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We must do this before we go Public.

This is because, on the day Public starts, all of a sudden, tag creation is limited to all but the highest of rep counts. Tag style will more or less be "locked in" on Public day.

So far, I see some major philosophies:


Loose Style

"Anything goes"

Inspired by arXiv

If you have a question about Number Theory, tag it number-theory. If you have a question about infinity, tag it infinity. If you have a question about calculus, tag it calculus.

Pros

  • More accessible to new people
  • Allows "Creative Freedom", and a broader range of questions

Cons

  • Tags will be in general less helpful because they have the potential to be very vague.
  • Can be abused by entering as many tags as possible that are vaguely related to your question

Strict-Style

"Tags are special."

Tags should only be made with very specific and community-established categories. They should be labeled with a prefix, such as nt.number-theory.

Because tags can only be created by users with decent rep counts, only users who are familiar with the system have the ability to create new tags, which should be done with much discretion.

Pros

  • Much more easier organization/searching
  • No vagueness about boundaries; tags are much much more helpful in identifying/searching questions

Cons

  • Less accessible to new people...however, new people will not have any problem locating the tags, due to SE's tagging suggestion system
  • Possibly slow process of introducing new tags that are accepted by the community

Combination

"Some are special, but allow some loose ones."

I do believe that this is the style used at Math Overflow; correct me if I'm wrong.

You have major categories like nt.number-theory, but also loose and minor ones like example or complexity-theory.

It will be important to establish where to draw the line between special, category tags and loose non-category tags. Otherwise we run the risk of confusion for everyone.


I could be wrong about all these things; please please please edit my post to more accurately reflect what these styles are. I have little background using strict-style or math overflow-style tags, so I bet most people reading this will be much, much more knowledgeable than I and qualified to list pros and cons and descriptions.

I have only established a skeleton that we can start filling in.

Anyways, answers to this question will hopefully contain which elements of all three of these camps we should borrow, and for what reason.

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Although it's tempting to fall into the trap of tagging just for the sake of tagging, remember that the main purposes of tags are:
Tags help people find questions on topics they are interested in.
Tags help people avoid questions they don't care about.

To that end, I don't think the exact wording of tags (nt.number-theory vs number-theory) is all that important as long as everyone knows the system. New users don't have any preconceptions about tags used here (unless they came from MathOverflow), so it's more important to have a tag system that is simple and easy to learn. The automatic tag suggestion goes a long way towards accomplishing that, but it can only do so much. If the real tag is nt.number-theory, someone typing in number-theory will see it suggested, and click it, but if we have both, and they refer to different things, new users will mislabel their questions 50% of the time.

I would like to see:
A tag indicating the question's approximate level, or at least what context it came up in: putnam, high-school, etc.
One or two tags indicating what branch of mathematics it deals with: number-theory, arithmetic, etc.
For more populated topics, what specific type of problem is being asked/what class it came up in: integral calculus and differential calculus are often taught in separate semesters.
For questions that arose in some other field, a tag labeling what non-mathematical field of study it belongs to. actuarial-science, physics, etc. (BTW, please ask more of these!)

Since questions are capped at 5 tags, I think this would provide a good mixture of the ways different users may want to filter the questions.

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  • 1
    $\begingroup$ +1 for tags for the level! $\endgroup$ – Noah Snyder Jul 23 '10 at 16:35
  • $\begingroup$ another enthusiastic +1 for level tags. $\endgroup$ – Jamie Banks Jul 23 '10 at 17:20
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No matter which system we choose, with the tag synonym feature one set could be entirely mapped to the other.

