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Some of you may have noticed that StackOverflow just inaugurated a Documentation feature. It's basically in adition to the Q&A traditional site. I was wondering if something of the kind would be possible and/or useful on Mathematics StackExchange. This would be different from simply answering your own question. There could be diverse examples of applications of mathematical concepts, or multiple proofs exposed for a certain theorem.

This idea does not seem to have been much discussed in the past (couldn't find any question about this on MSE). But now that this has been implemented in another StackExchange site, it becomes different.

Do you think that creating a big mathematical documentation would be possible? With the amount of knowledge in here, and many volunteer members, an incredible documentation could be built in a few years. Do you think this is useful? Or is there, in your opinion, enough of this on the Internet? I'm really looking for opinions here, with argumentation on whether or not this should be done.

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    $\begingroup$ I think this feature could possibly be useful for a couple of common themes. Since now it is only on beta on SO, I think we'll have to wait a bit. But thanks for the info about this. $\endgroup$ – quid Jul 21 '16 at 17:20
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    $\begingroup$ It says: "Documentation is broad, and it is a general reference. You aren't documenting a specific problem you're facing, you're helping others deal with an entire class of problems by documenting." That looks like the abstract duplicate that we store in Meta (or the tag faq). $\endgroup$ – user99914 Jul 21 '16 at 17:35
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    $\begingroup$ @ArcticChar I agree that it is in the same direction. One could hope that this new feature would make the use and organization of this or related resources more convenient, widespread, etc. $\endgroup$ – quid Jul 21 '16 at 19:39
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    $\begingroup$ I can imagine having "documentation" of some sort could be useful to dealing with some of the varieties of questions we get in high volume and often low quality - maybe "what have you tried?" could become "have you tried [this](useful.documentation.link)". $\endgroup$ – Milo Brandt Jul 21 '16 at 23:46
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    $\begingroup$ Thanks for the link. Because I have a Stack Overflow account, reading the documentation tour resulted in an educated badge. $\endgroup$ – Joel Reyes Noche Jul 22 '16 at 0:16
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    $\begingroup$ This documentation material would be plagiarized from the standard textbooks? Or, better yet, this is a place for cranks to put their favorite topics? Maybe wait until Stack Overflow Documentation is out of beta and see how it works, before we consider it here? $\endgroup$ – GEdgar Jul 22 '16 at 13:16
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    $\begingroup$ @GEdgar sure, this is not somehing to be set up as soon as possible. My question was rather about the concept, and if it were applicable to this site. If you wish to develop your point of view, please feel free to make it an answer ! $\endgroup$ – BusyAnt Jul 22 '16 at 13:18
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    $\begingroup$ @GEdgar I did not yet look into the details much, but contributions to doc are reviewed and content is voted on. Thus, there are means to deal with it just like there are means to deal with it now. But, yes, it's prudent to wait and see what happens on SO. $\endgroup$ – quid Jul 22 '16 at 18:35
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    $\begingroup$ While I'm a bit sceptical about the idea of a documentation for entry-level questions here at MSE, I find the idea of a documention in advanced topics rather intriguing. For example, learning the basics of inner model theory is pretty daunting (and painful at times) - for several reasons. A documentation of these basics, explaning different approaches, providing examples and highlighting some common mistakes, would probably be very benefitial for anyone who wants to get into this field. I'd be very happy to collaborate to such an effort, even if it doesn't take place at MSE. $\endgroup$ – Stefan Mesken Jul 25 '16 at 20:33
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    $\begingroup$ @Stefan Sounds that we got a lot of diverging points of view here, that's very instructive! $\endgroup$ – BusyAnt Jul 25 '16 at 20:37
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It has just been announced on Meta Stack Overflow that Stack Exchange is sunsetting Documentation. As they are freezing this on the site it was designed for, it's probably safe to say that it isn't coming to Mathematics Stack Exchange anytime soon.

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  • $\begingroup$ My experience with Documentation was dispiriting. I did see some opportunities for connecting StackOverfow answers with documentation posts, but there were setbacks with edits and deletions of my posts such that I felt things got torn down faster than I could build them up. $\endgroup$ – hardmath Aug 2 '17 at 16:40
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The central idea (paradigm) of StackOverflow Documentation is "Examples, examples, examples -- show beats tell."

Brief experience with the public beta suggests to me a tension between the central focus on (code) Examples (with supplementary specification of syntax) and the explanation of concepts and semantics.

My gut reaction is that this tension would be more pronounced if we apply it to the learning of mathematics. Yes, examples are very helpful, especially if skillfully presented in the right context of trying to understand general principles. However there remains a need for exposition ("tell") about concepts, and it seems to me that the current framework of SO Documentation omits a clear mechanism of having exposition shared across a family of related examples.

I am optimistic that this is being worked on, based on jumping into the chatroom for SO Documentation rollout. But it argues to me the wisdom of taking a wait-and-see approach.

