This is meant to agglomerate tags that need (occasional or regular) cleanup. That is tags that mean multiple unrelated things and need to be separated into more specific tags. Please follow the examples below and discuss specific needs in comments or separate questions, as necessary.

Conversely, some subjects are scattered over several tags and there it might make sense to merge some tags and to create synonyms. Proposals for such can also be added as answers.

As of August 8, 2017, the length limit for tags went from 25 characters to 35 characters. So now is a great time to allow inconveniently compressed tag names to stretch out a bit...

PS: If you want to cleanup these tags, please keep your rate down to a few posts per day so that your edits don't clutter the main page. Also note that merges can be done by moderators in one go without bumping questions. Thus, it is usually better not to carry out non-minimal merges manually (where non-minimally could mean more than three to five).

  • Can you simply delete all tags that have < x followers, where x is a positive integer the moderators set? – Bill Johnson Sep 24 '13 at 1:08
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    @Bill: That would delete a lot of seldom used tags, which is not the intent here. – François G. Dorais Sep 24 '13 at 1:10
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    Maybe not, François, but it would help to delete these tags. – Bill Johnson Sep 24 '13 at 1:48
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    @BillJohnson, another objection is simply that many people don't use the 'favorite' and 'ignored' system, but tags are still useful to them. I don't think there's any guarantee that every "interesting-to-someone" tag is actually a 'favorite' of anyone. – Scott Morrison Sep 24 '13 at 1:59
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    I completely agree with @BillJohnson that there are too many tags and I think we should try to get rid of quite a number of them. One could discuss what is the best way to go about this, but that there are too many tags for me is a given. (And I write this as someone who actually read the pages over pages of tags, more than once.) – user9072 Sep 24 '13 at 12:44
  • By the way, is there a particular reason why MO uses its own classification of subjects in mathematics rather than a tag system along the lines of the MSC ( – Stefan Kohl Sep 24 '13 at 13:28
  • @StefanKohl MO uses the (simpler) arxiv classification. – François G. Dorais Sep 24 '13 at 13:41
  • Only a small part of the tags are actually arxiv tags. -- The arxiv classification doesn't go very much into detail, which is -- besides the easiness of creating new tags -- probably the reason for the many additional tags, including tags with unclear meaning and outright 'clutter tags' (though some of the latter have been removed in the course of the thread…). – Stefan Kohl Sep 24 '13 at 15:32
  • @StefanKohl: Yes, feel free to ask for the deletion of some clutter tags. (It's best to ask a question on meta since a some users like to assist in cleanup efforts.) – François G. Dorais Sep 24 '13 at 15:42
  • @FrançoisG.Dorais: I think the main point are not single inappropriate tags. Contrary to the top-level arxiv categories, the MSC is already fully-thought reasonably complete standard classification, and I think adopting it for MO would probably remove the need to think about adding or removing tags, about which tags are appropriate and which are not and about which tag means what. Or do you see a reason for MO's partial reinvention of the wheel here? – Stefan Kohl Sep 24 '13 at 15:53
  • @StefanKohl: Users are able to create their own tags. The system was seeded with arxiv tags to get things going but there was no long-term plan to keep them. The main problem with MSC is that it's too large. – François G. Dorais Sep 24 '13 at 16:00
  • @FrançoisG.Dorais: Sure, there are 4 or 5 times as many 5-digit MSC numbers than tags in MO -- but contrary to MO tags, the MSC is an hierarchical scheme. Thus if e.g. using two of the three levels is sufficient for MO, one could well restrict to that. – Stefan Kohl Sep 24 '13 at 16:14
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    @StefanKohl, one problem with MSC numbers is that they are unintuitive numbers and so except for the ones I use frequently, I would not recognize most of them. – Benjamin Steinberg Sep 24 '13 at 17:12
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    @StefanKohl, the OP would still need to look up the code before posting. – Benjamin Steinberg Sep 24 '13 at 20:49
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    @BenjaminSteinberg: actually, they wouldn’t need to! The auto-complete system here is clever enough that if a tag is called e.g. “54-XX-general-topology”, it will be suggested when you start typing “topology”. Honestly, that would give a better lookup interface for the MSC than the current official ones… – Peter LeFanu Lumsdaine Oct 8 '15 at 14:53

16 Answers 16

The tags and are (unsurpsingly) used for both the 'order' and the 'geometric' meaning.

(I am not sure what to do here; perhaps it deserves a full question, but I thought I'd post here first to get some initial reaction.)

