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I followed with much interest the recent discussions on Meta about the community being perceived as unwelcoming to outsiders and the importance of looking for solutions (if any).

In order to do this, in my opinion we should first ask ourselves what is our idea of the scope and mission that MO should accomplish. I see (at least) three answers, that are not mutually exclusive:

  1. MO should be a help-desk for "professional mathematicians" (in a broad sense) regarding their study and research activity.
  2. MO should be a wikipedia-like repository of good mathematical questions and good mathematical answers, at a "research level" (in a broad sense).
  3. MO should be considered as an entertaining game, where mathematical knowledge is used to engage in some kind of stimulating intellectual competition (in a healthy sense), and reputation has the role played by the score in a chess tournament.

It seems to me that the corrective actions to implement in order to solve the "perception problem" depend in a non-trivial way on the importance that we give to $(1)$, $(2)$, $(3)$, and possibly to some other scope that at the moment I do not see.

So let me ask this (very) opinion-based, foundational question:

Question. What should be, in 2021, the primary scope and mission of MO?

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    $\begingroup$ This reads like a very loaded question "reputation sucks, am I right?". Could you please edit it so that you are not actively trying to suggest an answer, if the one in your last line really is your question? $\endgroup$ Jan 9 at 9:59
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    $\begingroup$ How can you read this from the question? I may be wrong, but its formulation seems to me completely neutral regarding reputation. And what answer am I suggesting? $\endgroup$ Jan 9 at 9:59
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    $\begingroup$ First of all, you start off with a long premise instead of just asking the question Then, you suggest two answers that are very broad goals and one that is way more narrow, in way that suggests a contrast between them, and you suggest that ranking them in order of importance is the key to answer. Anyhow, we can see what other people think, based on which comments they upvote. $\endgroup$ Jan 9 at 10:05
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    $\begingroup$ The premise is just to say that if you want to solve a (perceived?) problem, the first thing to do is to understand where you really want to go. "Narrow" is a matter of opinion, I do not think that entertainment is necessarily "narrow", after all many good mathematicians like mathematical puzzles and mathematical competitions, and IMO are considered an important event in our community. The three goals are just the ones that come to my mind, I am not really talking about "ranking them". I will delete "order of importance", leaving only "importance" to be more clear about this. $\endgroup$ Jan 9 at 10:12
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    $\begingroup$ @Federico Maybe you could be more constructive and say what you think the goals are. It is typical to write some initial thoughts and hypotheses in a question. $\endgroup$ Jan 9 at 12:37
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    $\begingroup$ I'm not sure the word "addictive" is that positive, but I'd say it should be viewed as entertaining (and I view it as entertaining, otherwise I wouldn't spend time here). $\endgroup$
    – YCor
    Jan 9 at 14:10
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    $\begingroup$ FWIW I am in favour of the parenthetical comments, because we are dealing with ill-defined concepts and some qualification is necessary $\endgroup$
    – Yemon Choi
    Jan 9 at 15:29
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    $\begingroup$ I put the quote mark and the parenthetical remarks because we had many sensible discussions in the past about what meaning we should do to the terms "professional mathematician" and "research level question", see for example meta.mathoverflow.net/questions/1654/… regarding the first one and meta.mathoverflow.net/questions/1024/… regarding the second one. $\endgroup$ Jan 9 at 18:01
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    $\begingroup$ What's missing in the three options for me is: learning. Posing questions to learn about some math concept (not because your research is stuck). Answering carefully to help others learn. Reading questions and answers to broaden your understanding of aspects of mathematics. $\endgroup$ Jan 9 at 18:54
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    $\begingroup$ I suppose that long-time MO users might remember some older discussions with related topics either here or on tea. I was able to find this one: What MO is for and what is your aim in participation? (December 2013) $\endgroup$ Jan 10 at 5:37
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    $\begingroup$ In case somebody wants to have a look at similar discussions on Mathematics Meta, there are, for example: Dissonance of purpose: What kind of site should MU be? (July 2010), What is the purpose of math.se; to learn to provide nice answers or just to get them? (January 2011) or What is the purpose of this site? (November 2015). $\endgroup$ Jan 10 at 5:37
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    $\begingroup$ @MartinSleziak: Wow that "dissonance" link is quite a flashback to how incredibly toxic Harry was over there until he finally got a huge ban. $\endgroup$ Jan 10 at 20:26
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    $\begingroup$ @NoahSnyder: I would be grateful if you could delete your last comment. It is ad hominem, inflammatory and unrelated to this discussion. $\endgroup$ Jan 12 at 7:16
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    $\begingroup$ I agree most strongly with 1 above. I think one reason why MathOverflow works so well is that many questions that arise in maths research are hard for most, but somewhat easy for at least one person. Finding this 'one person' is a problem brilliantly solved by MO. As a corollary, we should be tolerant of people that ask apparently basic questions, when they truly arise in research. (In this spirit, I have sometimes asked such questions, and had helpful replies, and I'm often been pleasantly surprised how much reputation I've got from answers that to me are quite basic.) $\endgroup$ Jan 12 at 15:57
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    $\begingroup$ "Score in a chess tournament" doesn't feel like a very close fit to MO reputation (and/or badges). Maybe something like bridge master points -- which unlike chess ratings are in part a measure of how much one plays in official tournaments? An extreme example: the late John Tate <mathoverflow.net/users/9848/john-tate> answered precisely one question here, which was enough to earn 1536 points ($2^9 3$ as it happens) and half of his 14 badges. There are 1000+ MO members with more reputation points, but very few are in Tate's mathematical league. $\endgroup$ Jan 16 at 4:19
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If I may add another purpose, it would be connecting mathematicians wordlwide. It is the first time in history that mathematicians from all over the world are able to discuss in a sort of a giant tea room, where they can ask questions to colleagues in an informal way, learn some curiosity and stay up to date with fields outside their current research. This is especially valuable for me, since I have been outside the official mathematical community for about 10 years now, and I guess that there are many other people in the same situation.

