What is (and what should be) the purpose of math.SE?
As far as I can say, various users have different views on this question.
- Some users view it as a repository of knowledge.
- Some users approach it as teaching opportunity.
- Similar to previous, but slightly different: It could be understood as some kind of help center for mathematical problems.
- Some people might view it simply as a competition among the users.
- There are probably many other possible different viewpoints. (Which might differ drastically or only in minor details.)
Various views are not mutually exclusive. For example, gamification is definitely an important part of the SE architecture. And even if reputation and badges should not be the main reason why some users come here, if they help to reinforce good use of the site (for example, if they incentivize users to ask good questions and write good answers), then that is fine. Similarly, if somebody comes here mainly because they like to teach mathematics and they strive to give very accessible and clear explanation in each of their answers, that also helps creating a repository of useful mathematical facts. But on some occasions there are clashes between users who have different views about what this site is/should be. Somewhat related point was mentioned also in this answer the the recent post: What do you think is the largest problem facing Math.SE today (July 2015)?
The view on what the purpose of the site is affect many things: What type of questions should be allowed? Which posts should I upvote? Which posts should be closed/deleted? To which extent is it ok to edit other people's questions? Is it ok to ask question simply because it adds some potentially useful contents rather than because it is a problem I have actually encountered? Which features could improve functionality of the site? And we could list here probably many other things.
The intention of this thread is not trying to find some kind of consensus among different (possibly conflicting) approaches to this site. I think that simply knowing how various users view this site could be useful. And I believe that meta is a good place where various opinions on this matter could be collected.
It is very likely that these issues have been discussed before on meta. (If not in a question devoted solely to this issue then in some comments.) If there is an exact duplicate and I simply did not notice it, perhaps this question can be closed. But we should keep in mind that this site evolves and the viewpoints might have changed since the past discussions.
I have found this older question which, however, seems to have a bit different focus: What is the purpose of math.se; to learn to provide nice answers or just to get them? (The OP asks about this in connection with the problem whether it is ok to post answer which is similar to the previous answer. And the main stress seems to be on difference between posting answer as somebody in order to teach somebody something and posting answer with the intention that I learn something while working on the answer.)
I have also found this post: Dissonance of purpose: What kind of site should MU be? Already from the number (id) of the post, you can see that it is from beginnings of the site. So I thinks that the positions might have changed since then.