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My adviser wants to be the first author
I am working on a paper after finishing my Masters. I did all the lab research and writing of the manuscript. My professor was only involved to guide me throughout the research and read my writing and give his comments.
Can I argue with him and tell him I am not letting the article to be published if he insists on being the first author?

Please specify your field, because author order has different meanings in some of them. For instance, in many areas of research, it's usual to order authors alphabetically.

Are there others involved? What would the whole list of authors look like according to you and him?

First author or joint first author? Since many fields can have papers with large numbers of people with small contributions it's common to highlight the "first authors", ie the people who put the most direct work into the paper. It's not unusual for a student and direct supervisor to be joint first author on a paper they both put many hours into.

@user49915 please post answers into answers, so they can be voted on

It isn't a good career move to counter your advisor in things like this. You need him to sign your thesis (already done) and to write you a good letter of recommendation - maybe still to come. If you anger him, whether rightly or wrongly, it will be you that pays the price.
As I said in a comment, this kind of "authorship" is common, accepted, and perfectly natural in some fields, even if it is a bit stupid.
Having joint authorship with a professor can actually be a help to your career, even if he takes first authorship. Some people will just assume that he did all of the work (no matter the order of authorship), carrying you along. Others will just assume that you did all the work and he is first author by courtesy.
This is something you can't control.
But a publication with your name on it anywhere is a plus for your career.
If you want to fight a system that you think is stupid, wait until you have some power and standing in academia to back you up. Otherwise you get squashed before you have a chance to fly.
Work with him and get a good letter.
I realize this isn't the answer you wanted to read. But think long term, not the short.

It is perhaps common, but it's neither universally accepted nor natural.

Thanks for your reply. Fortunately, I have already graduated, moved on and do not need his letter of recommendation.

Note that signing a thesis is a thing limited to some countries. I never heard of it outside of this site. It’s rather confusing to those who are not in a country where this is done.

@Wrzlprmft That's interesting. I would have assumed that an advisor, supervisor, or examiner needs to, at least figuratively, sign off on a thesis everywhere for the project to be considered completed. Otherwise, how is decided whether the student is done and has passed?

@xLeitix: Sure, the final thesis will be officially reviewed by the supervisor (and somebody else) and the candidate passes or doesn’t, but signing doesn’t play a prominent part in the process. My first thought when hearing about professors signing theses was that it was some kind of ritual after the fact, like an author signing a book.

@Wrzlprmft, presumably they "sign" something. A grade form or an acceptance document.

@Wrzlprmft I think you are reading "signing" too literally. What I think people mean is "my prof does not let me pass before this and that happens".

@Buffy: Sure, but that’s not very prominent. In my case, I never got to see those forms.

The problem with this approach is that, by accepting it, for the majority of people there wouldn't be a long term in Academia at all (because you are thus sponsoring a system based on anything but meritocracy).

@gented, sorry, but I don't understand your comment. Care to expand/explain?

@Buffy My comment was related to the fact that joint authorship for the most part only makes "rich people richer", namely automatically produces tons of publications assigned to people who in some cases didn't contribute much. Since unfortunately the mere number of publication is the main discriminator for an academic position we as community should work in the direction of changing the mechanism, rather than accepting it (but of course this is very naïve).

I agree with snapshots of this reply (do not undertake this with anger, do not try to fight the system). However, the need to help a student appreciate that expressing his or her sense of what is right in an honest, objective manner is the right thing to do seems to have been missed if not entirely subsumed in this reply. The best we should offer is not what seems to amount to "keep your head down, tow the line, and hope someday that maybe you will be the boss".

But think long term, not the short On the other hand, the "long term" for someone who does not want to pursue a career in academia is to realize that he will be listed as second on a paper which may be useful sometime in the future. Instead of being the first one. It may or may not have an impact (not likely) but by agreeing to be the second one it is irreversible.

Can I argue with him and tell him I am not letting the article to be published if he insists on being the first author?

Other answers have already indicated this is potentially a somewhat dangerous move if you plan on continuing with a career in academia.
However, I believe that you can, and perhaps you should. It would be especially useful in such an argument/discussion if you could bring examples of similar cases - with the same advisor or in the same department or subfield - where the advisor was credited last.
On the other hand, I notice you've written:

My professor was only involved to guide me throughout the research and read my writing and give his comments.

And I have to say - "only"? If he was guiding you the whole time and giving you comments all the time, isn't it possible that the research progressed in a way that he envisioned? Perhaps you're misjudging the extent of his contribution. While the work you did seems arduous to you, that's partly because you're new; perhaps for a more experienced researcher, you just did the "grunt work". I'm not saying that this is necessarily the case, but don't go arguing with your advisor unless you can be certain this point of view cannot be defended.
Also, regardless of the above - don't start this discussion with an ultimatum or with a declaration you intend to "bury" the paper.

Finally, another alternative I would suggest, on principle and irrespective of who did how much, is alphabetical order of author names. The practice of listing names by order of decreasing contribution is very problematic and IMHO should be opposed in general. Author names should be listed alphabetically, and if the authors do not explain who did what then people can just ask; or better yet - not ask. Of course, the advisor might theoretically be even more averse to that than to being listed second; it depends.

Thanks for your answer. He provided me with the resources (lab) and offered me to work in that project. However, I did all the experiments needed (without help) and wrote the whole paper based on my thesis. Of course, the research progressed in a way that he envisioned but it was because of my findings. As a student, I did what he wanted me to do but I don't think this disqualifies me from being the first author.

Whether or not alphabetical order of naming is done varies heavily by field. For example, in Computer Science this is almost-never done, whereas in Mathematics it is almost-always done. In lower-tier journals, the editor or institution may have influence, but AFAIK it would just be misinterpreted to do it unconventionally.

@imallett: It does vary by field, but I believe this should change. All paper should have authors listed alphabetically IMO.

@einpoklum The fact that one believes certain things should change doesn't mean they are near desired state now or will be there in 10 years. OP should not be asked to be the martyr for a perceived future good (of course, they can choose to become one). I personally do not so much believe in alphabetical ordering, because it disadvantages people which have no A or Z as first letter of their name. Unfortunately, psychology rules, and the first and last authors are more likely to be popping out from a page (disclosure: I have often been middle author and it didn't harm me, but that was luck).

@imallett Alphabetical ordering is quite common in computer science.

@chepner Gotta have some way of testing all of those sorting algorithms ;)

@user105565, What determines author order (in fields where you don't just go alphabetical) is usually who came up with the novel idea that motivated the experiment. Maybe it was the hypothesis that the experiment was meant to test, or maybe it was a novel way to test a previously-published theory. Who did the most work is not the main consideration. You haven't said enough for us to know which of you should be first author on this basis.

@imallett Not sure what area of computer science you're talking about but, in theoretical CS, alphabetical order is near-universal.