I prefer not to have any prefixes, because

  1. it is hard to draw a definite line which category is “established” enough to get the prefix. And if a tag's usage suddenly surge, should there be a massive tag rename?
  2. the prefix is chosen arbitrarily. e.g. why is [general-topology] chosen to be gn. instead of gt.?
  3. it's visually annoying :).
  4. no other SO-based platform except MO has this system.
  5. even if a user tags a question wrongly, a high-rep user could retag it, eliminating the “vagueness” argument.
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  • $\begingroup$ on point number five - This is true, but keep in mind the gargantuan flood of users we are likely to get in public beta and afterwards: anything we can do to lessen the proportion of things that need retagging will be very helpful to the usability of the site and time spent actually doing what this site is meant for, asking and answering math questions. $\endgroup$ – Jamie Banks Jul 23 '10 at 17:02
  • $\begingroup$ The explanation I heard for the prefix system was that it provided a fast and easy way for experienced users to find any category by typing three letters. This seems like a fine goal to me, and using tag synonyms seems like it would be possible to have more 'friendly' display names without the prefix and still allow people to use the prefixes to look up established categories. $\endgroup$ – Larry Wang Jul 23 '10 at 17:30
  • $\begingroup$ False. The abbreviations come from the arXiv. They are standard in the mathematical community. $\endgroup$ – 97832123 Jul 23 '10 at 21:28
  • $\begingroup$ @Harry: I'm not talking about why those particular prefixes were chosen. I know they are standard. I am talking about why MathOverflow uses prefix.full-name. $\endgroup$ – Larry Wang Jul 23 '10 at 21:45
  • $\begingroup$ @Kaestur: The prefix.full-name convention is only for those tags that arise from arXiv subject areas. You should lurk on MO and see how things work. $\endgroup$ – 97832123 Jul 23 '10 at 21:58
  • $\begingroup$ @Harry: I know that as well. I also know that they add value because they allow people who understand the prefixes to find a unique tag with three keystrokes. $\endgroup$ – Larry Wang Jul 24 '10 at 1:20
  • $\begingroup$ @Harry: This is standard if that subject is a category in arXiv. But this site is not research-oriented, and major subjects outside of arXiv's system will be used often (e.g. linear algebra). $\endgroup$ – kennytm Jul 24 '10 at 6:14
  • $\begingroup$ @KennyTM: You're missing the point because you don't use MO. Most of MO's tags are not of that form. In fact, we have a linear-algebra tag as well. $\endgroup$ – 97832123 Jul 24 '10 at 6:44
  • $\begingroup$ @Harry: Of course I know there's [linear-algebra] tag (and there's 278 [gn.general-topology] tag and 1 [gt.general-topology] tag). But in MO it's a subtopic of [ra.rings-and-algebras]. Because of the target audience here, 'rings and algebras' will not be a major category. Then it goes back to my point 1: should we make 'linear algebra' take the prefix? point 2: if so, what's the prefix is should use? $\endgroup$ – kennytm Jul 24 '10 at 8:03
  • $\begingroup$ @KennyTM: I think we should only use prefixes for arXiv subject areas. Unlike other people have said, the prefixes were introduced for mathematicians who are already familiar with the arXiv. $\endgroup$ – 97832123 Jul 24 '10 at 9:00
  • $\begingroup$ @Harry: But that totally voided the pros of prefixed tags, and I must stress again that this site is not mainly research-oriented, and therefore many users won't be familiar with arXiv or MO. $\endgroup$ – kennytm Jul 24 '10 at 12:07
  • $\begingroup$ @KennyTM: You're clearly stupid, since the argument for arXiv tags from the beginning was that learning them here would make it easer to "graduate" to MO in the future. $\endgroup$ – 97832123 Jul 24 '10 at 20:31
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I suggest we take a look at some of the actual tags currently created and see what we like and what we'd do differently (we need an overarching tagging approach too, but why not start with what's here). Others should edit this to flesh it out, but some immediate things I see are:

  • We have [nt.number-theory] and [number-theory], with the same number of questions in each at the moment. On reflection, the arXiv prefixes don't seem helpful, because although they might theoretically help people who are familiar with the tags discern which questions they'd be interested in, the majority of people using the tags will be new users who see no difference in the two.

*General point: It is likely that at any given time, the majority of the people interacting with the tagging system will be new users who have not read and are not interested in the FAQ.

  • Some tags seem to me clearly useless: [learning], or [intro], for example. (intro could mean anything from kindergarten to graduate school).

  • We currently have [summation], [series], [radius of convergence]. I'd suggest a [sequences-and-series] tag, which will pop up for anyone asking a question about either sequences or series, and separate out this (common) problem type from more general calculus or real-analysis questions.

  • We need a way to distinguish abstract algebra questions from solving simultaneous equations or the quadratic formula. This way needs to be as transparent as possible for both types of users asking an "algebra" question. Some of the more common dichotomies here should probably be explained in the FAQ.

