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I've noticed a common pattern among new users to use the tag, often times when the question has little to nothing to do with abstract algebra. I recognize that mis-tagging is an easy mistake to make for a newer user, because they don't really understand the necessity of choosing the right tag, and sometimes they simply don't know what subject their question would fall under. But seems to be a top choice for new users as a mis-tag. Here are just a few examples:

https://math.stackexchange.com/posts/468370/revisions

https://math.stackexchange.com/posts/456690/revisions

https://math.stackexchange.com/posts/465617/revisions

I suspect it may be that users are thinking of the subjective meaning of the word abstract, feel that their algebra question is sufficiently "abstract" to warrant the tag, but aren't aware that abstract algebra refers to a specific field of mathematics. In that case, it may be helpful to edit the tag excerpt in order to clarify not to use the tag unless the question is about the algebraic structure of rings, groups, fields, etc. I've seen a similar thing done on tags on other sites, like the glitch tag on the gaming site.

Has anyone else experienced this pattern? Does anyone else have any thoughts on this?

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    $\begingroup$ Meh, the set theory and logic tags have been thoroughly abused in the past three years. It's not a big deal, even if it is [very] tiresome. $\endgroup$
    – Asaf Karagila Mod
    Aug 15, 2013 at 16:55
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    $\begingroup$ (1) is definately incorrect. It is possible that (2) was simply encountered at the start of a course or book on abstract algebra, so although incorrect is understandable. However, (3) is Galois Theory, a bona-fide area of abstract algebra (for example, check out the second answer). (Although I suspect that that is just coincidence.) $\endgroup$
    – user1729
    Aug 15, 2013 at 19:02
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    $\begingroup$ I agree with user1729 about the third case. It is a borderline case where if the user had put in abstract algebra, I would have left it, but if the user had not originally, I would not have added it. $\endgroup$
    – Willie Wong
    Aug 16, 2013 at 7:50
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    $\begingroup$ And given the current state of the Wiki excerpt, I struggle to come up with a even clearer way to indicate what the tag is about. Can you perhaps give a proposed phrasing of the tag wiki? I imagine that in most cases of tag misuse, the users simply ignored the tag wiki altogether... $\endgroup$
    – Willie Wong
    Aug 16, 2013 at 7:52
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    $\begingroup$ Last comment: for new users, it can help that when you edit the tags leave a comment (or an edit summary) explaining why you retagged. This will help them learn what the tag is for. $\endgroup$
    – Willie Wong
    Aug 16, 2013 at 7:53
  • $\begingroup$ @WillieWong That's true. I guess this isn't as big an issue as I thought. I just thought it might be worth bringing up, but I'm glad to know that this isn't that big an issue. $\endgroup$
    – rurouniwallace
    Aug 16, 2013 at 7:55
  • $\begingroup$ They do this with lots of tags; “oh, my question has a function in it somewhere, so I'll tag it with functional-analysis”. I don't see any good solution. $\endgroup$
    – MJD
    Dec 12, 2014 at 15:45
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    $\begingroup$ My favorite is when someone uses complex-analysis because they feel their problem is complicated. $\endgroup$
    – Emily
    Dec 12, 2014 at 18:21
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    $\begingroup$ @Arkamis That's a nice one. Reminds me of when someone uses soft-question because they feel their problem is not complicated. $\endgroup$
    – quid Mod
    Dec 12, 2014 at 18:39
  • $\begingroup$ @MJD: I think that the logic related tags suffer the worst, perhaps. In descending order of misuse percentage (in my experience): proof-theory, logic, set-theory, elementary-set-theory. $\endgroup$
    – Asaf Karagila Mod
    Dec 12, 2014 at 21:23
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    $\begingroup$ The one I notice the most is using linear-algebra for any problem that involves lines and algebra (e.g., find the equation of the line through $(1,2)$ with slope 3). $\endgroup$
    – Gerry Myerson
    Dec 12, 2014 at 22:23
  • $\begingroup$ Maybe we make an "abstract-arithmetic" tag so that new users can use the word "abstract" in their question about algebra? $\endgroup$
    – Milo Brandt
    Dec 12, 2014 at 23:42
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    $\begingroup$ @asaf I forgot about logic itself, which is applied to all sorts of questions where the asker appeared to say to themselves “I guess I'll need to figure this out logically, therefore it should be tagged with logic…” $\endgroup$
    – MJD
    Dec 15, 2014 at 7:14
  • $\begingroup$ @MJD, I shiver at the very thought! $\endgroup$
    – Asaf Karagila Mod
    Dec 15, 2014 at 7:19

2 Answers 2

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I agree that the tag is somewhat of a "problem tag," yet it might be the "least of all possible evils." Here is why I think so:

The issue with "abstract algebra" is that is in fact not really (anymore) a field of mathematics, just like "modern algebra" is not a field of mathematics anymore; the adjectives became obsolete.

The reason the term is still somewhat common is, or at least so my impression, that it is common, in the US and possibly elsewhere, as a name for certain types of courses and textbooks, mainly at the beginning undergraduate level; named in this way to distinguish them from the "algebra" courses in high-school.

Thus, users tag questions with it that come up in their abstract algebra class or remind them of such problems. Sometimes this results in mis-tags but then often it is not that far off even if it is not quite correct, but mainly it results in actually quite alright tagging creating a family of algebra questions mainly at the beginning undergraduate level.

