I am playing with the Stack Exchange Data Explorer to compare some MathOverflow stats to arXiv stats. I was surprised to see, that in the last 4 years there was almost constant activity (measured by the number of questions). There is constant influx of new users (with a sharp step after joining the Stack Exchange network), but not many get a non-trivial reputation.

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  1. Is this data complete? (I am not familiar with the migration process from SE1 to SE2, so maybe lack of growth is only some kind of artifact.)

  2. If the data is complete, is it a sign on stagnation (i.e. we should worry, as it losses its impact OR it could reach a wider pool of people) or just saturation?

Remarks

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    Is that constant activity phenomenon visible for major tags? It would be interesting to see if there is a difference in trends between, say, PDEs and algebraic geometry. – Joonas Ilmavirta Mar 15 '15 at 1:29
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    @JoonasIlmavirta Yes, it is constant. Actually, it was my starting point - I wanted to see changes in tag usage, but discovered that it is almost flat (see this query: data.stackexchange.com/stackoverflow/query/284210/…). – Piotr Migdal Mar 15 '15 at 1:35
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    MO could be universal, but it's clearly not homogeneous, hence it can't be saturated. – Emil Jeřábek Mar 15 '15 at 11:36
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    There's been an increase in the number of off-topic questions after the migration, and these are typically unanswered. Do your answer-to-question ratios include closed questions? – Emil Jeřábek Mar 15 '15 at 11:42
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    @EmilJeřábek this is a relevant point, but there are less than 600 closed questions without answer, so about 1% of all questions (and less than 2500 closed questions in total so about 5%, some of them with very many answers) so that while this can have some effect I'd speculate it must be at least an order of magnitude smaller than what is reported. On the other hand, I find the 3.5 that is reported in itself misleading, as cutting of the first few month one is down to 2 or something like it. (Would deleted be included the situation were different, but I doubt that is the case.) – user9072 Mar 15 '15 at 13:47
  • I see, that makes sense. – Emil Jeřábek Mar 15 '15 at 14:22
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    Mathoverflow is also getting more and more picky with its topics. Many soft-question and big-list threads that were considered ok back in 2010 (and gathered massive amounts of upvotes) would probably be shot down today. The Math Educators site also reduced the audience of this site by creating a separated community. Neighboring disciplines such as statistics, computational science, physics, theoretical CS now have their own sites, too. I'm not saying all of these are bad things, but they are contributing factors. – Federico Poloni Mar 15 '15 at 16:19
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    all se sites have a temporal evolving dynamic aspect (apparently not well studied/ understood) where it appears, observationally/ anecdotally, (a) a lot of high rep users earn their rep earlier in site history & it becomes difficult for anyone to match them (b) site activity patterns shift over their lifetime eg gradual decrease in answers per question etc, votes, etc... what is desirable to "steer" for is a whole other question... fyi see also this excellent new se tag cloud graph/ analysis tool – vzn Mar 15 '15 at 16:50
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    @vzn: I'm pretty sure the OP was aware of your link, though it's nice of you to add it for others. :-) – cardinal Mar 15 '15 at 17:56
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    I would say that "the Math Educators site also reduced the audience of this site" is a belief and not a fact. It is plausible that some who lurked on MathOverflow stopped after MESE went beta, but that is a good thing as they found a forum on which they could do more than lurk. I suspect MathOverflow participation was affected but not decreased by MESE's arrival. I think a more telling statistic is participation in meta. If the core of committed users is declining, then MathOverflow has a serious problem. Gerhard "Easy: Make More Committed Members" Paseman, 2015.03.15 – Gerhard Paseman Mar 15 '15 at 21:11
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    I'm not meant to share the google analytics data in detail, but I can say that page views, while showing seasonal and weekly variation, are otherwise pretty close to constant since Day 1. – Scott Morrison Mar 15 '15 at 22:25
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    The average question score per month is also decreasing: data.stackexchange.com/mathoverflow/query/287159#graph. This isn't surprising: as the site grows, there are less eyeballs on each single question and less upvotes. Maybe the number of users that who only 1-2 reasonable questions in their lifetime is the same, but their overall reputation decreased. In other words, getting from the initial 101 to 200 in 2010 was as hard as getting to 150 now (in my opinion). – Federico Poloni Mar 16 '15 at 7:33
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    @FedericoPoloni: Since 2010 there were at least two changes -- firstly, the number of points per question upvote changed from 10 to 5, and secondly the association bonus was introduced with the move to MO 2.0. -- So what do you want to say with the numbers you give in the last sentence? – Stefan Kohl Mar 16 '15 at 9:54
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    @StefanKohl You are correct, I forgot about that. The fact that the average number of upvotes per question is decreasing is still true, but the picture of "how difficult is it to became a 200+ reputation user" is more complicated in view of this. – Federico Poloni Mar 16 '15 at 11:37
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    The reduction in points for question upvotes was applied retroactively, hence the statistics available in SEDE are computed as if it were 5 from MO’s inception. So it shouldn’t skew the results. – Emil Jeřábek Mar 16 '15 at 15:40

