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4:37 AM
@quid I guess such tag might be useful.
This post created two new tags and .
Q: Techniques to prove existence of solution to constraint satisfaction problem

Martin Van der LindenI am trying to prove (or disprove) the existence of a solution to the following constraint satisfaction problem for any $(\vec{u},\vec{v}) \in \mathbb{R}\times\mathbb{R}$, any $b\in \mathbb{N}$ with $b \geq 1$, and any $n \in \mathbb{N}$ with $n > b$. $\vec{x} \in \{0,1\}^n$ $\vec{y} \i...

A: Tag management 2016

Asaf Karagila Status: Removed from all questions Is the embedding tag really useful? There are way too many things that can fall under this tag. From elementary embeddings in set theory, in model theory, to embedding of topological spaces, and to many other fields. Seems like a recipe for a messy and use...

A: Tag management 2016

paf Status: Removed from all questions Is there a need for the existing tag algebraic-systems? It contains only 6 questions and I don't understand its purpose. Maybe can we merge it into the tag system-of-equations?

1 hour later…
5:49 AM
A: Tag management 2016

Martin SleziakThe tag trigonometric-equations has been created recently. It is still listed among new tags. At the moment there are 4 questions in that tag. As far as I can say, questions about trigonometric equations have been tagged trigonometry so far. And also trigonometric-functions and trigonometric-ide...

6 hours later…
11:39 AM
@MartinSleziak: I put the number-theory tag back in there, because the only correct answer needs quadratic reciprocity. The tag descriptions seem to imply that quadratic reciprocity raises the question above our usual elementary-number-theory. I'm not sure that reciprocity is enough, because my rule of thumb is that if I know it, it is elementary number theory. What do you think? — Jyrki Lahtonen ♦ 8 mins ago
@JyrkiLahtonen Retagging based on answer is certainly common practice and that's perfectly ok. The only question is under which tag quadratic reciprocity belongs. Your edit is certainly in accordance with the current tag-info. There was a suggestion on meta that this topic belongs to elementary-number-theory tag, but no consensus was reached. — Martin Sleziak 51 secs ago
Personally I would say that the division into and is quite a mess.
Q: How to differentiate between (elementary-number-theory) and (number-theory)

Martin SleziakThe tags elementary-number-theory and number-theory have been recently mentioned in this question: There are 1,732 questions tagged both elementary-number-theory and number-theory However, in that question these two tags serve only as an illustration of a more general issue. In this post I'd like...

Q: There are 1,732 questions tagged both elementary-number-theory and number-theory

Najib Idrissi(Prompted by this question) As you can see here, there are currently 1,732 questions tagged elementary-number-theory and number-theory. (For the record, there are respectively 9,252 and 10,636 question in these tags, so that's not insignificant) It's always been my impression that these sort of...

@Jyrki I am not sure to which extent this might help restarting the discussion and eventually reaching some consensus. But if you think that some of the bullet points in my answer belong to (number-theory) rather than to (elementary-number-theory), you might post a competing answer.
A: How to differentiate between (elementary-number-theory) and (number-theory)

Martin SleziakI think that: The tag elementary-number-theory should not be a subset of number-theory, the later should be reserved for more advanced stuff. My impression is that these two tags have been used in this way historically. (This is also what the current revisions of the tag-wikis say.) I don't...

(I am posting this here on the off-chance that you will have a look in the tagging chatroom after our recent discussions about tags in comments on the main site.)
I added my upvote to your tagging proposal @Martin, if it weren't for the weight of history (of tagging practice on our site) I think we should adopt that suggestion. Continue the discussion there, if the need arises. Not a hugely pressing concern. — Jyrki Lahtonen ♦ 1 min ago
2 hours later…
1:35 PM
@MartinSleziak thanks for the reply. Absent objections in the near future I'll create it.
@MartinSleziak Indeed. I continue to think should be the most general, and further precision should be given by additional tags.
2:11 PM
Yes you have explained that in your answer there:
A: How to differentiate between (elementary-number-theory) and (number-theory)

quidThe tag number-theory should be an all encompassing tag for questions in Number Theory. It thus would naturally contain elementary-number-theory, analytic-number-theory, algebraic-number-theory and so on. Granted, this is a broad tag but still it conveys some relevant information. More specific ...