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    There was an old discussion on tea about this. – François G. Dorais Jan 15 '14 at 15:27
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    Thanks for pointing this out, I should have known/checked. Yet, while in some sense there were even two: in the very old Ryan Budney suggested upon Mariano mentioning the problem, to have lattice-poset and lattice-subgroup In… the issue is somewhat different as I think in that request the order meaning was ignored and the issue was distinguishing between really geometric objects and more algebraic things (vaguely), and there is euclidean-lattice for the former. – user9072 Jan 15 '14 at 16:38
  • Oh I forgot to finish my idea... While the subject came up there was not much discussion and/or they were somewhat inconclusive (regaridng the matter I have in mind) except for Ryan's (IMO, good) idea that never got implemented though. – user9072 Jan 15 '14 at 17:58
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    For this, we should fix the terminology everywhere in mathematics, not only on the MathOverflow website. Also, let's fix "field" too while we're there. – Zsbán Ambrus Apr 9 '14 at 9:46
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    @ZsbánAmbrus what do you want to express precisely? – user9072 Apr 9 '14 at 14:38

There is a built-in system to automatically create tag synonyms by the nomination and voting of high-reputation users. Unfortunately, it appears that hardly anyone ever looks at this page (and the qualifications for voting are fairly demanding), so I'm posting it here to try to get it more attention. In particular, all of the synonyms marked as "pending" are languishing in neglect until they get four people (or a moderator?) to vote for them, though I think some of them are going the wrong direction.

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    It might be worth adding that to vote one needs to (at least I think so) click on the left tag of the two to get to its page where the voting possibility is. – user9072 Dec 9 '14 at 19:10
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    There is no way to discuss the synonyms suggested through this system, or is there? – Emil Jeřábek Dec 9 '14 at 22:28
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    @EmilJeřábek for all I know, no. If you do not approve of one, you can downvote it, and if it reaches score -2 (or something like this) it is deleted. – user9072 Dec 11 '14 at 17:40

The tag is mainly used for questions in a probability context but there are some other "Gaussian" things in there too, e.g., Gaussian binomial coefficients, Gaussian integers.

Perhaps, the current tag should be renamed to something more specific, like gaussian-distributions or gaussian-variables or something along these lines (not sure, suggestions welcome). And the (few) existing ones where it then does not fit could be retagged.

Note there is also a tag .

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    Is the dv against the renaming or against the tag being reserved for the prob context. Or against still something else. In any case it would somehow help the discussion if such things where communicated else it is anybodies guess what is the intent. – user9072 Sep 27 '13 at 16:46

The tags matrix-analysis (32 questions tagged) and matrix-theory (18 questions) should probably be merged, unless there is a strong difference between them that I am not aware of (incidentally, there is also matrices, 150 questions tagged).

The tag matrix-inverse (6 questions) seems overly specific and in my opinion it should be removed outright.