(If anyone thinks this would be better as a "comment", please move it...) This issue is something I've thought/worried about for some years. The most poignant "unhelpful" mechanism is that very-competent people can find "old" answers to questions related to their immediate question, and, thus, not ask a question. Meanwhile, relative-incompetents will not think of this, and/or will not succeed in doing it, and, thus, inevitably, ask the same old (and, necessarily, naive) questions.

The delicate issue in talking about more-or-less serious/research-level mathematics is that there is no trivial algorithm to distinguish "elementary" from "serious", so far as I know. Operationally, that essentially means that a person might feel obliged to look at many things ... that will prove to be silly/etc.

But, yes, after accumulating a corpus of apt answers to the (!) iconic questions, what next?

The "problem" is that, mostly, people ask the old questions over and over. :)

To my mind, the issue is about how to keep the site "lively", rather than as an archive of good answers to all the usual questions. It's less fun to look at a site that is just a log of redirections to archives. Um, but, ... ?!?

As a push-back, one might imagine "superceding" the "usual" questions and answers, by substantial disagreement about the premises (which are usually only slightly trans-PhD, and, thus, still steeped in lethargic/inertial standard-curriculum ideas about what is what.)

In summary: yes, it is entirely anticipate-able that a site that is even "highly-selective" pop-culture will be "saturated" in the sense that the most-common issues will have been raised before. Yes, it would be great to have a graceful mechanism to address this. Yes, it would also be a plus to sort things out, not dissing reasonable-but-cliched questions, but filtering on "genuinely-new" questions. I don't know how...

  • "will be 'saturated'...the most-common issues will have been raised before." It seems this should plague all StackExchange sites. So all might be heading for saturation and slow demise. – Joseph O'Rourke Mar 20 '15 at 23:22
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    At the present, the ArXiv repository alone is accumulating mathematics articles at the rate of over 10 new articles a day. (We can argue about the meaning of "article", or "new", or even "ten". I can imagine ten reasonable fresh MathOverflow questions stemming daily just from looking at the ArXiv math postings.) I see personal saturation (a particular individual getting tired) happening way before group saturation (everybody getting tired). As pointed in an earlier comment, the point is to keep recruiting fresh eyes to the forum. Gerhard "Beats The Drum Some More" Paseman, 2015.03.20 – Gerhard Paseman Mar 21 '15 at 0:35
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    @GerhardPaseman "over 10" is quite a modest way to put it; I think it is an order of magnitude away. – user9072 Mar 21 '15 at 1:35
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    @quid, if I can convince paul garrett that it is a potential source for at least ten daily questions fit for the continuation of MathOverflow, then I might successfully argue that group saturation will occur in time closer to the heat death of the universe than to now. Of course, the real point is to create more participants to continue the forum. Gerhard "Bam, Bam Bam Ba Bam" Paseman, 2015.03.20 – Gerhard Paseman Mar 21 '15 at 1:47
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    @GerhardPaseman: Although I don't disagree with your "fresh eyes" point, I do question the connection between newly posted arXiv papers and MO questions. But I like your "heat death" comment---And I hope you are right! – Joseph O'Rourke Mar 21 '15 at 13:35
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    Running out of good mathematical questions? -- Honestly this looks to me like a rather strange idea ... ! – Stefan Kohl Mar 22 '15 at 9:57
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    @StefanKohl, I did not attempt to claim that we are running out of good mathematical questions. Rather, that many good ones (and bad ones) have already been answered, and that competent people will find "old" answers to (such) good "new" questions... with no such self-censoring for "bad" or "bad new" questions, ... so that there's a dynamic that tends to cause "new" questions, statistically, to decline in quality over time, by being swamped by bad ones. – paul garrett Mar 22 '15 at 13:52

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