I do not share the same opinion, but I am certainly willing to go with the consensus. However, I am skeptical that some kind of consensus will be reached. (And on issue of importance like this we certainly cannot consider something around 5 votes a consensus.)
@quid But you will probably agree that this is not the way the two tags have been used historically on this site. So status quo seems to be that number theory is for more advanced questions, but the boundary is very fuzzy.
2:35 PM
@MartinSleziak Yes. But it is never too late to phase out a policy that causes more trouble and work than it solves. In my opinion there is just no need for a tag about "advanced number theory," since number theory is very diverse. I can see somebody following a tag on "algebraic-number-theory" or "analytic-number-theory" or "arithmetic-combinatorics" or "arithmetic-geometry" specifically. As said it'd be much better to spend the effort on applying proper subtags.
But without any suport on meta, how do you hope to persuade (or at least make aware) other users to change their taggging habits?
For example, Andres Caicedo used to retag plenty of questions in these tags - IIRC he was explicitly mentioned in comments to your answer.
@MartinSleziak you see right here right now I am trying.
And I also quite often use (elementary-number-theory) along the lines of my answer or the tag-wiki. And I think that I am doing the best I can to tag questions in the same way most users tag them and closest to what seems to be prevailing opnion.
@quid Personally, I will use those tags in the same way like before unless I see some clear consensus on meta.
But I will certainly try to avoid retagging wars.
@MartinSleziak I think the effort, undertaken in good faith, was just misdirected. Again a more useful thing would be to add additional tags to things tagged only number theory, like this question which is not advanced either.
2:51 PM
@quid Well, if I were to retag the question, I would remove and add and .
BTW we have already discuss this some time ago:

About (elementary-number-theory) and (number-theory)

