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In guidance How to ask a good question. it states:

Make your title your question
Use your title to convey as much information about your question as possible. Since the tags already convey the general subject area of your question, the title should communicate the question itself as faithfully as possible. If necessary, leave out hypotheses in the title, and in the body of the question, explain why the question requires those hypotheses.

and

Don't be afraid to make the title long
Titles are allowed to be anywhere from 15 to 150 characters long. 140 characters (the length of a tweet) of plain text take up about two full lines on the home page, so try to keep it less than that. But 140 characters is a lot longer than you might think. Too many people restrict themselves to 20 character titles. They're trying not to waste your time by making you read a long title, but they end up wasting more of your time because you have to actually open the question to see if it's interesting to you.

I was wondering why these two edits are rejected:

$1$.https://math.stackexchange.com/review/suggested-edits/1155227
$2$.https://math.stackexchange.com/review/suggested-edits/1155567

My idea is to put enough information in the title as much as possible like the guidance says, espcially about notions since not all notions are so widely used and may cause minunderstanding, but my two edits were rejected because "This edit does not make the post even a little bit easier to read, easier to find, more accurate or more accessible. Changes are either completely superfluous or actively harm readability."

Could anyone please what a good title should be? Thanks in advance :)

After comparaing these two almost same edits, I begin to realize it's much person-based.

https://math.stackexchange.com/review/suggested-edits/1155567 https://math.stackexchange.com/review/suggested-edits/1155916

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    $\begingroup$ Some were rejected whilst some were accepted because people have different opinions. Personally, I would have steered towards rejecting your edits. Titles which are too long and convoluted can put people off (me included!). For example, I would have rejected this one. The original title "Isomorphism of tensor product of representations" was indicative of the type of question, while the first line of the question tells me that $G$ is a Lie group, etc. When I am browsing my tags I can see the first lines of questions. $\endgroup$ – user1729 Feb 18 at 12:31
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    $\begingroup$ Basically: A title should be informative, but not necessarily self-contained. I does not need to ask the question outright; that is what the question is for. In my opinion, short titles are better. $\endgroup$ – user1729 Feb 18 at 12:33
  • $\begingroup$ @user1729 I know shorter is better, so I will change if and only if to $\iff$ etc. But in the question for example math.stackexchange.com/review/suggested-edits/1155567, we usually use $I$ to represent an ideal, so I think explain what $I$ here stands for is necessary. In my opinion, if you want to ask a concrete question (like the "Isomorphism of tensor product of representations" one ), the title should be clear and specific rather than too abroad unless you want some general methods to deal with a type of question. $\endgroup$ – Andrews Feb 18 at 12:46
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    $\begingroup$ I would also have rejected these edits - a title doesn't have to be totally self-contained, and sometimes short is better. $\endgroup$ – Noah Schweber Feb 18 at 15:34
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    $\begingroup$ A better use case for edits is where the title contains crucial problem details that are not included in the body of the Question. It is the body, rather than the title, which should have a fairly self-contained problem statement. $\endgroup$ – hardmath Feb 18 at 15:37
  • $\begingroup$ @NoahSchweber I know short is better, but if it doesn't contain ehough information, others may have no idea what this question is about. for example math.stackexchange.com/questions/3116102/… You have no idea what $\Bbb Z(i)^*$ is, and at the homepage you won't see first two lines of the body. $\endgroup$ – Andrews Feb 18 at 16:31
  • $\begingroup$ @Andrews I would take the response to this question as evidence that others may not agree with you on this point. $\endgroup$ – Noah Schweber Feb 18 at 16:33
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    $\begingroup$ For what it's worth, I think the second edit is significantly better than the first. The notation $\mathbb{Z}(i)^*$ is close to standard and in any case it is not hard to guess what it might mean. On the other hand, the original title of the second question was terrible because it gives no clue about what $I$ is and that is crucial to the content of the question. $\endgroup$ – Eric Wofsey Feb 18 at 20:08
  • $\begingroup$ Thanks for adding the quotes from the A good title section of the Meta Math.SE post on how to ask a good Question. As a result of this research demonstration I retracted my downvote here. That said, I think the advice to "Make the title your question" and "Don't be afraid to make the title long" do not justify putting the entire problem statement into the title. $\endgroup$ – hardmath Feb 20 at 16:54
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I think this gets ultimately to the purpose of the title in the first place: in my view, the title of a question is not in general supposed to constitute the entire question itself. Rather, its main function is to clearly advertise (in a good way) the question. That is, I don't think that it's reasonable to require that a question be answerable without looking at the body.

