(+1) One if the best questions I have seen here in quite a while! The answers should be very enlightening. For what it is worth, I would never have allowed my PhD students to publish without my name on the papers and I worked to make it the valid thing to do: everyone benefits from the win-win scenario.

Surely the end goal for a supervisor is to get their student to the point where they can "fly the nest", i.e. be independent in their research from conception to publication. In some fields/countries/supervisor-student relationships this point is reached before the end of the PhD (perhaps well before). In some, it's not reached til after the PhD student has finished, and maybe never.

Also, doesn't a student working independently reflect well on the supervisor, indicating they have guided the student successfully to that point?

The only cases I know where students publish without their supervisor(s) is in the field of mathematics and theoretical computer science. I would venture the following reasons: the students are highly advanced and super talented. All they need is an open problem from their advisor. It is quite normal for a researcher to prove an open problem by him/herself. Once a proof is found, there are no other 'contributions' to be made that qualify one as a co-author. If the advisor has a better proof, he/she probably will write a new paper.

I think it's more field- than place-dependent. There's an old poll on the meta site showing that the Academia.SE demographics is (or at least was) skewed towards CS and maths, where students publishing as solo authors is much more commonplace than in physics. And even in physics it seems more common in more theoretical groups than experimental ones.

Personally, i can't imagine how publication without the PhD supervisor being credited as a co-author would be possible without getting into dangerous waters and probably risking severe problems with the supervisor (even if they contributed little to nothing to the manuscript and hardly proof-read the paper before submission). However, I really like the idea of the "learning to fly"-aspect and would love to see this view prevail on a broader scale.

@pbaer: In my area of mathematics, a professor who forced themselves onto their students' papers would soon acquire a negative reputation for doing so. They would have more trouble attracting the best students and (especially) postdocs.

@AlexanderWoo And for good reasons! So far, unfortunately, I have been given the feeling that (in my field at least) it is less a compulsion than an unwritten law that the supervisor must be listed as a co-author regardless of input. Financing the PhD student seems to be seen as a large enough contribution to the paper to grant being listed as an author.

@astronat You have a point, but I suppose what you said is just different wording for moral grounds I mentioned.

@Prof.SantaClaus I agree that this scenario is possible in mathematics. In that case, what exactly is "supervision", other than saying "here is your problem. Go and solve it"?

@sleepy there is no supervision in this context. I have had very well-prepared students who do not really need my help. They function as a highly competent researcher. In other words, they are only 'students' on paper.

@pbaer: In mathematics in the US, most students are funded as TAs.

@sleepy - there is also a middle ground. An advisor might say "try this method" or "maybe this paper I've only looked at the abstract of might be relevant" or "what you suggest can't work because of this result in this paper which you should read", none of which quite counts as working with the student on the problem but is more than "here is your problem".

Not all fields are "lab sciences".

@AlexanderWoo: In my field(s), these kind of contributions (finding the right problem, methodology) are considered a major creative work worthy of authorship. Also see my answer.

@sleepy: After I have read your post (and your most recent update), as well as the four answers that are there so far, but I'm still not completely sure what precisely your question is. Is your main interest within this post to understand the motivation of some academics to supervise PhD students although they are not always co-authors of their students papers?

For comparison, my first publication was single-authored as a second-year undergraduate. Supervision and advisement are two different things. The prof whose class project I turned into a paper declined authorship; somehow their lab attracts a ton of top students.

@sleepy I think that what differentiate math of other areas is that it is much easier for students to do independent investigation. If they think that idea A can be used to solve problem B, they can at least start the process by themselves. And if the idea turns out to be useless, this is often a learning experience. In other areas one often needs to run time consuming AND expensive experiments, a student cannot do that by themselves... But writting ideas on a piece of paper is a different thing, and from time to time those ideas lead to some results which one maybe didn't even expected in

the beginning.... I do believe that, for the above reasons, the students in math have much more freedom controling their research. While the supervisor often guides them in a certain direction, it is only natural for many of us to also play around (independently) with ideas and techniques which can take us into a completelly different direction. Good grad students in math are more than capable of working on the project(s) suggested by the supervisor, and at the same time investigate for fun other things....In many other areas experiments make this likely impossible.

Publishing as a solo author in experimental physics is rather unusual, although it does happen. Even then it would probably be a paper on experimental fluid dynamics or something similar where one can carry out the experiments with simple equipment.