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  • $\begingroup$ So if I get you right, a MSE Documentation based on what SO Documentation is today wouldn't be a good idea, but with some amendments it might be feasable? $\endgroup$ – BusyAnt Jul 22 '16 at 19:33
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    $\begingroup$ @BusyAnt: Tentatively, yes. It might, for example, address what currently we try to manage with "generic duplicates". One of the goals of SO Documentation is to provide generic material that can be referenced within good Answers on the classic SO Q&A "threads". $\endgroup$ – hardmath Jul 22 '16 at 19:36
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    $\begingroup$ Especially given the first paragraph, I'm inclined to think that the mathematics version of the program is just a well-written textbook. $\endgroup$ – user296602 Jul 22 '16 at 19:38
  • $\begingroup$ @hardmath I must say I kinda like this point of view. I hope the question will still be worth debating in 6 months. $\endgroup$ – BusyAnt Jul 22 '16 at 19:38
  • $\begingroup$ @T.Bongers which first paragraph? $\endgroup$ – quid Jul 22 '16 at 19:44
  • $\begingroup$ @quid Of this answer, the part where it says that the paradigm is examples x 3. $\endgroup$ – user296602 Jul 22 '16 at 19:45
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    $\begingroup$ @T.Bongers: Often students complain that the write-up of math as "theorem-proof" omits these valuable Examples, so doubtless there is some need for "well-written" textbooks (tutorials?) that present them. But the SO Docs mission is a bit broader in that it is claimed essential developer documentation is "scattered all over the place". I have difficulty wrapping my head around what the analogous benefit for mathematics is. Yeah, there is a lot of math scattered all around. Could we even make a dint in the task of bringing it together? $\endgroup$ – hardmath Jul 22 '16 at 19:50
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    $\begingroup$ @T.Bongers Thanks for the clarification. This was my first guess but then I found it implausible, as worked examples in textbooks at least of a moderately advanced level are often rather scarce. (If all those texts should no qualify as well-written, I'd say there is a serious lack of well-written texts.) $\endgroup$ – quid Jul 22 '16 at 19:51
  • $\begingroup$ @quid Fair enough, but the vast majority of activity here seems to be in tags like algebra-precalculus, calculus (and related tags), elementary-*-theory, and so on. Many texts at this level do have a plethora of examples. $\endgroup$ – user296602 Jul 22 '16 at 19:55
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    $\begingroup$ @hardmath Honestly, I think we'd end up here if we tried. $\endgroup$ – user296602 Jul 22 '16 at 19:56
  • $\begingroup$ @T.Bongers yes, it should be more useful for some subjects than for others. But I do feel it could realistically be useful for some (not sure though it would work out in practice). $\endgroup$ – quid Jul 22 '16 at 20:12
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    $\begingroup$ @quid it seems like you have a pretty well-constructed opinion. Would you agree to make it an answer so we could properly dicuss it? $\endgroup$ – BusyAnt Jul 22 '16 at 20:21
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    $\begingroup$ @hardmath: I'm not disagreeing yet, but I do think there is a significant difference between learning programming by example (I have done that several times; or rather I know basic programming, I learned a new language or a new trick by examples), and learning mathematics by example. More to the point, I think that when you are where learning mathematics by example, you are probably not in the point where you come to MSE for that example. $\endgroup$ – Asaf Karagila Jul 22 '16 at 23:38
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Clearly, the simple answer is "wait and see" how SO Doc goes. It is "competing" (or, more specifically, attempting to not compete) with a number of existing documentation sites like MSDN and those for JavaScript, Python, Java, Common Lisp, etc. I believe many of these are not freely editable (though I suspect a number of wiki-based documentation sites are out there).

A Maths Doc would be "competing" more with Wikipedia, which is freely editable, of course, as well as sites like MathWorld, which are not.

Again, if Maths Doc also goes for a more Examples, Examples, Examples approach, it would avoid competing with the websites, but would then start competing with textbooks.

I would probably prefer to get a "collaboration" with Wikipedia to encourage editing it when questions are asked here because the Wiki information is not clear.

Nevertheless, I believe there would be a place for Maths Doc, probably next after the other the other programming-like SE sites, and at about the same time as Physics.SE, etc.

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    $\begingroup$ This is - to some extent - related to some parts of your post: Is MSE a good place to ask for help improving Wikipedia articles? and Questions concerning editing of wikipedia articles. $\endgroup$ – Martin Sleziak Aug 2 '16 at 9:44
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    $\begingroup$ There's PlanetMath, which currently has some stuff found absolutely nowhere else (not even stated on Wolfram), which I think is editable. There's also ProofWiki, which has lots of circular reasoning that needs cleaning up, but a lot of editors anyhow write proofs and link to any lemma they want to use without checking whether those lemmas are proven, making it a huge tangled mess. $\endgroup$ – user21820 Aug 14 '16 at 3:31

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