In this light, edits which add detail to the title are not inherently good, and may in fact be viewed (e.g. by me) as negative. Obviously the precise delineation is subjective, but I think the key point is that your mentioned edits may have been made with a particular role in mind for the title which is not in fact universally assumed.

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    $\begingroup$ (+1) for the point that a title is an advertisement, not the actual question. $\endgroup$ – T. Bongers Feb 18 at 16:40
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    $\begingroup$ Even if the title does not contain all details of the question, still it is good to make the question in some way recognizable or distinguishable. For example, "How to find the limit $\lim\limits_{n\to\infty}\left(1+\frac1n\right)^n$?" is definitely better than just "How to find this limit. Typical situation: If you look at results of a search, list of related questions, etc., you can locate duplicate much more easily with the more descriptive title. $\endgroup$ – Martin Sleziak Feb 19 at 6:33
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    $\begingroup$ @MartinSleziak Of course - that's what I meant by "clearly advertise." But I don't think that's what the OP's edits are (mostly) doing, really. $\endgroup$ – Noah Schweber Feb 19 at 21:22
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I'm glad that you're trying to help out, and I think that editing vague and unhelpful post titles is a good way to start (so I'm sorry in advance if a lot of the later post comes across as very blunt).

That being said, I think that many of these edits should have been rejected, even if they were approved. Titles should be descriptive of question content, but that doesn't mean that they need to contain all the symbols or definitions or assumptions introduced in the question body. Titles that are excessively symbol-laden are hard to read, unsearchable, and confusing. Let's take this approved edit as an example: granted, the original title is pretty bad but

$x \neq y\in$ metric space $M$, prove $\exists$ open sets $U,V$ s.t. $x\in U,\ y\in V$ and $\bar{U} \cap \bar{V} = \emptyset$

really hard to read. It's a jumble of symbols, with $\exists$ tossed into the middle of a sentence, and s.t. abbreviated when there's no need. It's also hard to understand at first glance - I have to unpack all the symbols and read it at least twice to understand what it's about. It's certainly not something that I could read aloud as written. Why not something like the following?

Prove that in a metric space, there are disjoint sets containing two points.

I don't claim this is a perfect (or even good) title, but it hits the key points: there's a metric space, there are points, and there is something about disjointness. Maybe put a phrase about the topology in.

The reasons for your edits are also a bit confusing:

I suggest the title should involve enough information as much as possible to avoid misunderstanding

If someone wants to avoid misunderstanding, then there's a perfect place for that: the question body!

In short: Notation is meant to clarify things. Excessive notation can be obfuscating, and notation being used to replace natural language words frequently is.

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  • $\begingroup$ Sorry for making you confused. As far as I was taught at school,"$x≠y∈$ metric space $M$, prove $∃$ open sets $U,V$ s.t. $x∈U, y∈V$ and $\bar U∩\bar V=∅$" is written in math language and is promoted(at least at school), while "Prove that in a metric space, there are disjoint sets containing two points." is more discriptive. Also, the guidance says "Use your title to convey as much information about your question as possible. Since the tags already convey the general subject area of your question, the title should communicate the question itself as faithfully as possible." $\endgroup$ – Andrews Feb 18 at 17:02
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    $\begingroup$ @Andrews T. Bongers' point was not that he didn't understand the symbol-laden title, only that it is difficult to read, as it is not written in natural English. A title like "Prove that any two points in a metric space can be contained in disjoint closed sets" (or something like that) is much easier to read and conveys essentially the same information. Again, the point of the title is to advertise the question. The nitty-gritty details should be in the question body. $\endgroup$ – Xander Henderson Feb 18 at 17:06
  • $\begingroup$ @XanderHenderson I understand. Maybe because I'm a student, I prefer a test paper style title rather than an advertisement style title. Since MSE is a Q&A website rather than an exam paper, I suppose the latter style is more readble and attractive. $\endgroup$ – Andrews Feb 18 at 17:15
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    $\begingroup$ @Andrew you seem to have the misconception that symbol-laden means more mathematical, more formal, or otherwise better. The truth is random, careless use of symbols only confuses and is certainly not better or more formal. If you do a quick browse of MathOverflow you'll find that rarely do mathematicians use symbols to obfuscate, and when English does the job, they use it. $\endgroup$ – YiFan Feb 20 at 1:20
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    $\begingroup$ @YiFan I think this is more of a problem about how many introductory proof courses are taught. Students make the transition from calculus into proof-writing and all of a sudden are strongly encouraged to phrase every proposition possible in terms of quantifiers and symbols. It's a good skill to learn, but too many have this notion beat into them that mathematics is all about symbols (or that the harder something is to read, the more advanced it is). $\endgroup$ – T. Bongers Feb 20 at 2:21

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