@DavidRicherby: In the field of DB systems (think SIGMOD, VLDB, ICDE, CIDR) papers authors are not listed alphabetically.

@DavidRicherby I would amend my comment to say "Applied Computer Science". Whereas, Theoretical Computer Science is, of course, (more-explicitly) a variety of Mathematics, and naturally follows those rules.¶ Personally, I see merits and disadvantages to both naming paradigms, but the point is it varies by field (even, as we see, by subfield), and randomly breaking conventions because you disagree with them is a good way to confuse people as much as elicit change. (That's not to say doing it anyway is impossible—just, that that's a significant consideration that I feel bears remembering.)

Can I argue with him...

Rather than taking a starting position where you want to get in an argument, a much better approach would be to try to have a mature conversation where you can each agree on what your contribution to the paper was, and what each of you feel is the appropriate criteria for first authorship.  Ask your supervisor for his opinions on this matter, and be open-minded and respectful.  If you have a different opinion, then let him know your contrary view, and let him know that you are feeling aggrieved.
It is not unreasonable for you to raise authorship concerns with your supervisor.  This is a conversation that is a legitimate part of joint research work, so you don't need to repress this.  However, like all professional matters, it should be raised in a respectful and professional way.  Begin by assuming good faith on the part of your supervisor, and don't start off framing the matter as an "argument" you need to have.  Try to figure out where you agree and where you disagree, and just be mindful to make sure you don't allow your frustrations to lead to escalation into an unproductive conversation.
Before raising this matter with your supervisor, it would be a good idea for you to read some material on authorship conventions so that you are able to put your case with some support for outside sources (e.g., see this report).  However, you should expect to have a preliminary meeting where your only initial goal is to exchange views on the matter, and then allow each party to go away to consider the views of the other.  An initial conversation on this topic might end in disagreement, but if you can support your own view with reputable outside sources, that is likely to be more persuasive than if you cannot.
These kinds of cases really shouldn't arise, since supervisors and students should always discuss authorship expectation before they begin a research project and papers.  I think your supervisor probably made a mistake in not discussing this up-front with you before the work on the paper was done.  Even if you are unable to resolve this particular disagreement, it would be a good idea to formulate clear expectations on future papers with your supervisor.  Inquire into the requirements he would expect for you to be first author on a paper.

I did all the lab research and writing of the manuscript. My professor was only involved to guide me throughout the research and read my writing and give his comments. ...

If that is an accurate description of the contributions (who came up with the research idea?) then it does not sound to me like enough to warrant first authorship on the part of your supervisor.  Conventions will vary from field to field, but in my understanding, the first author should generally be the person who did the most work on the paper.  (When I have supervised students in research projects they have always been the lead author on the resulting papers, except in one case where I did the majority of the work on the paper and wrote the first draft.)  Ethical guidelines on authorship, such as in the linked report, may give some guidance and references discussing authorship-order, so these are worth reviewing.
Please note that there are some reasonable counter-arguments to this view, especially within the scope of research done in a Masters degree.  In that context, research work is usually at a low level and the supervisor often has a substantial teaching and supervision role.  One might reasonably make an argument for first authorship of the supervisor in this case, but in my view it should depend on the specifics of the contributions on a case by case basis.

Occasionally (and more than occasionally in private / Ivy League institutions), professors will have their names credited as the primary author of a paper that was produced by their graduate advisees. In my view it is unethical, but in the eyes of some academics, it's customary. Some professors view their advisees as underlings to further his or her brand recognition in whichever field he/she works in.
in my view, your advisor is in fact not the author, if it's true that you did the research and literally wrote the paper. Before confronting him about it or giving him an ultimatum, I would go to another professor in your department whom you trust, and have a confidential conversation about the appropriateness of your advisor's demands versus the general attitude of the department. Sometimes you'll find that "nearly everybody does that" and sometimes they'll say "that's unacceptable."
If you consult with other professors and you get the impression that you are in the right, you will have more clout in dealing with the issue if your advisor becomes obstinate and makes a big deal out of it. But beware, all of the professors in your department are probably friends, or even worse they could be extremely factionalized. In either case, you run the risk of this "private" conversation being circulated around the proverbial "teacher's lounge."
Unless you are in an insanely competitive field at a flagship research university, I don't think this is going to blow up in your face. But only you can make the judgement for yourself.
After conversing with a trusted faculty member, I recommend you next present your concerns to your advisor, and see if he is willing to be reasonable about this. If he still isn't, this is a situation where you might need to get the administration involved, but they largely bend to the whims of tenured faculty members who bring in the big bucks with their research.
There should be a discussion here on the benefits versus detractors of submitting to your professor and having your name published second on the paper...versus not having your research published at all. I am a somewhat stubborn person and refuse to let anyone take credit for my work. But this might not be the most expedient approach for a person who is trying to get his/her name on publications under any circumstance. You'll have to decide which one you are, and I hope some other folks chime in on this particular subtopic.
addendum: If you produced your research using a program or model developed by your advisor, or some kind of privileged archival/digital/etc. access through your advisor that you'd otherwise not be able to use, I can see his demand being slightly more legitimized, so consider that as well.

While I respect your opinion here and agree with much of it, note that it isn't really an Ivy League issue. Some fields just expect that advisors and supervisors and such are first author. Fact of life that is hard to counter. Since it is expected in those fields, it seems odd if you do it differently. Use the professor to get your degree and move on with one or more publications.

This is the kind of counterpoint I was looking for. It is probably more expedient to allow the advisor to take credit if the promise of future publication or securing a job is high. There isn't too much consequence if the research is not groundbreaking. However, if OP developed some novel AI model that's going to change the world, I certainly would recommend he press the advisor on authorship.

@Umbrella_Programmer Many advisers are sane and value the contribution of their students, if they make a ground breaking innovation. In the case of a plain execution of a master thesis, I can understand an adviser claiming first authorship.

You should note that "important professor et al." usually brings more attention and citations than "student nobody knows et al.". Thus, I would not fight his decision.
Is his last name ahead of yours in the alphabet? Then you could ask him, whether you can make a footnote "Authors in alphabetical order", after writing him first.

This makes sense -- in some contexts the professor putting their name first could be seen as a form of endorsement, and depending on the professor and the field, that endorsement could be very valuable to your career.

I have faced the same issue several times when I was still studying. I have written three articles and was always in the second position. Of course this may seem "unethical" and not correct, but just take a look at what you have done on the topic so far and what your professor has done so far.
I can only speak for the field of meachnical engineering, but several points to mention in this field are:

Most probably you didn't start from scratch. You based most of your work on previous work of your professor, PhD-candidates and other students
your supervisor guided you through your thesis. Looking back at my thesis, I have to acknowledge that I'd have not been able to make my thesis in 6 months without my supervisor putting lots of effort in it. And also looking back I have to say that many good ideas were brought up by my supervisor and I was just there to "implement" these ideas. Also the "basic" idea on which the whole thesis was laid out was, of course, coming from my supervisor. Honestly: implementing ideas when being guided by a supervisor is the easy part in doing science. Being the one to guide others is the hard part.
your supervisor guided you through the process of writing the paper or even teaching you how to write the paper.
Having a "known name" as the first author always helps.