  • There is also matrix-equations but there is no matrix-algebra. I don't know what the differences could be; I hope somebody will explain. Are these tags used in significantly different ways? – François G. Dorais Jan 16 '14 at 4:32
  • The ones I have heard in real life are: "matrix analysis" for the study of matrix inequalities and advanced linear algebra (e.g. [[1]](…)); matrix functions and matrix equations (mostly numerical/applied; e.g. [[2]]( "matrix algebra" is not that common and typically used by non-mathematicians. "matrix theory" sounds strange to my ear. – Federico Poloni Jan 16 '14 at 5:29
  • My suggestion is as follows: make matrix-theory a synonym of matrix-analysis; I could consider merging them both into matrices, although that's a bit generic; Stet matrix-equations, remove matrix-inverse – Federico Poloni Jan 16 '14 at 5:32
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    re matrix-theory: I think this is an instance of a sort of general MO phenomenon, users add 'theory' to distinguish it from just the 'thing' that is perhaps too generic as a tag; we had some discussion on order-theory. For some q tagged matrix-theory it seems matrix-analysis would not fit. One could go over the list though and extract these things relatively quickly. For matrix-inverse, I am in favor of getting rid of it yet via a synonym, else people will recreate it, or even worse use just inverse which should also be listed here in fact. – user9072 Jan 16 '14 at 13:14
  • There are also various other tags containing matrix and matrices some very little used. Would you have an opinion on some more of them? – user9072 Jan 16 '14 at 13:16
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    Personally I'd keep matrices, random-matrices, matrix-analysis, nonnegative-matrices, matrix-equations and maybe sparse-matrices. I don't know what r-matrix refers to; if it's short for "random matrix" then merge. m-matrix and copositive-matrix can be merged into nonnegative-matrices. adjacency-matrices and matrix-tree into some variant of graph-theory I guess (not an expert). nilpotent-matrices, circulant-matrices, orthogonal-matrices seem too specific. – Federico Poloni Jan 17 '14 at 2:56
  • We should look for more opinions though, there are surely lots of other people with different viewpoints than mine on "matrix stuff". – Federico Poloni Jan 17 '14 at 2:58
  • Thanks. This looks good to me. The tag r-matrix was created for something called "R-matrix" in quantum algebra/groups (I don't know what it is though). It was misused a bit though. I think/hope I 'cleaned' it just now, and it is just this qa thing now, which one might keep (but I cannot tell); preferably with a tag-wiki so it does not get used again for dealing with matrices in the software R... For matrix-tree this is uniquely used and not even very relevant where it is used, I would simply remove it; for adjacency-matrix one could set up a synonym into algebraic-graph-theory – user9072 Jan 17 '14 at 10:53
  • Also talking about matrices, @FrançoisG.Dorais now that we have sysnonyms could you please set up the synonym matrices <--- matrix I think there is some risk of people not finding the tag due to the (unusual) plural. – user9072 Jan 17 '14 at 10:56
  • thanks for the retagging effort @quid. – Federico Poloni Jan 17 '14 at 11:10
  • @quid: When a tag doesn't exist, I don't think I have a quick way to create a synonym so it's just as easy for you to suggest it as it is for me. – François G. Dorais Jan 17 '14 at 17:01
  • @FrançoisG.Dorais oh, I was not aware of this, and I have to confess the fact that I can suggest syns did not really sink in either. I will try it some time soon and in the meantime voted on the syn. But also, while in this case it is true I could have suggested it, this is not always the case as a user (besides globally enough points) needs some score (namely 5) in the tag. – user9072 Jan 18 '14 at 1:15

As of August 8, 2017, the length limit for tags went from 25 characters to 35 characters. So now is a great time to allow inconveniently compressed tag names to stretch out a bit...

Perhaps we could collect here list of tags which now, after the character limit for length of tag name has been extended, could be spelled in full instead of a shortening. (This answer is CW - feel free to edit in here various tags that are currently shortened.)

Among possible suspects are the tags with name of length 25 - they can be found by this SEDE query: Tags with given length of name. (However, not all shortened tags use exactly 25 characters. Two examples are or .)

Shortenings to be expanded

  • vs. (Both names should be kept here with a synonym in one or the other direction. After all, people around here know what GCH is, so it probably can remain the master tag. But adding a synonym might be useful addition, since people looking for the tag corresponding to their might start to write something liked "continuum hypothesis" in the tag field.)
  • $\to$ , $\to$ (Maybe shortened names could be kept as synonyms - since MO users are probably used to them by now?)

Shortening which moderators already replaced

Synonyms with names longer than 25 characters

1There is a separate discussion whether there could be a better name for this tag: The tags (transcendence) and (transcendental-number-theory).

I suggest deleting the tag .

I would guess that the tag was intended to be about the decomposition theorem of Beilinson-Bernstein-Deligne-Gabber. It seems unnecessary to have a whole tag just dedicated to this theorem ( should suffice). What's worse, most posts with this tag are just about various "decompositions" in any area of mathematics.


I propose to deprecate . It seems redundant with other tags, very broad, and the usage seems inconsistent.

I feel it is comparable to the meanwhile removed and the deprecated .

(Explication on terminology: To deprecate a tag is not a technical measure. What it means is that the tag-description is changed to say this tag should no longer be used. Over time it could then be slowly phased out via retagging.)


I propose to deprecate . It seems redundant with other tags, very broad, and the usage seems inconsistent.

I feel it is comparable to the meanwhile removed and the deprecated .

(Explication on terminology: To deprecate a tag is not a technical measure. What it means is that the tag-description is changed to say this tag should no longer be used. Over time it could then be slowly phased out via retagging.)

I would suggest creating a synonym between and . (In either direction. The tag (models-of-pa) already exists, but IMO adding also a longer name (models-of-peano-arithmetic) might be useful.)

The advantage of the synonym is that users who are asking a question from this topic might start typing "peano" in the tag field. After adding the synonym, they would also see this tag, not only . (I'd guess that the name which is not that easy to find might be part of the reason why (models-of-pa) only has 5 questions and 3 followers.)

