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One convenient thing on AoPS that is missing on MO is the private message system where you can send and receive private messages to other users without figuring out who they are outside the internet and what is their e-mail, etc., or full disclosure of who you are yourself. The situations where you want to discuss something with some particular user or attract their attention to something in private are numerous enough, IMHO. Usually, we carry out such communication in comments, where it may be quite out of place (say, if X tries to attract Y's attention to an old thread A by posting such request in some active thread B in which Y is participating, or asks if Y would like to be a co-author or something else that can hardly be classified as "a topic of wide general interest").

I just wonder whether there is enough support to request such a feature within StackExchange (or, perhaps, to implement it using some other available platform and linking the accounts). If you just want to support/oppose the idea, without commenting on it, vote up/down but, of course, I would be interested in seeing all "pro" and "contra" arguments and possible alternatives as well.

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    $\begingroup$ Put a link to your homepage on your user profile and then people can email you if they want to get in contact privately. $\endgroup$ – Noah Snyder Aug 21 '13 at 13:58
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    $\begingroup$ That would work only if I wanted to add MO mail to my already cluttered inbox or if I wanted to set up one more "left" e-mail account (neither of which is the case). It also doesn't solve the problem if it is I who wants to start the communication or if I prefer to separate my MO identity from my other ones (even if some people here know me outside the web). The AoPS system makes the exchange easy by means of creating a private thread for two or more people where all the history can be viewed in one click. Besides, have you ever tried to send or to read an e-mail that is heavily $\LaTeX$-ed? $\endgroup$ – fedja Aug 21 '13 at 14:12
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    $\begingroup$ For messages and conversations that don't have to be private, chat is a useful substitute. You can invite other users into a chat room you created to discuss some issue. $\endgroup$ – Mad Scientist Aug 21 '13 at 17:27
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    $\begingroup$ It seems a bit orthogonal to what MathOverflow is trying to achieve, and I'm with Noah in thinking that email has solved this problem pretty well. $\endgroup$ – Scott Morrison Aug 22 '13 at 1:36
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    $\begingroup$ meta.SO: Any way to send a personal message to another user? It is tagged as status-declined. $\endgroup$ – Martin Sleziak Aug 24 '13 at 6:39
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    $\begingroup$ @ScottMorrison: could you expand a little bit on why it is orthogonal to what MO is trying to achieve? $\endgroup$ – Michael Bächtold Aug 24 '13 at 9:31
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    $\begingroup$ MathOverflow is trying to be a good place to get research questions answered (and, in order to make that happen, to be a enjoyable experience for people who like answering such questions), and secondarily to be a resource recording mathematical discussions that might usually be ephemeral. I just don't see re-implementing email or something like it as having much to do with those goals. $\endgroup$ – Scott Morrison Aug 27 '13 at 11:05
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I like it for the privacy aspect...I often try to get people with whom i have a problem to email me. Generally they don't, I've never been sure why. Two ingredients seem to be anonymity and the lure of playing to the crowd. But we have, for example, this thread from tea http://mathoverflow.tqft.net/discussion/1622/bounty-madness/ where Gerhard got really upset and F J had already mostly disappeared. As Francois said in closing the thread, "whatever happens next shouldn't happen here."

Found it: here is an MSE question https://math.stackexchange.com/questions/463046/sum-of-number-of-divisors-of-multiples-of-squares where some anonymous jerkoff wanted to continue the discussion in Chat. Which, for my money, is not a good place for a fight. It remains public, there is a public paper trail even if nobody notices for a few days. Just as important, chat is not a good place for discussing the really divisive feuds that go on, talking policy about some of the uglier things going on, just gossip in general.

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If you want to attract someone's attention to a comment of yours in a thread that's no longer active, you can page them using the syntax @fedja in a comment, without the need to pollute other threads. It will show up as a very visible notification on the upper left corner the next time they log in. If the user has email notifications enabled, they'll eventually get an email saying they have pending notifications in their inbox.

After establishing contact, you can interact in that comment thread, move to chat, or if you want more privacy move the discussion to email. If you want to initiate an email discussion without making your email public, once you have a live conversation on comments or chat, and if they agree to do so, you can provide your email in a comment and delete it after they have seen it.

Private messaging has been consistently declined across the Stack Exchange network, for a number of reasons:

The consistent response to this is that it's a bad idea, because:

  1. It could hide information from the community: useful information transmitted privately is unavailable to other readers, subverting the core purpose of the site.

  2. It could be used to harass other users ("Answer my question!", "Accept my answer!", "Yer momma so fat she overflows the stack!", etc...)

However, there is some value in being able to communicate with other users outside the context of a specific question or answer. This point was conceded with the implementation of a chat system: users on every Stack Exchange site can create and participate in chat rooms, integrated with the normal user accounts. There are still no truly private messages between users, but for those who want to chew the fat or discuss whatever outside the confines of the sites themselves, this can provide a viable solution.

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For normal users, the advice remains: if you want others to be able to contact you privately, add basic contact info to your profile's bio page.

While a private messaging system appears particularly helpful to Math Overflow - which is not as essentially a Q&A site as SO, and a bit more of a place to generally discuss research-level mathematics - I think it's not as useful as one might think. MO probably does have a lot more interaction and gives rise to a lot more off-site collaboration than other SE sites, but I don't see a strong incentive to keep it off the public record provided by the chat. If you want to collaborate on something that will give rise to a paper and keep some details private, you'll probably want to move to email soon anyway. If a discussion is getting ugly enough that you want it off the record, you should flag a moderator as soon as possible. (One course of action is then to have a moderated discussion to see if it can be resolved, and the moderator can later delete the chat.) If you just want to chew the fat in private, MO is probably not the place.

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    $\begingroup$ There was a kid on MSE, I gave a hint I felt was enough, then there were a half dozen comments of the "Answer my question!" variety. Certainly I disliked that. I had not really expected that would be the effect on MO, where questions are not primarily homework; but I suppose the potential is there. $\endgroup$ – Will Jagy Aug 25 '13 at 20:28
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    $\begingroup$ @WillJagy I don't really think it's an issue here, either, but I don't really see the need for it, either. $\endgroup$ – Emilio Pisanty Aug 26 '13 at 12:43
  • $\begingroup$ On the Stack Exchange side, on the other hand, developing such a system specifically for MO is hard and tantamount to developing that capability for all SE sites, which I can understand them being reluctant about. $\endgroup$ – Emilio Pisanty Aug 26 '13 at 12:44
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I see no need in a special private message system. Those people who don't mind receiving e-mails give their e-mail address in the profile. (For example, I receive private messages from MO members from time to time, and send them when I need).

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