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I would like to propose an informal side room the mathematics forum maybe called "Mathematics_SideRoom" or "Mathematics_Informal" or "Mathematics_Opinion" or "Mathematics_Discussion" or Mathematics_ChitChat" to fill the gap between the formal Mathematics forum and the Mathematics LiveChat forum. Users that have a question that doesn't quite fit the strict guidelines for the Mathematics forum due to being unable or unwilling to show their attempts at a solution or the question is somewhat subjective, are forced to find and join other websites outside of StackExchange. I understand that this might seem like a duplication of the live chat side forum but it is not. The live chat is a bit too chaotic with questions mixed in with replies to different questions and limited latency with messages disappearing after 2 hours.

The intention is that the sideroom should remain a subclass of the main Mathematics forum so for example, when a user replies to a question or leaves a thread in the sideroom, they are automatically defaulted back the main forum. If their are any reputation points for up and down votes in the sideroom, they should be a small fraction of the reputation points that would be gained in the main forum.

The sideroom is not intended to be a complete chaotic "free for all" Their should still be rules for questions. Eq questions should still be about a mathematical question but the user should not be penalised for a mathematical question not being objective enough or requiring opinion based discussions. Questions like "What is your favorite way of solving quadratic equations?" or "What do you think of this mathematical method or proof?" or "Looking for suggestions on how to improve the mathematical curriculum in my class" would be allowed.

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    $\begingroup$ Over on Physics there is the Problem Solving Strategies chat room, supported mainly by one long-time user. Set a similar one up for math and invite folks over to it. $\endgroup$
    – Jon Custer
    Oct 14 at 15:41
  • $\begingroup$ @ Augusto There is the precedent that the live chat sub forum is not a strict one question - one answer Q&A forum. The proposed sub forum is not a Stack Exchange forum site in the normal sense but a auxiliary side forum to a main forum, a bit like live chat. $\endgroup$
    – KDP
    Oct 14 at 15:43
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    $\begingroup$ So just open a chat room and maintain it. You need not authorization to open a chat room, just make sure you have enough rep points for it on the site in question. $\endgroup$
    – Augusto Vasques
    Oct 14 at 16:47
  • $\begingroup$ *Stack Exchange, not StackExchange (the last section) $\endgroup$
    – Peter Mortensen
    Oct 16 at 1:39
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    $\begingroup$ If you mean a chatroom, the tag (chat) would be suitable room. You could also have a look at various rooms mentioned here: List of chatrooms. And at other rooms associated with site. $\endgroup$
    – Martin Sleziak
    Oct 16 at 10:25
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    $\begingroup$ @AugustoVasques Strictly speaking, the OP cannot actually create a new chatroom - that privilege requires at least 100 reputation points. $\endgroup$
    – Martin Sleziak
    Oct 16 at 10:26
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    $\begingroup$ @MartinSleziak ... "that privilege requires at least 100 reputation points." Interesting: Someone proposing things for the site who has been here for only 9 days. $\endgroup$
    – GEdgar
    Oct 16 at 14:18

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I can understand your frustration with the unstructured format of chatrooms with respect to keeping track of a topic. Although replies are chained together, it does not provide the Q&A format of StackExchange communities (by design).

If you were sufficiently motivated to start your own StackExchange adjacent forum, I would recommend looking into the Teams concept. See the link "Create free Team" along the left margin of the desktop version of this page.

It would involve quite a bit of work on your part, and certain limitations to the functionality you are familiar with here. You will for example need to recruit participants willing to share an email address with you, in order to enroll them in your Team (giving them access to your "Teams for Stackoverlow" private community).

The functionality is roughly the same as on generic StackExchange sites. There is voting up/down to furnish reputation points. However there is a limit to the number of team members you can involve ("up to 50 teammates" but this can be overcome by converting one of several paid plans). Also there is no MathJax support, although $\LaTeX$ formatting can be achieved by starting ChatJax on a page. See robjohn's post for more information.

In short you should not expect the StackExchange powers-that-be to do this work for you. Really only you know at this point what your vision is for a "side room", and it would bear some exploration by you to see if it can gain participation by others.

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