Of course it felt bad to be the second author in articles when I wrote my thesis, but looking back it seems like the right way. Perspectives change when you are on the other side and you see the "real" workload of being a supervisor. :)

You underestimate the work your adviser did. He choose the topic, he figured out what to prepare (or get prepared) that you can have a topic which fits the requirements of a master thesis regarding amount of work and depth of knowledge.
Eventually you will do a PhD and supervise bachelor or master students yourself. Then you will learn home much work it is to advise a student well and to prepare a topic.
If the adviser is able to figure out a topic leading to a publication, that is superior and ennobles your work. As far as I know engineering, math, physics, computer sciences, and human sciences, most master theses are not worth to be published. These are rare exceptions!

If the OP's description is accurate and they did indeed do the work and write the paper, then the mentoring that you describe would merit co-authorship but not 1st authorship.

There does not appear to be anything in the OP's question that specifies that the supervisor chose the topic, etc.  Can you explain where you are getting this information?

@Ben Are you serious? A master student picking his own topic and it gets publishable without massive guidance by the adviser? This is so unlikely or OP must be such a genius, that it should be mentioned in the question. This answer is not only meant for OP but for the bulk of people facing the same problem.

@KennyPeanuts From the question I don't know. If everything was prepared, the student run some repetitive lab tasks, wrote the text along existing papers and did not add any intellectual value, then certainly not. This could be backed by "I did all the lab research and writing of the manuscript."

A master student picking his own topic and it gets publishable without massive guidance by the adviser? — Sure, why not?  My master's students have done it.  Hell, I know undergrads who've done it.

@JeffE I am in the wrong field. My first paper took me two years as a PhD, that was not bad in my group.

Or maybe you just didn't get lucky.

I would suggest to him that you be the first Author, but he be the corresponding author. In my department, for a tenure package (for example), professors are rewarded equally for first author or corresponding author papers. I don't believe this is that uncommon, and would be a win-win for both of you.

You face three issues.
First, what is the merit to you of being first author versus being co-author on a journal with only two authors? This question is independent of your "feelings" about being first or second. Can you make an objective statement that says your future success in your field of study absolutely depends on you being first rather than second author on this publication?
When you can categorically make a statement that is this strong, you need to make it and do so now. By comparison, when your best statement on this issue is no more than the equivalent of a nebulous understanding that "it gives me more exposure in my field", you should weigh the two other factors more heavily.
Secondly, what is the merit to your advisor of being first author versus being co-author? This is the mirror question to the above. For example, does an upcoming tenure and promotion decision for your advisor depend absolutely on the number of first author papers that he/she has published?
You should at least discover the background for this question. You may claim an injustice is being done to you by your advisor based on the first issue. Yet how far have you gone to appreciate where your advisor stands by mirror comparison?
Finally, what are the rights that each of you bring to the table in order to complete the publication? In your role as the primary worker and documenter for the work (taken at face value as being truly stated), you have a right to negotiate authorship. Your advisor however may be due full acknowledgement due to his/her greater role of having provided all of the ideas behind the research. To what extent did he or she completely initiate the work that you did, proposing all of the approaches that you took and defining all of the analysis that you were to do? Perhaps your advisor does have a greater right to claim first authorship because of his/her greater role in setting, maintaining, and directing the success of the work.
These issues are what you face at a negotiation table. It is not an argument table ... it is a negotiation table. The negotiations should be done up front, hopefully before the publication is started.
In practice, at this point, you should first decide whether your case has strong merits on the three issues above. Regardless of your decision, you should still talk with your advisor to clarify what you understand about them. You should strive to present your case honestly, not argumentatively. You should do so even with the understanding that you may have accept the pre-ordained outcome of being a second author, not a first author. At best, you may make a strong and sufficient objective stand to sway your advisor to appreciate the greater need that you have to be the first author. At worst, you will leave the presentation as a second author but knowing that you will not be carrying an unreconciled resentment about what you could have done but did not do.
Finally, discussing this with your advisor may not be an easy task. You may already face a sense of being held hostage to the power of your advisor to sign away your thesis or your future career. Do not let this fear put you in a place where you believe that you cannot at least assemble and put forward an honest, objective, and balanced case for your views. You may never change your advisor's mind regardless of the strength of your case. When you learn to state your case with no need to win it under situations of authority, you will learn how to do it better the next time at the outset when it may count even more.


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Are authors of papers okay with receiving questions from people in industry?
Would authors of a paper be okay with fielding technical questions about the paper (implementation, theory, etc.) from a person in industry?
I see this as a moral grey area because an engineer in industry is in some way profiting off the work of a researcher without necessarily paying them for the time they took to respond to emails, etc. On the other hand, is the researcher responsible for clarifying details about their paper regardless of who they are being contacted by?
Of course, this will vary from person to person and the length of the engagement, but I was just wondering what the general attitude towards this situation is.

Most people are pleased when anybody has found their work useful or interesting! Someone in industry with a professional interest in the paper is much more likely to get a good response than a question that looks like it has come from a crackpot.

WHen they publish their work, I assume they expect people to profit off it. They were paid by whoever sponsored the research, there's no expectation that people who find it interesting will pay them again (unless they want to hire them).

The engineer is paying the researcher through the company which pays taxes to the state which founds the research. That's the whole concept. And publishing a paper is just a necessity of spreading that research. Best would be to put it directly into everyones head. Notice though that this is about retreiving results and not about asking to research. That would be a different story.

@Mayou36: Not all research funds come through the government.

Researcher make money off each by that measure- getting grants is big money and gaining knowledge helps them get some.

Yes. To some sensibilities, including my own, this is the point of academic research (at least in applied STEM areas). We want people to use our work.

My limited experience is that primary authors are often non-responsive, usually because they have graduated and moved on to other things, while the other authors (often professors at universities) usually do reply to questions.

@alephzero I would shorten that to Most people are pleased when anybody has found their work. Period. :)

I certainly don't see anything immoral about asking questions.  You may want to mention your affiliation, which will clarify the issue and perhaps also help the author give a more useful response.
The author doesn't have any particular obligation to respond to your questions or anyone else's, but probably will if they are interesting and well thought out.  Academics generally would want to encourage anyone who is interested in their work.
If your questions get very involved, to the point where an academic might consider suggesting a collaboration, you may want to consider offering the author a consultant contract.

+1 If you ask to clarify something they said in a paper, then it's perfectly okay. If you ask "How would I apply this technique to my situation", then you should be hiring them as consultants :)

Replace "you may want to mention your affiliation" with "you should always mention your affiliation." Your affiliation helps to show that the intent of the question was serious, even if the actual question turns out to be dumb because you misunderstood something basic.

