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  1.  
    I was invited to join this discussion, so here we go.

    Actually, I was part of the original discussion in 1997 and 1998 that led to the creation of the math arXiv categories. So this is a familiar topic for me.

    I think that it would be very nice to encourage or possibly somehow require standard tags, in addition to roll-your-own tags. And it seems that the arXiv subject structure, while not perfect, still works reasonably well.

    I think that the period is useful to distinguish a standard code tag such as dg.differential-geometry from an ad hoc tag such as dg-algebras.

    As for the names, I agree that some of them are long-winded. Actually I have sometimes been among the most strict of the people involved in wanting short names. My advice is that, as long as the two-letter codes are there, don't take the names too-too seriously. One thing that you might do is eliminate "and" and "of", because they don't do a whole lot.

    "Rings and Algebras" is a problem name and not the best choice in the arXiv classification. A better name that has been suggested is "General Algebra", although you can't really use that as the standard unless it changes at the arXiv. But you could make it ra.rings-algebras.
  2.  
    Oh also re Scott Morrison's comments, math.ag would also work well enough as a name. I have no strong opinion between that and ag.algebraic-geometry. Mainly I think that you want standard tags as a subset of all of the tags, and I think that the period is useful for making a distinction.
  3.  
    Let me also mention that there are some other tricky mistakes and tricky non-mistakes in the math arXiv classification. For instance, the moderators have been careful to define functional analysis to mean "functional analysis which isn't just operator algebras, because those people do something different." This is usually an easy call; arXiv authors don't always know at first, but they get used to it. The main case that's unclear is Banach algebras; it's a question of whether people have in mind ideas in the spirit of Banach spaces, or ideas in the spirit of C^* algebras, or both.
  4.  

    Re: [math.ag] vs [ag.algebraic-geometry]. I really object to the first one, and I'm liking the second one more and more. In my mind, one of the points of using the arXiv abbreviations is to make things easier for people who know the classification, without making things hard for people who don't. With either version of the tag, I can get it by simply typing ".ag" or "ag." (respectively) and selecting the tag from the drop-down box. But people who aren't so nimble with the arXiv abbreviations will start typing "algebr…", and the tag [math.ag] won't show up, so they'll end up creating a new tag, and the moderators will always be running around merging [algebraic-geometry] into [math.ag]. Also, as I said before, [math.ag] doesn't communicate very much information to people who are looking at the question and don't already know the abbreviations.

    Since moderators still can't rename tags (only merge tags), if you see a question at the top of the home page that needs an arXiv tag, or has an old version of the arXiv tag, please retag it. As soon as one instance of the correct tag exists, a moderator can easily convert the rest of them.

  5.  
    But the deeper reason for the arXiv tags is standardization, even though I admit that the standard isn't perfect.
  6.  

    I'd like to chip in with support for something implied in Anton's post (2 above unless someone posts something while I'm writing this). One thing about tags is that there is some (bizarre) algorithm for suggesting tags as you write. So to make a tag truly useful, it should be sufficiently close to what someone who doesn't already know the tag might type by hand so that when they start typing a possible tag, the already-existing tag will be suggested.

    The conclusion being that perhaps the most important factor in choosing canonical names is how the suggestion algorithm works. The obvious search on meta.stackexchange threw up too many posts for me to bother looking through them all right now, but maybe that's a useful bit of digging someone could do (or perhaps someone already knows it).

  7.  

    First some minor comments, then my ideal solution.

    I object to math.ag as a tag. It is not intuitive to people who don't already know what it means. Of course, I do know what it means, but there are plenty of areas where I don't. COmplex numbers, ComplexAnalysis or ComplexVariables? Is SEt theory a category, or is that a branch of LOgic? And I plan to use the site to ask plenty of questions outside my fields of expertise.

    If we use ag.algebraic-geometry, we should probably have a FAQ like "Why are people using those funny two letter abbreviations?"

    I seem to differ from everyone else, but I'll state my ideal solution. I think it would be fine to simply say "Please use at least one broad area tag. A list of standard broad area tags, based on the arXiv classification system, is here." Then "here" would be a link to a static page listing the subject tags. I don't see why we need to make the tags look odd and be harder to remember.

    People have mentioned ease of retagging. Can't we just solve this with a boolean search? For example, here are all the questions not tagged with number-theory, representation-theory, algebraic-topology, algebraic-geometry or logic. We could even have a link on the Tips and Tricks page to a search for all questions without arXiv tags, for the benefit of anyone who wants to do retagging.

  8.  