I have posted this as a separate answer (and not among other length expanding suggestions) since this answer is also a good place where to discuss whether (peano-arithmetic) and (models-of-pa) should be separate tags or the questions should be under the same tag. (I am slightly more inclined to keep them separate, but it would be much better to know what users who are active in these tags think about this.)

The tags and should be merged; the first being more used, and also in analogy with the tag , I'd suggest to embed into .

Making a synonym $\to$ would also have the advantage that the latter tag is suggested when people type "ring". (Note: has already been embedded in .)

  • Re: does not include the word "ring" in its wiki, and hence is not suggested when people type "ring". In fact, the tag-wiki does not influence whether the tag is shown when you type something in the tag field. This is influenced only by tag names (including tag synonyms). – Martin Sleziak Feb 18 at 15:59
  • @MartinSleziak right, thanks. Btw the edited tag-wiki for noncommutative-algebra now mention rings, but this means that it will be suggested from typing rings only when they'll be made synonyms. – YCor Feb 18 at 16:10
  • I have edited your post to correct the information saying when the tag is suggested. (And to some extent also to make your post shown if somebody views the last activity in the question.) When you have time, please do edit the post further to get it to the form you are satisfied with. – Martin Sleziak Feb 19 at 7:22

The tag was created recently in the question: Is the sum of a Darboux function and a polynomial necessarily a Darboux function?

Generally, one-word tags (where the word is part of the name of some mathematical object or area) tend to be problematic, since they are likely to be used for some other stuff which contains the same word/adjective. For example, if somebody asks a question about Darboux sums and they are looking for a suitable tag, they might simply use this one. Since there are many things named after Jean Gaston Darboux, we might end up with a tag containing questions asking about various completely unrelated things.

Judging by the question where the tag was created, the intention was clearly to create a tag for Darboux functions (and maybe also closely related Darboux's theorem). One additional problem with this that many people know this under the name intermediate value property and not everybody is familiar with both names.

My suggestion is that: Instead of the tag for Darboux functions should be called . And it would be useful to create also tag and make the synonym between the two tags. (By creating a synonym we achieve that if somebody knows only one of the two names - Darboux functions and intermediate value property - and they are looking for tag about this topic, they can find it whether they are searching for "Darboux" or "intermediate".)

  • There is only one question with this tag. Is there additional interest in fixing this? – François G. Dorais Feb 18 at 19:02
  • I suppose that by your comment you suggest to remove the tag. I have no problem with such solution if the topic is too specific to have a separate tag. But I still think that if there is a tag for this topic, (darboux-functions) is a better name than just (darboux). There are a few other single-word tags which seem slightly problematic, too. – Martin Sleziak Feb 18 at 20:38
  • The tag (darboux) has been removed. – Martin Sleziak Oct 26 at 8:16

I propose to merge and .

Both have a comparable number of questions (total 249 and 171; only 38 are both tagged both, and hence 382 questions are tagged at least one).

Mathematical rationale: Recall that a monoid is a semigroup with a unit. Every monoid is thus a semigroup; every semigroup yields a monoid by adjunction of a unit. This is a little nuance but the two subjects are much too intertwined to justify a distinction. For instance in the study of monoids one naturally considers non-unital subsemigroups, notably ideals.

In the tags for ring analogues (commutative algebra, non-commutative versions, C*-algebras, etc), there's no such distinction: it would make little sense, for the same reason: too closely related objects, studied by the same people.

Practical rationale: the above distinction is not very well reflected in practice: a significant number of questions tagged refer to monoids.

So I think one should merge them. Actually one could even create and put the latter two as synonyms; it has the advantage of avoiding a 1-word tag and would be a tag with a consistent use (in that currently the questions about this subject are quite consistently tagged in either and and occasionally both). It's a minor variant (if not, one has to choose between the two and sounds a bit better, just because it rings more bells and possibly sounds less restrictive). This latter point is, anyway, unessential.

  • There are differences between looking at semigroups and monoids just like there are differences between locally compact spaces and compact spaces despite the fact that you can go from one to the other by adding a single point. The difference comes because the morphisms are quite different. A simple example is every finite monoid which has no non-trivial homorphic image is a group except the multiplicative monoid of the 2-element field and this is an easy exercise for a graduate algebra class. For semigroups there is an additional infinite family that non-specialists are unlikely to find. – Benjamin Steinberg Mar 9 at 14:22
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    @BenjaminSteinberg I'm aware of the difference (and I thought that I made it clear in my post). The distinction between non-unital rings and rings is also essential. But the subjects are too intertwined, this is my point. It's exactly as absurd as making a tag distinguishing compact and locally compact topological spaces, or distinct tags for unital and non-unital rings. Fortunately there's none. – YCor Mar 9 at 14:25
  • ... or a tag "pointed-sets" :) – YCor Mar 9 at 14:51

I suggest to burninate .

