answers should be answers. (I know this sounds facetious, but there is no simpler way to put it. There is a flag for something being "Not an answer" for a reason.) So it is most likely not OK to post "something" as an answer which is not a complete and correct answer, or a partial answer, or an incomplete answer. (There may be exceptions, but I cannot think of one.) For example, we frequently delete things posted as "answers" that are questions about other answers, or corrections about other answers etc.

Now, turning to the specific case of your answer. The first version of your answer is not a complete and correct answer, not a partial answer and not an incomplete answer. (As per what I defined above.) This already points to it being potentially not useful. But more specifically, it was just some computations. It is entirely reasonable to be considered not an answer, and as such, should have been flagged as such and elaborated upon or deleted. To be honest, I say this almost objectively.

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    $\begingroup$ For clarity, is this answer (a) representative of the moderating team's collective policy, (b) representative of your policy as a moderator (i.e. it indicates how you will moderate as an individual moderator), (c) the opinion of the moderating team, or (d) your opinion as an individual user / moderator? $\endgroup$
    – Xander Henderson Mod
    Jul 2, 2020 at 20:58
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    $\begingroup$ @Xander (b) and (d). $\endgroup$
    – Aloizio Macedo Mod
    Jul 2, 2020 at 21:01
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    $\begingroup$ I second this. I'd stress that it is possible to post two comments in case one is too short. There can be rare reasons why an answer-box is really needed for technical reasons in which case one may consider an exception; the current case is maybe close to that, but this should have been stressed more. $\endgroup$
    – quid Mod
    Jul 2, 2020 at 22:13
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    $\begingroup$ Thirded. It seems like this may also be (c). $\endgroup$
    – Alexander Gruber Mod
    Jul 3, 2020 at 14:56
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The answer box is meant for answers, not comments.

The Stack Exchange model is meant to facilitate the construction of a high-quality database of questions and authoritative answers. Stack Exchange is not a social networking site, nor is it a site for collaboration or discussion. On the Stack Exchange network, the "Answer" box is for answers. It is not meant for long comments.

It is suggested elsewhere that if an answer is really just a long comment, then it ought to be marked "Community Wiki", though it is worth noting that there is an implicit assumption here that "not an answers" are a problem, i.e. they should not be treated as normal answers (they should either be converted to comments, or marked CW). There was also an attempt to discuss this issue, but little discussion actually followed.

It may also be worthwhile to read through my question about whether or not it is acceptable to leave hints as answers. The consensus here appears to be that hints are fine, as long as they lead to an answer. The extended comments-as-answers under discussion here don't even rise to that level—the answerers themselves don't even know if their comments will lead to an answer.

My conclusion is that the consensus leans towards the following statement:

If your answer is really a long comment, then it shouldn't be posted as an answer. If you must post your long comment in an answer box, then you should, at the very least, (a) clearly note that the answer is not an answer, and (b) mark your "answer" Community Wiki.

I originally said that, in light of the above, it was appropriate to delete this answer (note that I am linking to a particular version of that answer). It was remarked by KReiser that this might have sounded harsh, which was not my intention, so let me try to rephrase: the original version of the answer consisted of a table of data, which was interesting, but didn't really answer the question. It very much was an extended comment. As such, I am sympathetic to the users who voted to delete it. An equally reasonable outcome (in my mind) would have been for the answerer to mark the answer as "Community Wiki". The best possible outcome would be for the answerer to expand their remarks, as they have done.

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    $\begingroup$ (-1)You seriously disapprove of people working together towards an answer, making partial contributions, which quite often and entirely naturally are too long to fit into 600 characters? I am of entirely the opposite opinion. I frequently upvote other people's partial answers or extended useful comments. It's all part of doing mathematics. It all works pretty well, even though it is not a perfect fit for a rigid Q&A format. Most people seem to appreciate these sentiments. And of course most of the time there is no need for long comments or partial answers. Which is great when it happens. $\endgroup$
    – Calum Gilhooley
    Jun 30, 2020 at 13:57
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    $\begingroup$ That's the intent of Community Wiki, Collaboration. $\endgroup$
    – amWhy
    Jun 30, 2020 at 17:10
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    $\begingroup$ @CalumGilhooley I have presented an answer which, to the best of my ability, reports the consensus of the community. The phrase "You seriously disapprove..." is an implicit attack against my sincerity and my desire to discuss this issue in good faith. I would be happy to discuss this, but I am not going to reply further to someone who accuses me of lying or otherwise misrepresenting my opinions. $\endgroup$
    – Xander Henderson Mod
    Jun 30, 2020 at 18:46
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    $\begingroup$ @XanderHenderson I have been careful not to engage with you, but I must ask you what you mean by "Stack Exchange is not a [...] site for collaboration [...]", which seemed, and still seems, clear and unambiguous (and extremely narrow, dogmatic, and overly rigid) to me. I must also insist that you desist from doing exactly what you and amWhy have accused me of doing. I have never once questioned your sincerity or good faith, or accused you of lying, or intentionally misrepresented your opinions. Meanwhile, you and amWhy have accused me of a string of character flaws. Pause and reflect. $\endgroup$
    – Calum Gilhooley
    Jul 2, 2020 at 6:24
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    $\begingroup$ I also think you are mistaken in your (evidently sincere) belief that your actions represent the consensus of the community. Rather, I think you are pushing one particular opinion, to an extreme degree (and you are encouraged in doing this, by amWhy in particular, and no doubt also by several others who broadly agree with you). Of course, I could also be mistaken in my own sincere belief. I'm not great at judging consensus. $\endgroup$
    – Calum Gilhooley
    Jul 2, 2020 at 6:46
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    $\begingroup$ @CalumGilhooley In just this comment thread, you have accused me of insincerity, narrow dogmatism, and being unable to think for myself. The worst that I have done is accuse you of being condescending, for which I apologized (and all of those comments have been deleted, anyway). I would be happy to engage with you, but not before you cease these personal attacks. $\endgroup$
    – Xander Henderson Mod
    Jul 2, 2020 at 18:42

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