    All this retagging has seriously messed up my list of "Interesting Tags". I've listed "functional-analysis" as one of my interesting tags, but that doesn't seem to match "fa.functional-analysis". Where they merged? If so, it's a bug that the lists of "interesting tags" don't also get updated.

    Whatever the case on that particular issue, it'd be useful to be able to go through the list of tags and select a whole bunch as "interesting" instead of having to put them in one by one. Is there a way to do this, does anyone know?

    (If I don't get satisfactory answers from you lot, I'll go and bug the meta guys on S[OE]. You have been warned.)

  9.  

    Help! This has gone critical! We have functional-analysis, fa-functional-analysis, and fa.functional-analysis!

    I know you want to get it right, but can we have a system that is nearly alright and that is stable for a little while?

  10.  

    @Andrew: relax, everything is going to be okay. There is now just [fa.functional-analysis]. You (or somebody else) should post a bug report on meta.S[OE] about favorites not updating when a tag is renamed. Then post a link here so I can go vote for it.

  11.  

    @David, I agree with you.

    I think it could be useful to summarize possible tagging solutions. Here are the ones that come to my mind, listed in the order of my personal preferences:

    1. Algebraic-Geometry
    2. algebraic-geometry
    3. AG-algebraic-geometry
    4. AG.algebraic-geometry
    5. math.AG-algebraic-geometry
    6. ag.algebraic-geometry
    7. ag-algebraic-geometry
    8. math.ag-algebraic-geometry

    Note that solutions 1, 3, 4, 5 use uppercase letters in the tags which is currently technically impossible, but theres' a meta.SE feature request by Anton about that.

    By the way, at least on Meta.SO, it's technically possible to designate top-level tags and require that every post has at least one of these.

  12.  

    Here's the bug report about a user's tags not getting updated: http://meta.stackexchange.com/questions/2777/interesting-tags-dont-update-with-tag-merges

  13.  
  14.  

    Can we have some tags regarding how important the questioner regards the question? Well, I know that we can, and I've started doing it with the [[idle-speculation]] tag. What I mean is: can the Big Guys do this too so that others see this happening and copy it. If possible, I'd like this in with the "choose a tag from the arxiv classification" message: "choose a tag that indicates how serious this problem is to you".

  15.  

    @Andrew: what would the alternatives to [idle-speculation] be?

  16.  

    i-thought-about-this-for-a-day, i-need-this-for-my-thesis, i've-been-working-on-this-for-ten-years :)

    I don't think that a tag would be useful here, as I can't think of why I would ever want search for idle-speculation (although I might want to ignore it.) But I do think it is a good idea for people to give a general idea of how long they have spent thinking about something.

  17.  

    @Scott: wot David said.

    I don't think tags are just about searching. I think that they also give information about the problem. As they are always displayed (in particular, in the list view) then they are a good way to provide context for a problem. So if I see a problem that says "loop group" but then see that it is marked "ag.algebraic-geometry" then I'll probably skip it. Similarly, if I see a complicated problem that says "idle-speculation", again I'll skip it.

    As an example from "history", take Ben Webster's question on whether or not there are "scaling up" operations on topological spaces that correspond to "scaling up" of rings. That felt like an "idle-speculation" question so I gave an "idle-speculation" answer. However, knowing whether or not it was idle speculation or crucial-for-thesis would have altered how I answered.

    Similarly, Theo has asked some very technical questions in differential topology. I doubt that anyone just knows the answer. I could think about them for a bit and maybe make one or two suggestions as to how to proceed. But exactly how important are they? How useful would it be for me to do that? If they were just idle-speculation, then I won't bother. If they were "crucial for thesis" then I would.

  18.  

    I don't think this is a good use for tags. Wy not just state in your question how seriously it is to be taken?

  19.  

    Because that's not prominently displayed in the list view.

    Why isn't it a good use for tags? Are tags purely for searching by? Aren't they supposed to be so that I can see in the summary view whether or not it's worth looking at the details? In that case, what I really want to see is:

    1. General area: am I even going to understand the question, or be able to make a sensible contribution?
    2. Urgency: should I look at it now, or come back to it later when I've got more time?

    What more do you want to know in the list summary?

    How often do people actually search by tag? You could look at the logs and find out: I'd be quite interested to know. Are tags useful for limiting searches to see if a question has been asked before? Do people really search by tags to find interesting questions to ask? How, exactly, are people using tags? How can you help people make the most of tags?

    I'm trying to give you my answers to those questions. I don't expect my views to have any more weight than anyone else's, but if I don't tell you what I think then that's not helpful to either of us!

