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User retention rates on MathOverflow
To me it looks like (up to a rescaling) this data says that it's "similarly difficult" to get high reputation as it is to quit MO.
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Requests for reopen and undelete votes for closed and deleted questions
I was not involved in the closing but I witnessed it. I suspect it was the passive nature of the original question, asking other people to do all the work, when the question-asker could have done the work himself. In the end, that's what happened. I think people would have been happier if the question was asked in more of a can-do tone. But presumably the question-asker did not know it's as easy as it is to do this kind of analysis.
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Why are the number of profile views displayed?
Well, the reason is that the decision is written into the code for the software. But that's kind of tautological. It sounds like you're asking why the SE developers made that decision. It's a measure of curiosity. Some people have lots of views because they're "famous" (for mathematicians) and others because they're really aggressively annoying. It's a curious measurement. There's probably other reasons!
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User retention rates on MathOverflow
The basic help page is here: data.stackexchange.com/help The language used is T-SQL, which is a Microsoft variant of IBM's SQL language. It might be easiest to start by modifying other people's scripts, and reading on-line sql tutorials.
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Local vs. Global MO in relation to "Polymath" efforts
@Francois: you give the impression of being sad about nobody coming forward with interest in a position that has seemingly never been publicly communicated. That seems kind of odd. Why not tell people about it?
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Undelete request, Question 67384
There's a big gap between doing what is legally required of yourself and in being considerate, nice and/or doing the right thing. Anyhow I'm not trying to make a big point here either.
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Undelete request, Question 67384
I think it is more appropriate to have someone re-post an essentially equivalent answer. Presumably the user wanted to delete their account for a reason, we might as well respect that. I think such actions can help build trust among those suspicious of how we might use their contributions.
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Does deleting an MO account delete other StackExchange accounts?
I can confirm what Joel says. I believe I created an economics or quant SE account and deleted it shortly after with no affect on my other accounts.
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On "How does the work of a pure mathematician impact society?"
@Ricardo: It appears you missed this: math.stackexchange.com/questions/447063/…
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On "How does the work of a pure mathematician impact society?"
It's a duplicate of a thread on MSE, so yes it should be closed. If people really think it's best on MO they should have migrated it. But it does not appear to be a good question on either forum.
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Can I ask on the main question board about what are the recent research in some area?
One of the main problems with broad philosophical questions is they attract people who would rather just get into a long rhetorical discussion rather than people who are really invested in outcomes.
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What should the "hover text" for the MathOverflow link on all SE sites be?
One could get all Saunders Mac Lane and say "people employed with jobs that say mathematician in the job title".