As someone who does research with close-to-industry applications, I would love more industry involvement and questions.

This is not a moral grey area - asking is totally okay.
In my country (Germany) researchers at public research institutions are even expected to answer. It's called "third mission" (the first two being research and teaching respectively).
Besides this "third mission" I shall pursue (helping to bring their research to industry), I would be pleased to learn how my research would be helpful in practice and would love to help the company. Just explaining some details is no problem at all. If this develops into some severe counselling one could start thinking about payment, but actually, this is often how collaborations between universities and companies start.

Same in the US as well, public schools will have something in their mission statements about economic development and serving the public.

There’s a distinction between asking an author for clarifications on what she/he has done and asking said author to do more work.  The former is fine.  The latter... well... I wouldn’t assume an author would necessarily do it unless this extra work would be of some benefit - v.g. additional publication - to said author.

I tried it and got positive feedback.

Would authors of a paper be okay with fielding technical questions
  about the paper (implementation, theory, etc.) from a person in
  industry?

I was asking myself the same question 1,5 years ago. I work also in industry and was interested in some technical details. I asked my boss for a budget and then contacted the authors offering budget if needed.
I did this several times. My experience: If it takes <15-20min to answer your request, they are happy to help for free. Discussing a budget only made sense for them if the effort was 1-2 days effort or more.
Only problem i would see is if you have questions that would take away a few hours of their time, then its too much to do for free, but too less to consider a contract. But i think asking is always fine, if you show that you respect their time.
(All based on my (limited) experience of 3-4 contacts and my own reasoning,...)

In the mentioned situation of "too much time to spend gratis, too little to set up a contract", you might consider whether you expect to ask for more of their time in the future, or could plan to knowing that it's available. It might be worthwhile paying a retainer for some number of future hours of assistance, or writing a more open-ended agreement that would extend beyond that immediate need.

It's fine.  You might even learn something.  They can share practical knowledge and you can explain some things about the paper or bounce ideas around about things that aren't publishable.  Really, it would be good if it happened a lot more than it does, but the two sides are usually so unable to bridge the gap.
Obviously if someone takes a lot of your time, than you should ask for a consulting contract.  But this is really rare that you have that much to offer.  I would instead view it as a good form of networking.  There is a world outside the ivory tower and it can inform your research (and teaching) to know something about applications.
Of course you don't have any obligation to explain the paper if the interaction is tedious or unpleasant.  But I would be open to positive interactions.  Have ended up inviting a person in for a talk and vice versa.  Granted I was doing research that had a fit with industry (and vice versa).  But also, I was open to the interaction and enjoyed something outside academia.  Business manager was a cool dude too, funny and good taste in wine.

Would authors ... be okay with... questions about the paper... from a person in industry?

Yes, within reason.
By the way - don't forget that readers outside our "clique" sometimes notice things like implicit assumptions, and occasionally even an error (!)

I see this as a moral gray area because an engineer in industry is in some way profiting off the work of a researcher without necessarily paying them for the time they took to respond to emails, etc.

This is actually a good point, but perhaps more on the collective level than on the individual level. Industry bases a whole lot of its for-profit activity on science and tech developed in universities, and employ engineers and technicians trained in universities/colleges - yet they repay academia with very little money (donations + fraction of taxes) and other resources. Of course this changes by country, but it's definitely the case for most of the world's large tech giants.
So, bottom line:

On the collective level, try to get your superiors to donate to the author's institute, in recognition of their contribution to your company's success. You'll very possibly fail, but you can try. Donation can be in the form of money, hardware, or manpower (e.g. someone who would teach an advanced course relating to his/her professional specialty at the company).
If you expect to require significant effort explaining, consider asking your direct superior for budget for a few consultant hours. If you're in the same country as that person consider even inviting him/her to talk about the paper's findings, adapting it to the background of employees of your companies and allowing for a lot of audience questions.

Yes, definitely feel free to inquire.
Others have noted the general value of an inquiring, but there is another aspect.
When someone from industry inquires, it means that you are potentially doing the academic a favour!
@Dirk mentioned the German 'third mission'.
Elsewhere in the world it may not be so formal, but academics are constantly being asked to justify their funding in terms of its 'real world' applicable or economic value.
You help the academic understand how what they do is applied and how that creates economic value.
They might even be able to use that information directly in grant application, or perhaps in less formal situations.
Additionally, as someone in industry you might understand that when you create a product you thrive on feedback from the market. For an academic, you are potentially providing that feedback, helping them understand which areas of their work is relevant and potentially shaping where they wish to spend their time.
Note: The academic is always on the hunt for funding. Take care to not give false signals in regards whether your organisation might provide that.

As a researcher with a strong industry background, I tended to find a disconnect between the actions of my industry (software development and data science) and the research being conducted by the academics.
I would be delighted if an industry practitioner asked for more details of my academic work and certainly would regard it as a mark of prestige.  There is no downside I can see to engaging with such a person - providing, of course, they are not expecting you to contribute significant amounts of your time and resources.  If this is the case, then the answer above is correct - they need to be paying for a consultant.

Not guaranteed. Depends lots on the person and how much time they have. Quite some authors of papers expect to get paid for any kind of consulting - which is what answering any question outside of work would be for them.
They often have their fair share of questions from students which is their job to answer on work-time. It is not so weird to imagine they would expect compensation helping people (who usually make more than they do) for doing any work for them.

When I taught English at a local university and had them write research papers,  I was always trying to steer the students towards looking at professors at our own university!
My goal in part was to connect Published Research with People Who Researched/Wrote This.
There is not some giant up on high handing down Scholarly Sources, but people, often teams of them, some of them graduate students, are the ones creating it. So they TOO can question the research, wish a study had been designed differently, or want to combine information from different fields.
Alas, as Batman almost said,

[Freshmen] are a superstitious and cowardly lot,

so many were not yet ready to cope with this much intellectual responsibility.  But a few now and then were, and that was always fun.

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A life of PhD: is it feasible?
In the next year I will (hopefully successfully) graduate from a PhD programme in pure mathematics. The location is (continental) Western Europe, the topic of the thesis is arithmetic geometry, if it matters. During my PhD experience I have found out the following things

being a pure math PhD student is a relatively stress-free existence for me. I can just waste all my time learning some math and occasionally writing some papers;
the stipend does suck but I am frugal person from a very poor country so I do not care that much (nor do I have a family to feed);
if I could, I would not mind spending what is left of my life in a PhD programme. In particular, I do not feel any intrinsic motivation to try to get a tenure-track position.

The question is: is it feasible for me to keep applying and getting accepted to pure math PhD programmes before I die or decide to retire? To clarify, I don't really think that I will be a problematic student; during my PhD programme, I got 3 publications accepted in reasonable journals (rank A in AustMS ranking) and I think I could maintain a similar rate of work.
Are there any "magic words" I could tell the committee that considers the applicants to improve my chances?