  20.  

    @Andrew: I would guess that the more questions accumulate, the more important searching by tag will be. That will, after all, be how you look to see if your question (or one sufficiently close to it to be useful) has already been asked. Thus I suspect it may be a bit early to draw conclusions from search statistics. The tags you are talking about will only have short-term interest, I suspect, but that is no argument against using them.

  21.  

    I agree with David that this doesn't feel like a good use of tags. If a question (or question title) doesn't interest me, I just can't imagine changing my mind and working on it just because it's "urgent", and if a question is interesting, I'm going to think about it even if it's not really important to the person asking the question. I like when people include some information about how much they've thought about a question or why they're interested, but promoting this information to be included in the tags seems like it would send the message that it's acceptable to say, "guys, I really need this ... chop chop, do my work for me." Something about using tags to indicate urgency feels dirty to me. If I really want to get an answer, I'll put more time into make the question clearly written and well motivated. If I don't get an answer, I'll add a bounty, or I'll try to break the problem down into "smaller" questions. I don't want to give anybody the impression that adding the tag [urgent] is a substitute for putting in some work.

    See also this meta.SO post

  22.  

    I don't know how urgently people usually need answers to math questions, but I've recently posted a programming bug I absolutely couldn't get myself and it was solved in two hours. And the followup? Answered in 3 minutes.

    That's good enough speed for me!

  23.  

    "Urgent" in time-wise is not what I'm getting at. It's more about whether or not the person has a deep motivation for asking the question or not. I agree that on the whole the reason I'll look at a question depends mostly on the question, but the reason I'll keep coming back to a question depends on whether or not I feel that the asker is invested in that problem, if I can use that horrible term.

    But I feel as though I'm losing this one heavily so I'll bow out now while I still have some dignity left!

  24.  

    Honestly, everything I answered/asked/retagged so far has been purely for my enjoyment.

    Gosh, to imagine that my interaction with MO could be useful and important for somebody is a cool idea. Actually, I'd be glad to work in that mode as well.

    @Andrew, I think this particular idea will not work, but a trial is fine with me.

  25.  

    At Greg Kuperberg's request, I've displayed a full list of arXiv subject tags at the bottom of the ask page. Any feedback? Is it too much text?

  26.  

    Whether it's fortunate or not, the current de-facto policy seems to allow linear-algebra and soft-question as top tags as well. I'd mention them for completeness. The same may apply also to arithmetic-geometry.

  27.  

    @Ilya: I think we should gently push for every question to have an arXiv tag for now. The arXiv classification suggests that [linear-algebra] questions should also be tagged [ra.rings-and-algebras].

    To that end, 500+ reputation users may have noticed that I've added some text to the sidebar (under the tip):

    Want to help? Consider retagging questions with no arXiv tag.

    If you click the link, a red box should appear around any question that doesn't use any arXiv tags (actually, it just checks if any of the tags contains a dot, but non-arXiv tags shouldn't be using dots). Please let me know if this misbehaves in any way or if the functionality can be improved somehow (e.g. highlight the questions some other way, or include a link to this tagging guide). Also, are there other tasks that should be encouraged/facilitated in a similar manner? For example, once we have some 10k+ rep users, we could encourage them to look over questions which are candidates for closing/reopening/deleting (10k is the threshold beyond which you have access to that information).

  28.  
    If you click on the "questions with no arXiv tag" that Anton added, you'll see that most of them are soft questions. The only arXiv tag that could fit them would be [gm.general-mathematics], but it doesn't exist! Should we maybe create it to replace soft-question, or perhaps use it concurrently?
  29.  

    I'm not sure. gm.general-mathematics is sort of the catch-all tag on the arxiv for junk and crackpots. :-) May that matches our [soft-question]s, I don't know!

  30.  
    I don't like the [gm.general-mathematics] tag either. Maybe, in order to place all questions under some dotted/arXiv tag as Anton was suggesting, we could create [sq.soft-question] :D
  31.  
    Regarding retagging, it is possible to make it such that when a question is retagged it doesn't reappear on the top of the front page? When someone gets overenthusiastic about the great retagging campaign, it can saturate the front page, making the front page less useful as a device to see where new content has been added.
  32.  
    @Peter: I did that today. Sorry about it. Scott sent me an email telling me that mass retags can be done by moderators without getting the questions bumped up to the top of front page. There's a meta thread where requests to the above can be posted:
    http://tea.mathoverflow.net/discussion/34/tag-mergerename-requests/