8:00 AM
Elementary probability problems and more advanced probabilistic concepts should definitely not be merged. These are handled very differently and require very different levels of mathematical knowledge. As an analogy: imagine if we merged number-theory and elementary-number-theory – what a disaster that would be! — URL yesterday
From the comments, it seems that the situation in and is not good. (Not enough users to maintain the two tags, probably they are used rather inconsistently.)
I still think that it would better to have a discussion about those tags in a separate question - but I have doubts whether the discussion would bring anything new. (I suppose many users are aware of the problem.)

10 hours later…
6:11 PM
Why the ´holomorphic´ tag disappeared?

6:28 PM
@Isabellatrix Which tag do you mean exactly? I see that there are tags , , .
The tag is a synonym of complex analysis. (And it seems that the synonym was created in 2016.)
The fact that the tag is a synonym means that if you add , it is automatically changed to . Is perhaps this what you wanted to know?

@MartinSleziak I meant this one. IIRC, days ago the tag was there explicitly. Now if I add the tag, it automatically disappears

If you look at the list of tag synonyms, it says that it was created May 28 '16. (If I understand correctly what the columns on that page mean.)
Ok, so maybe I misunderstood something. Wayback Machine shows it as a separate tag in February 2017.
Google Cache shows version from January 3 - there it is shown as (complex-analysis).

well, it's gone now. IMO the tag was fine, to classify better

6:47 PM
I have asked on Meta Stack Exchange about meaning of the column with the dates: What does the column “created” in the list of tag synonyms mean?

7:37 PM
@Isabellatrix So it seems that May 28 '16 is the date when the synonym was proposed. It was approved in March 2019.
At least that is what I get from this SEDE query.
And also from queries showing all tag synonyms and all approved tag synonyms.
The suggestion to look at SEDE comes from rene's answer: What does the column “created” in the list of tag synonyms mean?

8:02 PM
@MartinSleziak so users have been using the tag since May 28 '16, right?

Probably even longer, May 2016 is when the tag synonym was proposed.
Possibly query from this post might help: Can you tell who created a tag.

when was gone?

The query found posts from May 2016: data.stackexchange.com/math/query/542457/… This is the oldest occurrence of the tag I can see: math.stackexchange.com/posts/1766403/revisions
I don't see older occurrences with these two queries, either: data.stackexchange.com/math/query/927958/… data.stackexchange.com/math/query/883845/…
Perhaps I should explicitly point out that on the question "Existence/non-existence of Holomorphic Function" you can still see both tags. Similarly for other questions that haven't been edited after the approval of the tag.
2

Let $D=\{z\in \Bbb C:|z|<1\}$. Show that there exists a holomorphic function $f:D\to D$ such that $f(\frac{3}{4})=-\frac{3}{4}$ and $f^{'}{(\frac{3}{4})}=-\frac{3}{4}$ Show that there exists no holomorphic function $f:D\to D$ such that $f(\frac{1}{2})=-\frac{1}{2}$ and $f^{'}{(\frac{1}{... @Isabellatrix The synonym was approved on March 23 2019. @MartinSleziak how does this answer my question :) i don't get it And what is your question? You asked when the tag was gone. The tag isn't gone - it is a synonym of another tag. Probably I misunderstood what you're actually asking. 8:14 PM @MartinSleziak it's gone because, when I suggested an edit to 'add' that tag (and then the suggest edit it's approved), then the tag doesn't appear. Well, as I said, the tag is automatically changed to (complex-analysis). (Because it is a synonym.) days ago, was different, the tag appeared as expected If a synonym is cancelled, then you'll be able to add the tag. (Tag synonyms can be cancelled only by mods. Of course, there has to be a good reason to do so.) @Isabellatrix As far as I can tell, the synonym exists since March 2019. (So if somebody tried to add the tag to some question in February 2019, it would be added. If somebody tried to do so in April 2019, it would be changed to complex-analysis.) For example, you have edited this question on January 1. You can see that the questions has (complex-analysis) tag. (Although I cannot be sure whether you were trying to add (holomorphic-functions) there.) To the best of my knowledge, it behaves in this way since March 2019. (By "behaves this way" I mean that (holomorphic-functions) is automatically changed to (complex-analysis) when editing.) I don't really understand what you mean by the most recent message. sorry, i'll write differently If you want to know what are consequences of cancelling a synonym, perhaps the explanation given here would help: What happens with the tagged questions when a tag-synonym is cancelled? 8:28 PM @MartinSleziak "If a synonym is cancelled, then you'll be able to add the tag." if it's uncancelled, then users won't see it anymore? and so on and so forth? What you mean by uncancelled? That the synonym is created again after being cancelled? At the moment, if you add (holomorphic-functions) it si automatically changed to (complex-analysis). (Because there is a synonym between those two tags.) @MartinSleziak aha, and then all of the questions that 'used to have' such tag, will have that tag again. Tag path-integral in Physics SE @Isabellatrix The questions which had the tag before approval of the synonym and which haven't been edited after the creation of the synonym. Here is a quote from the post I linked above: > This means that questions tagged before the synonym was introduced (and not edited while the synonym was in place) will have that tag after the synonym is removed. However no question created while the synonym was in place will be tagged . As I said, at the moment (holomorphic-functions) is automatically changed to (complex-analysis). If a mod cancels the synonym, they will behave again as two separate tags. The question what happens with the questions that used to have tag before is a bit more complicated - but it is explained in the answer I linked. (And the quote above is the jist of it.) @MartinSleziak ok, so for instance a question that had (holomorphic-functions), (but due to the synonym) now doesn't have it, will have the (holomorphic-function) again if mods cancel the synomym? 8:38 PM No, if the question no longer has (holomorphic-function) tag, then it won't have it even after cancelling the synonym. But as I shown on an example above, some questions still do have the tag. For example, the question "Existence/non-existence of Holomorphic Function" got this tag before the synonym was created and it hasn't been edited after the synonym was created. After considering it twice, I think it's better to delete tag and create , not . For those who know, funtional integration is equivalent to path integral. For those who don't, they won't use for line/contour integrals. So it still has the tag. 2 Let$D=\{z\in \Bbb C:|z|<1\}$. Show that there exists a holomorphic function$f:D\to D$such that$f(\frac{3}{4})=-\frac{3}{4}$and$f^{'}{(\frac{3}{4})}=-\frac{3}{4}$Show that there exists no holomorphic function$f:D\to D$such that$f(\frac{1}{2})=-\frac{1}{2}$and$f^{'}{(\frac{1}{...

That means that if the tag synonym is cancelled, this question will have the two tags. (Unless somebody edits the question before that.)