The idea of PhD programmes is that you give back more to the society than a few papers and a low CO2 footprint. Also: What if you don't get into a new program when you're fifty? You think you'll still be thought hireable in industry? Also how to you want to buy a flat and save money for your retirement days?

PhD scholarships and postdocs aren't awarded only on the basis of the likelihood that you will produce a certain amount of work during the PhD, but also on your potential to have a successful career afterwards. Being a permanent student isn't a career, plus you're taking a spot from someone who does want a career.

@phd You might be interested in this related question: https://academia.stackexchange.com/q/108709/93566

@ElizabethHenning +1 if only for "plus you're taking a spot from someone who does want a career." To the OP, even if you somehow managed to convince university after university to admit (and fund) you as a grad student, given the very limited number of slots it's extremely unethical behavior.

@ElizabethHenning Actually, taking seven or eight spots from somebody who does want a career.

I can just waste all my time learning some math  As you seem to place no value on mathematics, your time or (more importantly) other people's time and resources, I doubt we can dissuade you from this selfishness.  I can only hope that screening committees can spot this too.

You may not have a family to feed now, but maybe your elder parents may need your support in the future. You might also happen to find someone special with whom you would like to build a family with. By sticking to a low stipend, you are preparing for neither case, and maybe you are building a barrier against finding that special one. For the benefit of society (and likely yourself), I'd advise against this plan, unless you come from a wealthy enough family, such that you don't need to worry at all about retiring.

What is it exactly about being a PhD student that you like so much? It's probably better to figure out the answer to that question and then search for jobs with similar benefits.

@StephenG That strikes me as an ungenerous interpretation of OP's humble comment. I think anyone who wants to spend their life as a math PhD student likely places a high value on math, and considers doing math to be a good use of their time.

@Karl I wouldn't say a low CO2 footprint is guaranteed for a PhD student. I suspect mine is pretty higher than the average citizen with all the flights for conferences

@littleO With respect, the OP is the one saying they'll be wasting their life studying maths, not me, not someone else.  The OP places a high value on living the life style of a student (!), not on the pursuit of mathematics.  That's my reading based on their words.  I think I'm being fair.

Never is too late! Follow your favorites and do not waste your life by pursuing something you do not like. Maybe you're talented and engaged in some other field. A consultation session (with a professional one) may work for you.

You look like PhD is the way for you! :) And the magic words for committee are: "I have papers in journals X, Y and I am going to publish in journals X, Y, Z" :-) This was my experience. I prepared myself in all possible areas and this was the only thing they were interested in :-D

What are the different options for a research-focused role?  Research Assitant, Research Associate or similar titles are what I know of.  How do junior versions of this differ from a PhD student and what about them do not appeal to you?

The currently most upvoted answer makes it clear that the answer doesn't depend on individual factors and preferences but is "no, it's next to impossible".

Holding a PhD in math would usually disqualify you from being admitted into a PhD program in mathematics. Even if it does not do so officially, I'd consider it next to impossible to get scholarships.
That said, being a postdoc in math is not really much different from being a PhD student. However, even being a postdoc forever is not easy. Many funding sources have restrictions on how long ago your PhD may have been - after 5 years you already have fewer options, and continuing long after 10 years will see you face exclusion from many funding sources, as well as a strong social pressure to get a "proper" job (i.e., a faculty position).

"Doesn't it only matter whether the research gets done or not?" -- no, if this is a professor's only concern, they would have structured the project differently (e.g., assigning it to a permanent scientist, or hiring a sub-contractor). Post-doc positions are specifically intended to bridge between recent graduates and permanent positions, and involve a mentorship component.

"being a postdoc in math is not really much different from being a PhD student" -- It is. The teaching load is higher (and it's actual teaching, not just grading/TAing), at least in the places I know of. And usually no one is explicitly expected to mentor you, though sometimes you can still get an informal mentor.

@darijgrinberg In some countries postdocs have no teaching duties, and they get some mentoring, though less than a PhD student.

Okay, I should indeed have specified that i was talking about the US.

@phd do you know any reasons why there is time limitation on the postdoc positions? - I think you don't understand the purpose/use of postdoc in math.  It's not a like a research scientist/postdoc in some field that's just meant to assist the professor's research.  They're meant to be transitional positions, and are a way of bringing in fresh blood and ideas.  But there are permanent positions that are essentially research only, e.g. CNRS.

@phd I get the impression that a lot of it--at least on the biomed side of things--is a naked attempt at gaming "time-to-job" (or, more specifically, time-to-R01) statistics. It's agist nonsense but...that's where we are.

@phd  Same reason that you can't just sit at the rank of Major in the military until you retire - you either go up or get out because there's a queue of people behind you who need your job as the next step in their career.  If you're not going to take the next step there's big pressure to get you out of the way for someone who will.

@phd "any reasons why there is time limitation on the postdoc positions? " Since it's mean to be a transitional position, people could assume that if you're not out of it within 10 years you may not be the best performer, or the one they want to send money to.

@J... This is the same argument as 'let other people have a career' from other comments. But is it necessarily good? We may live in a career-centric culture, but it's not universal. In some cultures 'career' is a dirty word. If a person is actually better at his/her position and doesn't want to progress, is it better to remove him/her just to let others try? (Esp. given that in our society too often progressing in career means assuming more and more managerial role, which not many people are good at). So, if the OP shares such values, this behaviour wouldn't be perceived as a sin.

@Zeus I wasn't making a value judgement - only an observation.  In any case, as you say, managerial roles aren't for everyone.  Universities need to keep new blood rolling through so that they can catch the few outstanding candidates for promotion.  If that conveyor gets blocked up with people who have demonstrated that they are disinclined to assume such managerial roles then the school necessarily gives up opportunity to find someone who isn't.  Resources are finite and, so, status quo.

I want to highlight that in many countries and institutions, there are research scientist jobs where (almost) the only expectations of the job is doing research.

In the U.S. at least, maybe also Canada and Western Europe, in science (math, physics, chemistry, etc.), contrary to legend, graduate school can be a very wonderful, low-stress, idealistic time of life, if one has no partner, no children, no mortgage, no car payments... to worry about, and simple tastes.
On one hand, yes, in some ways grad students are exploited by The System (low pay), but, on the other hand, there is a short-term (5-year!?!) job security, interesting work, and no increase in (student-loan?) debt. And grad students are not terribly experience teachers nor researchers, so there is some kind of quid-pro-quo apart from the low salary.
At my university, it is possible to maintain that lifestyle and employment style by being a "teaching specialist": low pay forever, substantive uncertainty about employment from term to term, but very low stress/responsibilities otherwise. Some people do apparently deliberately choose such a lifestyle. Why not?
But, as @Karl mentions, if nothing else, what about planning for old age? Low pay-ins to pensions (and/or Social Security in the U.S., apart from other complications) will result in low pension payouts later.
Part of the point here is that aiming at "postdoc in perpetuity" almost universally at best would collapse back to "getting paid like a grad student, with no security, no pension". In particular, not getting paid nearly as well as post-docs, in any case.
So it's not that it's impossible to have that lifestyle, but that there are details and complications that would almost surely make you very unhappy later, without any option to go back in time and change things.
(And, yes, I'm sympathetic to your impulse, not being very materialistic myself, etc., but the realities of aging (not to mention having a partner and kids or other dependents, possibly including one's own parents at some point) have long ago burst that bubble for me.)