  • Some tags are ambiguous, or simultaneously too general and too specific: [gradient], for example, or [recursive]. We want to avoid things like [normal], etc.

    • I'd make the same argument about the [infinity] tag: It's appealing to new users not particularly familiar with mathematics, maybe, but the concept of infinity pervades all of mathematics; the tag is too broad to anyone who is more versed in pure mathematics. This is not a "that's dumb" accusation. But if we have an [infinity] tag, it wouldn't be a tag you'd want to ignore - almost anything related to math could pop up there - but at the same time most of the questions would likely be ill-formed, and people might block the tag with that expectation.
  • I kind of like the tag [pi]. There are going to be a few recurring questions about ideas people have gotten in their heads from pop math and other curiosities, and I think having a few such localized tags solves this classification problem neatly. People who have more mathematical or historical questions about computing pi, history, etc, will probably know how to tag accordingly, or can have questions retagged at worst.

  • I like tags like [group] for this reason: lots of people will come with questions about such ubiquitous objects, and not enough familiarity with the jargon and theory to label it abstract-algebra or something else that unifies it. However, I don't like the tag [natural-number], so I'm particularly open to being wrong on this one. The two strike me differently, but I don't actually know how to distinguish between them as a matter of policy.

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  • $\begingroup$ An additional reason to disfavor learning and intro is that everyone is learning, and many people are not humble enough to label their own questions as introductory, or even react well when others do it for them. I agree completely on the sequences-and-series, normal, and group tags. $\endgroup$ – Larry Wang Jul 23 '10 at 19:29
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In any decision, I say favor the thing that's easier for new users.

My reasoning is pretty "selfish": I assume that MU will have many more users than Math Overflow (that's its purpose). So there will be many more new users than existing ones.

I, for one, would not want to spend half my time on the site correcting misused tags, so a looser system works much better.

Two specific points:

  1. "less accessible to new people...however, new people will not have any problem locating the tags, due to SE's tagging suggestion system" - not sure this is true, although if it is, then some of my points above are less important.

  2. "Can be abused by entering as many tags as possible that are vaguely related to your question" - That's why there's a limit on tags (5, I think), and this hasn't been a problem on Stack Overflow.

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  • $\begingroup$ I don't agree with the idea that MU's purpose is to have more users than MO. Its purpose is for mathematics at a lower level than MO. MO also accepts questions from neighboring fields, as long as they have graduate-level mathematical content. $\endgroup$ – 97832123 Jul 23 '10 at 11:09
  • $\begingroup$ It's not MU's purpose. But the amount of people doing research-level mathematics is vastly smaller than the amount of people who just want to ask a simple Math question. $\endgroup$ – Edan Maor Jul 23 '10 at 11:54
  • $\begingroup$ your point 1 is true to some extent, but I think what he was saying is that a new user who wants to label a question number-theory can just type that in, and the appropriate nt.number-theory tag would be suggested to him. $\endgroup$ – Larry Wang Jul 23 '10 at 14:31
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I don't believe that all questions that are mathematical problems should have the ArXiv two-letter prefixes. The right way of interpreting [nt.number-theory] is that it raises some issue of interest to number theorists. Any question that nearly all final-year undergraduate mathematicians could answer does not deserve these tags.

Example: Why is the decimal representation of 1/7 “cyclical”? has the [nt.number-theory] tag: wouldn't it make more sense if it was tagged [arithmetic] instead? What has this question to do with the distinctive kind of mathematics that number theorists do? I would not expect to see such a question treated in an undregraduate course entitled "Number Theory".

I answered basically this question before, MathOverflow tags + others ?.

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  • $\begingroup$ Well, arithmetique is the word in French for number theory ;). $\endgroup$ – 97832123 Jul 23 '10 at 11:06
  • $\begingroup$ @Harry: Touchée! $\endgroup$ – Charles Stewart Jul 23 '10 at 11:11
  • $\begingroup$ @Harry: To put this another way, I don't think there is a fact of the matter about whether such a typical "arithmetic" question would more deserve the label [nt.number-theory] or [ra.rings-and-algebras]. $\endgroup$ – Charles Stewart Jul 23 '10 at 12:12

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