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  • $\begingroup$ “Abstract algebra” is certainly a distinct domain of knowledge about algebraic structures in maximal generality. Due to clueless textbooks (and possibly stupid teachers) 90% of newbies think that abstract algebra means “any algebra outside algebra-precalculus”. Why so many people on this site despise me that even posting asserting “abstract algebra is not really a field of mathematics” became upvoted? Apparently because it says something contrary to me. $\endgroup$
    – Incnis Mrsi
    Dec 13, 2014 at 7:28
  • $\begingroup$ To keep things structured let me repeat what I already commented on your post in a somewhat different way: there is a subject called Universal Algebra, or General Algebra, that also has a tag universal-algebra, which seems what you describe. Also, parts of category theory an possibly model theory touches upon some of these things. $\endgroup$
    – quid Mod
    Dec 13, 2014 at 11:48
  • $\begingroup$ I stand by the assertion that "abstract algebra" is not a name commonly used for any field of math. To wit you can check the MSC, which I would consider as something authorative here; "abstract algebra" appears once and in passing in "05C25 Graphs and abstract algebra (groups, rings, fields, etc.)" in particular note the parenthetical remark. $\endgroup$
    – quid Mod
    Dec 13, 2014 at 11:49
  • $\begingroup$ Damn… shouldn’t “abstract algebra” be burned then, as an unwisely overextended thing? Aren’t group-theory, ring-theory, and algebras enough? $\endgroup$
    – Incnis Mrsi
    Dec 13, 2014 at 12:17
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    $\begingroup$ In a perfect world where everybody would make some effort to tag properly, yes. However, in reality, I am of the opinion that having this tag has the benefit that the many students that have some abstract algebra class will find easily some tag that matches somewhat; if they don't many might just tag whatever; for example, "algebras" should get a lot of usage then because it is "almost" the same word as algebra. $\endgroup$
    – quid Mod
    Dec 13, 2014 at 12:22
  • $\begingroup$ Let’s continue the argument at meta.math.stackexchange.com/questions/6356/… $\endgroup$
    – Incnis Mrsi
    Dec 13, 2014 at 13:30
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Just started to write a request myself, after noticing that tagged questions constitute a mix of group/ring theory and an outright pollution.

Yeah, abstract algebra is a valid topic, but 90% newbies do not understand what is it about. Let it, for great justice, be includeable only by established users.

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  • $\begingroup$ Pushing ⇩ compensates for shortage of arguments, as anywhere on StackExchange. $\endgroup$
    – Incnis Mrsi
    Dec 12, 2014 at 12:38
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    $\begingroup$ I don't think anyone needs to explain why new users should be able to ask questions about abstract algebra. Maybe new users should be warned that the abstract algebra tag might no be mean what they think, but outright prevent them from using it? What? $\endgroup$
    – Najib Idrissi
    Dec 12, 2014 at 12:40
  • $\begingroup$ The StackExchange system is restrictive and discrimination based on rep points is pervasive. There are many things that, in theory, newbs “should be able to” (such as showing more than one link to MathWorld, Wikipedia, or Encyclopediaofmath), but they don’t. @Najib Idrissi, do you criticize outspokenly such forms of discrimination that actually hinder users to make useful contribs? Based on your rejection of my edits, I do not expect it. $\endgroup$
    – Incnis Mrsi
    Dec 12, 2014 at 12:48
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    $\begingroup$ Could you not write "newbs"? I can accept "newbies" but "newbs" feel like (1) insulting to newcomers (and one step from "n00bz"); and (2) an internet abbreviation, in contrast with acronyms which are somewhat reasonable to use, abbreviations just look like modern internet laziness. Unless you're texting everything to the site (which I don't think is possible, unless you've set a machine hooked to a cellphone that can take your SMS messages and post them here) or paying per keyboard stroke, there's no need for abbreviating -- even less so when the abbreviation only saves two letters. $\endgroup$
    – Asaf Karagila Mod
    Dec 12, 2014 at 14:00
  • $\begingroup$ Thank you for addressing that issue. $\endgroup$
    – Asaf Karagila Mod
    Dec 12, 2014 at 14:21
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    $\begingroup$ Could you explain to me what abstract algebra then is if it does not contain (basic) group and ring theory? $\endgroup$
    – quid Mod
    Dec 12, 2014 at 14:41
  • $\begingroup$ @quid could you explain to me what abstract algebra then is if it does not contain “x + y = 1 → y = 1 − x”? Likewise a silly question. $\endgroup$
    – Incnis Mrsi
    Dec 13, 2014 at 7:34
  • $\begingroup$ @quid well, I can show you two Wikipedia articles developed by me where algebra is more abstract than in common group/ring theory stuff: en.wikipedia.org/wiki/Zero_object_%28algebra%29 and en.wikipedia.org/wiki/Left_and_right_%28algebra%29 . Do you feel the difference? $\endgroup$
    – Incnis Mrsi
    Dec 13, 2014 at 8:06
  • $\begingroup$ Thank you for the examples, this seems rather like Universal Algebra to me, which indeed is a field of mathematics, and also has a tag universal-algebra. $\endgroup$
    – quid Mod
    Dec 13, 2014 at 11:36
  • $\begingroup$ I do not understand this answer for 2 reasons. (1) your own re-tagging is slightly odd: tags are really just a way of organising questions in a way which allows people to find them, and if I want to find a basic ring- or group-theory question then I need go no further than the abstract algebra tag. (Also, I do not think that the "abuse" by academics is an issue - Fraleigh has a book called "abstract algebra", and I see no issue with its title. Just because a subject is not an area of active research does not mean that it is not a subject) $\endgroup$
    – user1729
    Dec 13, 2014 at 14:32
  • $\begingroup$ (2) I understood the question which you link to to be a notation issue by someone who was reading a book on abstract algebra. Therefore, the tag gave context. If it was tagged "graph theory" and they were asking about the symbol $\Gamma$, then I see no issue. From the asker's point of view, these examples are synonymous. $\endgroup$
    – user1729
    Dec 13, 2014 at 14:33

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