I've seen a lot of questions on Mathematics Stack Exchange where none of the answers have been accepted. I think that sometimes people are unaware of what assumptions they are implicitly assuming, and cannot be taught how to make it clear what their question is. I believe that sometimes when somebody can't get an answer that solves their problem, they can be nudged to resolve their confusion all on their own because that's what they're interested in doing now that they could not get an answer that resolved their problem. Only after they solve the problem themself will they have a real feel for what they were missing earlier. Another person's answer explaining what they are missing may not always give them a real understanding at first. I believe that sometimes when somebody derives a contradiction, it gets them to learn how to think of things another way and come up with an explanation of how their past assumptions could be false.

I think it's a win win. Sometimes the person who had the question might easily get nudged into solving the problem themself becuasue they have their own personal interest in coming up with a solution and thinking of an explanation. Once they already came up with the explanation, they might want to write it down in an answer and explain what their confusion was and their resolution to it. This in turn will provide valuable information to some of those who read some of those answers. They will learn what types of confusion people tend to have and how they resolved their confusion. Researchers could then use that information to research how to educate people if they wanted to.

You may think this isn't a very good question because it's about whether we should do something. It may be worth considering taking the time to figure out your opinion on the matter and write it in an answer because there is another already existing Stack Exchange question https://matheducators.stackexchange.com/questions/11813/should-we-program-calculus-students-like-the-physicists-seem-to-want-us-to about whether we should do something. It may be worth considering allowing some questions of that sort because some people may be happily willing to put up the effort of researching their opinion on that matter and writing an answer that expresses it.

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    $\begingroup$ If a person posted a question long ago, and you want to encourage that person to post an answer if, in the meantime, he or she has come up with a solution, you are going to need some way to find out whether that person has managed to solve the problem. How are you going to do that? Are you going to leave comments on 10,000 old unanswered questions, asking whether OP has managed to solve the problem? Do you think OP will remember whether he/she managed to solve some homework problem from a class he/she took years ago? Do you think he/she will even see your comment? $\endgroup$ – Gerry Myerson Feb 26 '20 at 5:46
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    $\begingroup$ To answer the question in the title: it's already encouraged here. I share Gerry Myerson's view that it would be useless to encourage more. $\endgroup$ – Jean-Claude Arbaut Feb 26 '20 at 5:54
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    $\begingroup$ I don't think there's any harm in dropping a comment to this effect, and so there's nothing really wrong with the suggestion, although I agree with the observations above that it may have limited success. It's a good idea but it doesn't have to be a widespread policy. $\endgroup$ – rschwieb Feb 26 '20 at 17:01
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    $\begingroup$ @rschwieb I see what you mean. Maybe they don't feel like doing it and might not like being told to so it. However, if everyone just happened to naturally have a different way of thinking where they take everything anyone ever says as a suggestion and not an order, we could just post it as a Mathematics Stack Exchange help page with no problem. Then they would feel free to do what ever they feel like doing and completely make their own decision and like looking at that page in case it helps them figure out how to do a better job of what they want to do. Then after enough time, they may be like $\endgroup$ – Timothy Feb 26 '20 at 17:08
  • $\begingroup$ "You know what, I like that idea, I'm going to follow it." I am only aware of that issue occurring in Mathematics Stack Exchange in such a way that my suggestion is a potential solution. I am not aware of it occurring in any other Stack Exchange website. That's why I asked in on Mathematics Meta Stack Exchange. It seems to me that it should be almost exclusively in Mathematics Stack Exchange that somebody asks a question based on a result being counterintuitive. $\endgroup$ – Timothy Feb 26 '20 at 17:12
  • $\begingroup$ Here is one such question: math.stackexchange.com/questions/779097/… :) $\endgroup$ – Moishe Kohan Feb 26 '20 at 17:13
  • $\begingroup$ @MoisheKohan That's actually my own question. I guess it's not quite a coincidence. I guess the fact that I wrote "counterintuitive" in that question was a sign that I was more likely to be the type of person who would write "counterintuitive" in a comment here. I'm talking about questions like math.stackexchange.com/questions/204632/the-concept-of-infinity and math.stackexchange.com/questions/885329/…. That question of mine is different. There, I had already figured out that the counterintuitive was $\endgroup$ – Timothy Feb 26 '20 at 17:24
  • $\begingroup$ possible and figured it was a very complex problem to determine the answer. Also, I feel that the accepted answer to math.stackexchange.com/questions/204632/the-concept-of-infinity gives very valuable information to the mathematical community. The fact that the answer was written the way it was and got accepted gives us some insight into what confusion people tend to have and how to explain things to them in a way that they will understand. $\endgroup$ – Timothy Feb 26 '20 at 17:27
  • $\begingroup$ Sometimes I see a question on Mathematics Stack Exchange where none of the answers got accepted. I'm not looking for problems. Since none of the answers got accepted, decided to read them to see if I could figure out why. For some of them, it seemed like since none of the answerers had the same confusion as the OP, they didn't know how to figure out and address the confusion of the OP. I felt like maybe I could figure out what the OP is really confused about. That's what I was trying to do for the question at $\endgroup$ – Timothy Feb 27 '20 at 0:18
  • $\begingroup$ math.stackexchange.com/questions/2106003/…. Then my answer got a score of -2. That's kind of annoying. I don't know how other users think. I only know how I think. I have no choice but to refer to my own answer. $\endgroup$ – Timothy Feb 27 '20 at 0:20
  • $\begingroup$ Many, probably most, of the Comments I post are trying to "figure out what the OP is really confused about" or (to put it more charitably) where their challenge lies. In some cases the OP omits the motivation for asking, so Readers have to guess at what kind of answer would be edifying. But this information is best supplied as an edit to the Question rather than as an Answer post. $\endgroup$ – hardmath Feb 27 '20 at 13:48
  • $\begingroup$ @hardmath Once when I was 25, I thought I figured out a proof that I can think of a way to generate an uncomputable number. I kept checking it over and over again and again and still coming up with the conclusion that it is possible to. Two years later, I finally caught my own mistake. I believe it's to do with the fact that if you extend number theory using all theory intuitive assumptions and rules of inference, you get a system where you can assert that everything that's provable is true but any statement you can prove in the system, you can also prove the provability of in the system. I $\endgroup$ – Timothy Feb 27 '20 at 18:37
  • $\begingroup$ believe the system is strong enough to be inconsistent. Because I once had that question myself, I thought about it more even after I caught my mistake and was once thinking how in theory, a kid might come up with the same incorrect conclusion as I had before. I now think I might eventually have the ability to resolve their confusion by explaining how it's a circular argument and they're introducing a circular definition of something. Or maybe I could derive a contradiction from certain intuitive assumptions. $\endgroup$ – Timothy Feb 27 '20 at 18:43

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