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  • $\begingroup$ Good answer. But perhaps this is somehow included in scope 1, right? $\endgroup$ Jan 11 at 9:54
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    $\begingroup$ Not really. To me, a help desk evokes the following situation. I am stuck on something I am not very familiar with, so I ask for help on that topic. But there is much more that one discusses in a tea room: new ideas, puzzles, concepts from a completely different subfield... $\endgroup$ Jan 11 at 9:57
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Can "Having some fun while learning some math (at the PhD level) together" be it? I bet many regular users would have that in mind when they think about MO. And it's not like we are asking for millions of dollars from the government to maintain this little corner of the internet. Most of my collaborators (over 40 at this point) are not on MO, and they would just be amused when I told them something MO-related.

PS: since you mentioned 2021, shouldn't we be thinking more about things like, um, future of (wo)mankind? (-:

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    $\begingroup$ Humankind. ( ◠‿◠ ) $\endgroup$ Jan 10 at 8:44
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    $\begingroup$ I feel MO is less fun that it used to be, but it seems like it's for a bunch of different reasons, not all to do with MO. $\endgroup$ Jan 10 at 23:31
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    $\begingroup$ @DavidRoberts, may be it's us, I noticed many other things that are less fun than when I was younger. $\endgroup$ Jan 11 at 0:31
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    $\begingroup$ I think MO started as a game, and our behaviour here was funny and light-hearted. Now we are considering it very seriously, as shown by all the discussions we had in these days. Looking at some of the comments, I'm afraid that the amusement is over. Perhaps this is just as life goes. $\endgroup$ Jan 11 at 6:45
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    $\begingroup$ Let me provide a silly example. In the (very) old days, I remember there was a question like "Solve this integral! I need it now", and I commented something like "Hoover my living room". Of course it was a joke ("bring your humour with you"), just to make evident how annoying an imperative request can be. Nowadays, I would never make such a joke: someone could take a screenshot, post it on Twitter or Facebook and I would spend two days explaining that it was not my intention to use my privileges of male white professor to make a student cleaning my house. Nowadays, I just close the question. $\endgroup$ Jan 11 at 8:39
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    $\begingroup$ @FrancescoPolizzi Likewise, I have a vague memory of responding to someone's rather vague question of how something should be done by saying "with great vengeance and furious anger", which is the kind of silly geekery I indulge in among friends or in "casual online mode" but is not the response I would give to, say, a student in one of my classes $\endgroup$
    – Yemon Choi
    Jan 13 at 19:52
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    $\begingroup$ @DavidRoberts I think we may be experiencing something similar to what (I imagine) facebook went through in the early days; initially it was a fun little thing between friends, both useful and amusing, and now it's a platform powerful enough to help stage coup attempts and radicalize nations. MO isn't quite there yet, but as its prominence grows so does a need for more serious introspection and potential correction. As spiderman put it, 'with great power comes great responsibility'. $\endgroup$
    – Alec Rhea
    Jan 15 at 11:01
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I would say that the MO splash screen: answers the question: "We're working together to build a library of detailed answers to every question about research level mathematics." --- so this is #2 on the list.

"Building a library of answers" is the scope and mission of StackExchange. I don't think any other answer to the question in the OP is possible within the constraints of that platform.

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  • $\begingroup$ Goal 1 is kinda there in service of goal 2 though. $\endgroup$ Jan 9 at 13:41
  • $\begingroup$ true, but I guess that goal 2 serves many purposes, and also caters to an audience of users who are not "professional mathematicians"; for some users goal 3 would be the motivation to participate --- we don't want to constrain users in how they make use of the platform, do we? $\endgroup$ Jan 9 at 13:48
  • $\begingroup$ No, of course not. I was just saying that people who use the site for goal 1 (probably the majority of people who are asking questions) still help the accomplishment of goal 2. That's all =]. $\endgroup$ Jan 9 at 13:50
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    $\begingroup$ For what it's worth my own personal use of MathOverflow, both as questioner and as answerer, has always been driven by #1 on the list, which is probably why I am not active on other SE sites $\endgroup$
    – Yemon Choi
    Jan 9 at 15:28
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    $\begingroup$ Despite the prominence of that quote, I don't think it describes MathOverflow well. That paragraph begins by saying "MathOverflow is a question and answer site for professional mathematicians", which I find more descriptive and closer to #1. $\endgroup$
    – Matt F.
    Jan 9 at 23:36

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