Also, the stress of constantly applying for new postdoc positions

+1 for "if one has no partner, no children, no mortgage, no car payments... to worry about, and simple tastes."

no children, no mortgage, no car payments, simple tastes, wait aren't those the basic features of being a monk?

@candied_orange, exactly. The monastic concept of academe. :)

Academia:  all the benefits of taking holy orders without that pesky vow of celibacy!

Although being 30 or 40+ in a college town might as well qualify you as celibate, since you will probably end up being the "creeper" at most bars you go to

@paul_garrett  monks otoh have an interminable position ;-)

There's no point in trying to do repeated Ph.D. programs in the same field when you can easily replicate the lifestyle you want in the normal way. If you don't want to pursue the tenure track, go to a less good institution and get a part-time teaching job. It won't be much money but it will likely be more than you made as a Ph.D. student. Continue your studies and publishing. You can work with folks from other insitutions in order to keep up your intellectual progress.
There is no easier thing than finding a lifestyle that works for a smart, hard(ish) working, highly skilled person who is happy with an extremely low salary in a developed country.
There is nothing special about a Ph.D. program except that it prepares you for better things.

+1 but then of course, without a PhD program, you don't have a mentor who does some occasional mollycoddling. ;-)

I'm not going to answer the explicit question as others have done it pretty well, but I'd like to address the underlying assumption.

being a pure math PhD student is a relatively stress-free existence for me.

But first, let me congratulate you for that! I don't have any data but I'm pretty sure that most PhD students wouldn't describe their PhD experience as stress-free... so good for you!

During my PhD experience I have found out the following things

You have discovered things about yourself during the PhD. You will also discover new things about yourself after the PhD... even if what you do after the PhD is another PhD. What I mean is that you shouldn't be afraid of what happens after the PhD: you feel comfortable in this environment now so it's natural to wish to keep it, but actually it's likely that you will like other environments as well. Actually it looks like what you like is simply academia, so why not give a try to postdoc positions?
A friend of mine used to say that a PhD is like an initiation ritual into "academic adulthood". For many PhD students the end of the PhD is a time for questioning: self-doubt is very common, fear about the future, sometimes even depression. While it's common to go through this stage, it's important to keep in mind that we might not always see things clearly about ourselves, especially at the end of a long-term project like a PhD. In my experience most people realize what they really have learned (including about themselves) during their PhD only after graduating, because it takes a bit of perspective to see the whole picture.
In conclusion my advice is: don't be afraid, be open to opportunities and keep enjoying the science :)

As the others mention, staying in math would be hard, but if you keep jumping to closely related fields, then it should be possible. For instance, you might find a professor in Eletrical engineering or one of the other "mathy" fields who is working on a topic that requires only a little bit of domain-specific knowledge.
I know a few people (less than 5) that have 2 PhDs. I think one of them was applying for a 3rd. They lived in a poorer Eastern European country, so the pay actually wasn't that bad. Furthermore, finding a job in industry would have been difficult due to their advanced skillset. So although getting more than one PhD sounds crazy, it wasn't actually that crazy if you think it through.
In principle, the others are right though... a Postdoc is intended for people who want more academic training in the same field.
EDIT:
There are 2 overarching scenarios that I have seen lead to someone getting more than 1 PhD. We might as well enumerate those:

Vanity. In Germany, when you get a PhD of a certain type, you can call yourself Dr. (e.g. Dr. Foo). If you get 2 PhDs, then your title is Dr. Dr. Foo. And this could technically go on ad nauseam. Once I saw somebody who insisted on being addressed as Prof. Dr. Dr. XXX. In principle, you could be Dr. Dr. Dr. if you really wanted to (although this doesn't seem to be the desire here).
Some countries have very little industrial technical sophistication. So if somebody wants to stay in their country after a PhD, then they are almost forced to either take a mind-numbing job in industry, or try to find something in academia. However, due to the high number of people in a similar situation, jobs for professorships or other paid academic jobs are hard to come by. So in principle, if one is curious enough to explore other disciplines, then getting a PhD in another field is not such a bad option. I would imagine that at some point a professorship would open up to a person with 2+ PhDs, but there is also the question of whether you would want to become a professor. The work of a professor is often quite far removed from pure research. So if you want to only do research, being a professor is not necessarily a good path.

Two PhDs is extremely unusual. I have never heard of anybody with three. The asker is proposing to get eight or nine. Why would anybody want to be an advisor for somebody doing their third, fourth, fith PhD?

Why wouldn't somebody want to advise somebody like that? If they are bringing in a lot of background in other fields, I would have gladly accepted such a person in my group. In fact the hot trend in research lately is crossover work, and such a person would be immensely helpful

Because somebody whose only interest in is getting a never-ending PhDs has shown that all they're interested in is narrowly focusing on one aspect, and probably doesn't have the breadth of big-picture knowledge needed for effective interdisciplinary research. Because, after four years, they'll just say "OK, done with that. Time for something different." and go back to square one instead of moving forwards.

I admit that that is possible, but then that would be reflected in their research

I concur with @DavidRicherby. Doing multiple PhDs (certianly more than two) is a sign only that someone is unsure of where they want to go, only that they like being an academic. It shows a penchant for serial specialism rather than generalism (i.e., big-picture knowledge or highly interdisciplinary work).

There used to be someone in my office who was doing a second PhD but I have never heard of anybody doing a third in my life.

Two PhDs can make sense if on different fields... One of the best imho profs I ever had had two, one medical, and one in computer science... He's been doing neural networks... But yeah these very rare are exceptions, and different field is key... People refer to the institution from which you got your phd as where you come from, in a way it would be like having been born in two different places...

The main problem with doing more than a single PhD, is that usually you won't be admitted to the program when you already have a PhD. The sole exception, as far as I know, is vastly different fields, e.g. Physics and then become a patent attorney and do law, or become interested in some historical feature and do history. Staying in the same field, as the OP wants, is from my experience (also Western Europe) not possible.

It is immoral and anti-social of you to try this. So don't.
You're asking about feasibility, but are ignoring the detrimental effects such an attempt, or practice will have on the academic community and PhD candidates in particular.