It has 7 occurrences at the time I'm writing.

4 of them are concerned with the meaning of discrete series in the context of the classification of unitary representations of semisimple Lie groups or analogues (the "space" of irreducible unitary representation typically has a "discrete" and a "continuous" part.

3 others are unrelated, more related to something which is related to both keywords, and are themselves pairwise unrelated.

All 4 above have the parent tag . (Unfortunately there is no coherently used tag which would focus on the well-defined domain "unitary representations", or its more specific "classification of unitary representations of semisimple groups", although these are quite broad. Maybe I'll propose something for this issue later but I first should have a more systematic overview, which will be time-consuming.)

We can't expect every user here to be aware of the specific representation-theoretic meaning of . Also this tag is used too scarcely, compared to the effective occurrence of discrete series, to be useful. This is why I suggest to burninate.

The tag has a number of completely different questions. There's a definition in probability theory, as an increasing sequence of $\sigma$-fields. There also appears to be some completely different meaning in homological algebra or some other areas (too far from my own for me to understand).

Is this notion worthy of its own tag in any of these cases? (For probability I don't think filtrations need their own tag; I'd just use .) If so, a more specific tag should be made and an appropriate wiki written. If not, then perhaps the tag should just be destroyed.

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    The probability theory notion and the algebra notion are actually essentially the same (a nested chain of substructures), though in practice the ideas needed to think about the two are pretty much unrelated. – Eric Wofsey Oct 8 '15 at 21:29

I'm not sure if this is the right place to raise the issue, but I don't really like that has been merged with . In my opinion, this is the same (in a smaller scale) as merging combinatorics into discrete mathematics. There are many problems in discrete-geometry that have nothing to do with combinatorics.

  • That merger was done on December 15, 2014. We can't undo the merger but we could remove the tag synonym to allow future uses of combinatorial-geometry. A test for doing this is to propose a tag info blurb which demonstrates how the two tags are different. – François G. Dorais Aug 3 '17 at 22:28
  • @Francois So I should propose a tag info for combinatorial-geometry? I would write something short and simple, like Combgeo. is the study of combinatorial problems that involve geometry. Btw, how can the description of discrete-geometry include that "It is closely related to [...] combinatorial geometry" if the latter is a synonym of the former? – domotorp Aug 4 '17 at 8:47
  • I'm not sure I can see a problem. For the distinction it's enough to use either the tag "discrete-geometry" or the combination of "discrete-geometry" and "co.combinatorics". – YCor Feb 18 at 19:27
  • @YCor Then this should have been done when the merger happened, right? Not to mention that I don't recall seeing anyone ever applying both tags. I also don't think it's good to make people double-tag almost all the time, because a large part (but not all) of discrete geometry is combinatorial geometry. – domotorp Feb 19 at 13:44
  • @domotorp co.combinatorics is a top-level tag so basically every question pertaining to combinatorics gets this tags (unless it has comprises too many topics, but this concerns a very small minority). Usually when anybody ask such a question without tagging combinatorics, somebody adds the tag. As discrete-geometry, the topic makes the tag natural, and also it is regularly added. Adding another tag which basically is relevant iff two other wider tags are simultaneously relevant, would in practice just increase entropy. – YCor Feb 19 at 14:26
  • @YCor I would challenge the statement that every question pertaining to combinatorics gets the tag. Check graph-theory; the majority of the questions doesn't have co-combinatorics: – domotorp Feb 19 at 21:48
  • @domotorp some people say that every question in graph theory should also be tagged combinatorics. In any case, a very large majority of these questions would perfectly fit in co.combinatorics – YCor Feb 19 at 21:55
  • @YCor That's my point - people still don't label them co.combinatorics, so you also shouldn't expect people to label the ones that have combinatorial-geometry or discrete-geometry. – domotorp Feb 20 at 7:23
  • I know it's hard to rely on a good labeling and acquainted users can help by editing tags. In any case, in such situation the entropy (I mean the mess) is an increasing function of the number of relevant tags. – YCor Feb 20 at 15:45

There are tags and . Neither has a wiki or guidelines for usage. The tag seems to be more popular. Should these be merged?

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