Jan 30 '15 at 7:46, 15 hours 1 minute total – 151 messages, 4 users, 2 stars

Bookmarked Feb 2 '15 at 15:37 by Martin Sleziak

It seems that neither of us changed the opinion since then.
Yes. No problem with that tagging, except that I find the removal of NT pointless (though not really harmful). My point is though had the energy that was used to delete tags from old dually tagged question NT-ENT been spend on adding tags to questions tagged only NT then it would have been more useful overall.
Well, that is not entirely true, if tagging the question you linked by number-theory is considered incorrect. (Which to me seems to be the prevailing opinion and also agrees with the tag-info.)
Removing (number-theory) while retagging a question is not much more work than retagging a question and leaving it there.
Having said that, I do not explicitly look for questions tagged (number-theory) and retag them as (elementary-number-theory). But if I stumble upon a questions which I consider incorrectly tagged, then I try to retag it in the best way I am able to think of.
Of course, I might be wrong in saying that this is the prevailing opinion, but most retags of experienced users that I have seen tend to be in this direction. (But too many questions are tagged differently for this to be considered conclusive.)
@MartinSleziak my main problem is that I do not understand what problem is solved by considering this as "incorrect."
Also the voting on meta seems to be along these lines, but there are too few votes to consider this conlusive.
A thing I might get behind is to abandon number-theory as a tag altogether, on the grounds that it is too broad.
3:01 PM
@quid There are users who are good in advanced topics in number theory. Probably it is useful to have a way in which they can ignore questions like proving transitivity of $\mid$ and devote their time to the questions which are more in a need of experts.
Briefly said, the argument to keep them separate is similar to and . I cannot imagine merging these two tags.
There are no experts in advanced number theory.
So experts in number theory.
When Andreas Blass comes to this site and clicks on set-theory tag, I certainly prefer if he sees questions which require somebody as knowledgeable as him rather than seeing questions at level of proving associativity of $\cup$ and occasionally something more advanced.
Or let us say JDH. Or which-ever known set-theorist occasionally visits math.SE.
I think that number theory is different in that it is more diverse.
I agree that this is basically tagging questions by level of sophistication, which is generally agreed as wrong. But in the case of set theory and number theory, these tags have existed for a long time.
@quid But you agree that in set-theory there would be very strong opposition to join the two tags into one, right?
@MartinSleziak yes.
3:07 PM
To be honest, I do not answer questions from number theory very often.
I think that opinions of the people who are active in the tag should be important when defining the tag's content.
In the case of set-theory Asaf Karagila and Andres Caiceido do many retaggings. I'd say that they de facto curate these tags.
I am not sure whether there is a user active in number-theoretical tags who was involved in discussions about tagging.
As I said before, I have no problem follow the consensus, if some kind of consensus is reached. But at the moment it seems (at least to me) that the consensus is that (number-theory) is for more advanced questions. (Even the tag-info says so.)
@MartinSleziak Bill Dubuque
He is kind of a special case. It's difficult to have a serious discussion with him, in my opinion. (Of course, I might be wrong.)
Then what about me?
As I said, I have no problem adopting the position you're arguing for, if there is more wider consensus for it.
I see your point. But I think that there are also some advantages to keeping more advanced questions separate.
In any case, even if some consensus among users of this chatroom is reached, it is still not enough to consider it consensus of the community as the whole.
3:23 PM
Well, no. But it is remarkable that neither of us two could think of a number theorist in favor of that separation effort.
The best I can do is to promise that I will not touch (number-theory) tag, if you really consider the retags which I do misleading. (Or whatever was the word you used.)
Apart from Bill Dubuque and Adam Hughes (and perhaps you), can some of the users involved in that discussion be called number theorist?
Did Gerry Myerson comment on this?
When I look at top number-theory users, the names which I knew outside this site are Gerry Myerson and Matt Emerson.
Will Jagy is certainly a number theorist.
Sorry. Yes I mean Matt Emerton. He is notable enough to have a Wikipedia article.
Eric Naslund is a grad student in number theory like Adam Hughes.
I know that Gerry Myerson published some important papers about uniform distribution theory, which belongs under number theory. (I'd guess.)
3:29 PM
Jack D'Aurizio did his PhD in number theory.
It seems that you know enough about users of this site. Or are you just quickly checking the information in profiles?
Incidentally the only one I checked now is Adam Hughes
I would also count Charles as number theorist.
Dietrich Burde is maybe more in algebra but has an active side interest in number theory.
Yes. As I said, those two users are the only names which I would know even without encountering them on this site. I am certainly not claiming that other users there are not knowledgeable.
@MartinSleziak reading that page one could get away with the impression he is mainly notable for MO though :-)
(That was meant as a comment about that Wikipedia page not him.)
It seems that we digressed. I wanted to check whether some "number theory experts" contributed to the discussion on meta. (By experts I mean people who know enough about both the subject and about this site to be able to contribute.)
Which is not easy to say without reasonable criterion who should be considered expert.
If we consider bronze badge as the criterion, then I guess that most users who comment there would qualify as experts.
(Not me, though.)
Perhaps we can conclude this in the way that I will stop removing (number-theory) tag. And I will hope that some discussion on meta will lead to some kind of consensus one day.
3:50 PM
@MartinSleziak I have to deny being an expert in real-analysis. :-)
Ok, my whole digression about opinion of experts was probably blind alley. (I am not sure whether that is the correct idiom in English.)
is another tag with somewhat unclear usage. But that one is probably not that bad.
@MartinSleziak I do not care that much about the NT tag being preserved. As I said, I think it is a bit pointless but not harmful if it is removed. In the specific case you also added a specific tag, so the tagging was improved by your action in my opinion.
What I find unfortunate about the current situation is that to focus on elementary-nt and nt, maybe overshadows what would be more relevant in my opinion, namely to use more specific tags too.
In any case, changing (number-theory) tag would be a large retagging effort. Even if we try to retag only questions where it is standalone tag.
Thinking about perhaps the best solution, and maybe a way out, is to deprecate number-theory altogether.
If there is going to be some major retagging of questions of this tag or if the tag should be deprecated, that is certainly a major change. I would prefer to see some discussion on meta with something at least akin to a consensus before that.
4:07 PM
@MartinSleziak more than 3000 that's a lot.
It seems that (algebra) was around 600 or 700 when I first learned about the problems with that tag: chat.stackexchange.com/transcript/message/5031497#5031497
4:24 PM
hey I wanna ask something related to linear algebra. Can I ?
@AsMa this room is for questiosn about usage of tags. It is likely you do not want to discuss tags do you?
You could either ask in the general math room or on the main site.
@AsMa Here is link to the main chatroom and here is link to linear algebra room. The first of them has certainly more users.

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