Universities and academic staff members invest resources - including time and money - in PhD programs. Young graduates aspiring to train as researchers need those resources. You'll be taking other PhD candidates' positions.
You would be making PhD-level researcher skills available to universities for the price of a PhD salary/stipend. That undercuts us - everybody else - who have expenses and need to support a family, or buy a home (someday...) and so on. You would be hurting us.
You have an obligation to pass on your knowledge to other, younger and less experienced, students and researchers. From your description, it seems you expect not to have to teach nor to advise younger students during your subsequent PhDs. Don't shirk that community responsibility.

I suspect it many not be psychologically beneficial for you to be "stuck" in that place in life, but that's very speculative and I don't have evidence, so I'll just put it out there as a possibility.

@DavidRicherby: I think OP implied s/he won't be teaching. See edit.

I added "during your subsequent PhDs" to highlight the difference between the asker's plan and the plan of somebody who's leaving academia. Roll back if you don't like it, of course.

I don't think OP should be made responsible for the lack of good positions in research and education. It's a policy matter, nothing an individual can do anything about. Should one also feel guilty for taking a six year full-time position, even if six two-year part-time positions could be financed with the same money? We're sitting in one boat, solidarity would be more useful than blame-games.

@henning There is a clear difference between offering to do, e.g., half a job for half the pay (job-share, which is only useful if somebody else only needs half the money) and offering to do the whole job at reduced pay (undercutting other workers and generally driving down wages).

@einpoklum henning was trying to set up some sort of equivalence between job-sharing and your point 2.

@DavidRicherby: Well, still not quite getting it but I will restate my earlier answer. I'll rewrite my earlier comment then.

@henning: If OP drove a low-efficiency gasoline-based car, s/he isn't responsible for the climate crisis, but s/he would be contributing to it. On the micro level - it's quite possible the next place OP applies to get into as a PhD candidate only has one position open at a time in a certain subfield, and s/he will take it while someone else who wants it, doesn't get it. As for 6y full-time vs 6 x 2y part-time - please explain the context in which these two-year part-time positions would be relevant.

You might consider making, for example, a PostDoc in some more or less computer science field. I guess you will be able to find a connection between arithmetic geometry and some kind of theoretical computer science. (I know Emmanuel Haucourt, a bright researcher and a very nice guy who made the connection between topological algebra and computer science)
Then, I do also recommend to not only care about theory, but also a bit about practice (at least, being able to develop some free software research prototype).
I know excellent mathematicians who became computer science professors with a stellar-level software engineering ability (one of them is Roberto Bagnara, the architect of the PPL....)
With such a resume, even if you don't stay in pure academia, you will continue doing a lot of math. Both in industry (think of large corporations like IBM or Google or MicroSoft or SAP) or in applied research institutions (like Fraunofer institutes).
The point is that, at high enough level, computer science is a sort of math. I'm guessing that arithmetic geometry is strongly related to cryptographic techniques. And these have a lot of highly qualified jobs, even in industry. The lifestyle is almost PhD like (but the pay and job stability is better, with of course more pressure).
As others told you, getting a second PhD might worth it only if you want a tenure-track, purely academic (university) career. If you want anything else, the second PhD is a loss of time. But a PostDoc in a different field is very different story. So my suggestion would be to start a PostDoc in Computer Science (in a theoretical field close to your current skills).
NB. Not even wanting some kind of job stability could be consider as dumb behavior (and is hurting you).
PS. I am almost 60 years old and still employed at CEA, in France, and in 1985, when I entered it, the lifestyle was PhD like (I actually started my PhD at university, but defended it while at CEA). But not more today.

It would be a pretty pointless endeavour.
After circa 50% -> 100% of one (1) PhD you should probably have managed to crank up your general study speed and techniques so that you can perform quite a bit faster on your own without distractions like

teaching courses to MSc and BSc student,
dealing with rewriting papers,
finishing your courses,

endlessly nagging on you. To voluntarily head back in for a second or even third one would be a huge waste of your productivity. ( If you're any good, that is. ). The reason people don't quit when they feel they have reached this level where self study would be more efficient is that they are simply a bit scaredy-cat:y of looking like "drop out"s. It's quite natural. Most humans are a bit scared of that.

Once people have finished a PhD, they no longer have to teach or rewrite papers? News to me!

@DavidRicherby : Sure, if they stay in academia.

And the asker does want to stay in academia, as shown by their desire to just spend the rest of their life doing PhDs.

@DavidRicherby We do not know this. All he says is that he did not find it so stressful and painful he could not imagine keeping doing it. Maybe he would prefer other better alternatives if he could think of any. We don't know what his alternatives would be. Maybe he imagines doing PhD to avoid the increased other duties often associated with taking a step into academia, getting some more permanent position entailing more duties than "PhD student" usually does.

If you're suggesting that the asker should leave academia and do something else, your answer should make that much clearer. Because if they do stay in academia, they'll have to teach and they'll have to rewrite papers.

@DavidRicherby: I do not know asker well enough to give them an advice like this. A decision like this needs to come directly from them.

There is someone who works in my office who actually seems to be doing just that.  She is doing a second PhD even though she apparently already has one, but I'm not sure if there is some loophole because she obtained the first one in a different country or something like that.
In general, it's not a viable option though.  It's like having multiple Bachelor's degrees.  Some people do have two Bachelor's degrees, where they somehow re-trained and paid for the second degree in order to change career paths.  In the same way, they are likely people who have two PhD's (or equivalent) for some reason related to change of career path or something like that but in general living from one PhD to the next is not going to be possible any more than a person could just perpetually live doing one Bachelor degree after another: at some point funding is just not going to exist as you can't just fund someone to be a perpetual student indefinitely.

I guess the second PhD is self-funded, so not what OP has in mind.

Having two Bachelor's degrees is also a possible outcome of simultaneous double-majoring at (some?) colleges.

It's possible, I have two Bachelor's degrees myself but I did the second time simultaneously whilst working full-time, so I am sure it would be possible to simultaneously do two at the same time depending on the college.

@henning then there's Really no point. Why pay out of your own pocket to let others decide what you should use your time for when you already have "stamp of approval" saying you have learned to decide that stuff independently on your own now.

@mathreadler exactly.

To improve your chances, I would suggest you to move to a country where multiple doctorates (and titles) are seen as a positive. As far as I can tell, this is the case in my country, Austria (and especially in the humanities). I know a few people with two PhDs and also a few people with three. It's also not uncommon to see signs from lawyers or (medical doctors) displaying two PhDs.
And, there is this guy: https://www.nachrichten.at/oberoesterreich/Das-ist-Doktor-Doktor-Doktor-Doktor-Doktor-Doktor-Norbert-Heinel;art4,843952 (article from 2011 in German, professor with 6 PhDs, two more are planned).

Austrians love their titles, but the Austrian Doctorate is often self-funded. Certainly the chances of getting a second funded PhD position are not better than elsewhere.

@henning: Sure, but as I read the question, OP does not specify that they want to be funded by the PhD position (and not by, say, a side job).

Don't enable OP's inappropriate academic and life choices.

@einpoklum: I don't see what's innappropriate about that. As said before, there are people here doing exactly that. For inappropriatness, that's in the eye of the viewer. I, for one, see OP's plans as much more ethical than working for a big company and helping them making profits as most people do.

@user109737: I may write my own answer to explain. But in a nutshell: Those people are 1. preventing others from being PhD candidates, and 2. Are making available post-PhD-trained researches at PhD salaries,  undercutting the rest of us. I think it's probably a bad place to be personally and psychologically but that's a minor and speculative point.

@einpoklum: I am respecting your opinion (and I like your answer), I don't completely agree (especially if OP gets his funding from other jobs). Our disagreement is probably due to education seen differently in different countries: Here, university level education (including PhD) is seen as something one does because they are interested in the subject, not something one does because they need it for their career.

@user109737: 1. It's an education but it's also a limited-term position. 2. Regardless of the person's individual motivation - there are social interests, which are no less important in this case. IMO.

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text:
Whose lab is it?
As a follow-up to this question:
Who does a lab belong to? Is the lab the sole property of the PI (lets assume a simple/small lab with a single PI bringing in all the intramural and extramural funding) or is it a joint venture of the PI and the research staff?

Should the PI call the lab "our lab" or "my lab"?
Should researchers (Undergrads, PhD students, Post Docs, Research Fellows) call the lab "our lab", "my lab", or "my supervisor's lab"?

It's the lab of whoever feeds data to the database for the face recognition algorithm of the self aiming laser gun that's installed inside. On a more serious note, this might be different in different countries, cultures or academic sub cultures/faculties.

Just to add to the cultural differences, it also depends who you are talking to at the certain moment. The PI could say my lab or our lab, depending on his culture or how much he wants to stress that it's the PI's lab. But my lab would not sound awkward. For researchers, I think that when someone represents the lab in a meeting/conference/etc our lab is more appropriate. Talking to fellow/equal-level researchers from other labs, my lab would not sound bad (and definitely would not show taking ownership). But this might all be from my culture... I agree with the comment above.

What's the difference in saying my class and my teacher's class?

Do any of the personnel working in a lab "own" it?  In the legal sense, probably not: the university owns it.  Even if the lab is entirely funded by grants from the PI, legally those grants are still being paid to the university and not directly to the PI.  So I think you mean some more informal sense, in which case...some people will say one thing, some another, some will care, others won't even notice the difference.  I'm not completely sure this is answerable...

The PI certainly doesn't own the lab- he can't sell it.  He can't even take the equipment to another institution without the permission of his institution and the funding agency.

@PeteL.Clark I mention grants, not because of "ownership", but as a way of indicating that the lab only has a single PI and not a bunch of PIs, CIs, and independent researchers.

I voted to close not as opinion-based but as dependending on many factors. It's also unclear what's the specific problem you're trying to address.

TLDR; every member of the lab can call it "my lab" or "our lab". It's all the same.

Just because one says "my lab" doesn't meant that he/she can exercise ownership over it. It is similar to saying "my country" or "my class".
If the question is about rights of property, then it depends on who bestowed the rights and what exactly are those rights.
In the usual case, the management of the institution would give a set amount of rights to the professor to be in charge of a given place. If the professor wishes to form a lab, he/she may do so and appoint an in-charge for the lab. It could a PI or in several cases, the professor him/herself.
If the PI is the professor who erected the lab, then obviously the lab is owned by the professor. If the PI is someone else, the professor could choose over the rights s/he could delegate to the PI. Examples of such rights could be

right to rule over certain/all projects done in the lab
rights over the control of lab property
right to guide the students assigned to the lab

There are also labs which are maintained by a community of members in the institution.  Technically, everyone in the lab owns it in such a case, but the place itself belongs to the management of the institution.

As usual, the answer depends on the country.
In my country, all the equipment belongs to the university, even if it was paid out of PI's grants. If a PI moves to another university, the equipment doesn't move.
Thus, if one strictly looks at the property, no one in the lab would have the right to say "my lab" or "our lab", because it's the university's lab.
But of course, no one looks strictly at the property, and what it counts are the people working inside the lab: for them, it's "our lab". Moreover, usually, almost everyone contributes to the grant requests.
When I was a PhD student, in the group where I did my PhD, we had separate lab rooms for each different experiment, which were run by different people: when speaking among us, I'd have said "my lab" to mean the room where I was running my experiment.

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text:
Who should be excluded from reviewing
My question may be a duplicate of: Sound reasons for excluding a reviewer, but it is motivated by What do you do when you are asked to perform an official review for a journal of a manuscript written by your supervisor?. Because there is an obvious conflict of interest between a supervisor and supervisee this answer claims the manuscript never should have been sent to the current student. The issue I see is how is the editor supposed to know if the potential reviewer has a conflict if they are not listed as a reviewer to exclude.
I essentially never list anyone in the excluded reviewer box. I would likely alert the editor if I was asked to review a manuscript from current and past collaborators, supervisors and advisees as well as colleagues in my current and past departments. This becomes a long list of people to include in the excluded reviewer box and it is not clear to me that it is helpful to the editor. Are there standard people that go in the excluded reviewer box?

Well, current supervisor and supervisee have probably the same affiliation, and this should be a hint to the editor, even if the supervisor is not explicitly listed in the excluded reviewer box.

What to do when the field is rather small and many of the potential reviewers are at the same time collaborators of one of the authors?

@LeonidPetrov by giving the list and reasons to the editor, they can make an informed decision rather than randomly trying people until they find someone with an "acceptable" conflict.

You don't have to do the job of the editor and list every possible collaborator with whom you'd have a conflict of interest. If these people are asked to do the review, they should be the one to warn the editor. You can list people that you think wouldn't be obvious, but again you are under no obligation to do this.
As the first question you link to alludes, excluding reviewers is mostly because you think they'd be unfairly biased against your work.

I always understood that you propose the reviewers according to the instructions and when there is no conflict of interest, e.g. avoiding friends, current or very recent collaborators, your supervisor, etc. You propose who you think would be a good reviewer and unbiased towards your work, like a researcher more or less well-known in his field.
Then you propose to exclude reviewers that you think would be exceptionally biased against you, e.g. people you are in bad terms with, competitors etc.
I believe it is the job of the editor to make sure that there is no conflict with the reviewers proposed (or the reviewers he can find in his list from the journal) and of the reviewer to notify the editor that there is a conflict of interest and thus he/she is unable to do the review.
Meaning that the exclude list is not (to my understanding) a list of potential reviewers that they might be positively biased towards you, but a list of potential reviewers who (you think) would be biased against you.

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