text:
Advice for struggling PhD student
Let me begin by saying my Ph.D. program has been a disaster. I'm 26 and I'm finishing up year 4 in a physics Ph.D. program. I have no publications and I'm completely burnt out. I have no idea what to do.
I went into a physics Ph.D. straight out of undergrad. My advisor told me to focus on coursework to get a master's first so I did. Right around year 2 I got my masters and was ready to start research, but my advisor's wife suddenly died and he was gone for almost a year and a half. Money ran out and I had to get a teaching position to make ends meet. I tried my best to do what I could, but it's very hard to be an experimental physicist with no money. I actually got a small grant on my own that helped, but it wasn't enough. Additionally, our university grad student union went on strike for a month or two that slowed everything down.
About a year ago another professor joined the department and hired me on. It was ok for a while, he had money and I was finally getting paid to do research. Since he was building up a new lab I was helping put together all the equipment.
Now there are a few more students, all at least 2-3 years behind me, who are in the lab. I'm still expected to put the machinery together while they are getting data from experiments and actually contributing to research. They aren't collecting data, they've been given older unpublished data to analyze. Every time I bring this up I'm just told to be patient.
As of right now, I'm going into year 5 with my name on absolutely nothing. I don't see a light at the end of the tunnel anymore. My department claims 5-7 years is average but there are a lot of 7,8,9 year students here. If this would only take 2 or 3 more years I'd consider staying, but it feels like I basically had to start over halfway through.
I have one patent application in progress, one fifth or sixth author paper in progress, and a completely written review paper that I was told to not publish. My advisors won't even let me propose a thesis, saying it's "too early". I guess I just want to hear what other people would do in this situation. I was recently offered a job in industry by an old friend that pays pretty well (~$85K) which seems so tempting right now. I feel like such a failure and I think I've wasted the past four years of my life. Does anyone have any thoughts on my situation? I'm very lost in life right now.
Update: thanks for all the responses. It helps to hear other perspectives. I talked to my advisor and he keeps telling me I can graduate in two more years if I focus. I don't think I believe him. I have until Monday evening to take this job offer and I think I need to.
Update 2: I think I just quit. I spent 80 hours in the lab this week (again) only to be told I'm still not doing enough. Every day I got more and more projects piled on my plate and they all involved putting equipment together for other people. I was told by my advisor that he doesn't believe my project will even work anymore. It's just not worth it

I know someone that left a Physics PhD after 4 years for similar reasons (unhelpful advisor and troubles with their experiment). The most helpful thing they did when thinking about quitting was talking to the Graduate Student Advisor in the department, who helped them get an MSc out of it before leaving. Does your department have an advisor you can talk to?

Yeah, I made sure to get my masters because the original advisor wanted me to focus on that first. I've talked to the academic advisor but he's less than helpful most of the time.

If you don't mind me asking, does your friend regret it?

They only left within the last 6 months, and I'm afraid I haven't spoken to them since, so I don't know. But I do know that they were planning on applying to fixed-length PhD programs in Europe after taking some time off, so it sounds like for them it might have been a case of getting out of a "toxic" environment rather than leaving academia for good.

And FWIW, I am also a physics PhD student (theory) about to start 4th year, and I have some of the same feelings as you (no publications etc). I don't have any advice, except to say that your feelings might be more common than you think

Yeah, it's rough. I can't stand academia anymore and I kinda think I just want out. My parents really don't like the idea, but it's not really their decision

I think you are overlooking another option: take the job offer from your friend, and re-evaluate whether or not you want to pursue a PhD in a year or two. It is entirely possible to leave academia and come back, although you may encounter additional questions/scrutiny from people who have taken a more linear career path. And with a bit of distance, some savings, and a [hopefully] better work-life balance, you may even find that you prefer life outside academia.
Anecdote from someone who has lived through this:
I was in a very similar situation during my physics PhD, although by the end of my fourth year I was also severely depressed and my largely absent advisor was always pretty neutral about my ability to graduate. I decided to continue in the program for two primary reasons: I was somehow convinced that I could salvage the situation and graduate in 2-3 years if I put in enough effort, and I had no idea what else to do with my life (a research career in my sub-field was still my dream job, even though I was miserable in that department). A year and a half later, my advisor decided that I would never graduate and dropped my funding. No other professor was willing to take me as a student -- I heard from a trusted third party that someone had started a smear campaign against me so I had a terrible reputation on top of my low research output -- and I left the university with 'just' my masters.
While I was (and still am) angry about the way I was let go, I do agree with the decision. It was a relief to openly acknowledge that my situation at that university was untenable and not going to improve, plus it was the kick in the pants I needed to find another job. I ended up teaching as an adjunct professor for some time and did a lot of soul searching to figure out what I wanted out of life. Ultimately, I decided to apply to other graduate programs, was accepted, obtained my PhD, and am now working as a postdoc in the same sub-field I started in (and am loving it). It remains to be seen if I will be able to find a permanent position, but my current collaborators have been nothing but supportive and encouraging about my future prospects.
If I have any regrets about the situation, they would be that a) I did not leave my first PhD program sooner and that b) I allowed my advisor to ultimately make the decision to leave for me by cutting my funding. Very few people have since asked me about my first PhD program (even during interviews), so I rarely need to explain my 'missing years'.
The decision to stay or leave is yours, and unfortunately no one can tell you what is best for you. However, I would leave you with just a few thoughts:

You mention that you don't really trust your advisor anymore. What
would it take for you to trust their word again? Are you likely to
get it? Can you honestly see yourself finishing your PhD without that
trust?
Has your advisor given superficial/generic comments about your
graduation, or concrete details? Based on my own experience, I would
be skeptical of the situation if your advisor only gives hand-wavy
assurances.
Look up the 'sunk cost fallacy' and see if this applies to your situation.

Best of luck!

I have found this graphic really helpful for staying motivated in the PhD and reminding me that many, many people go through this. Sounds like you have hit the trough :)
The most concrete advice I've gotten is that the PhD is an endurance sport rather than a sprint. So if you want to finish it sounds like you might need to just persist and stick it out. But I know how you're feeling and it is awful.
Concretely, I can see a few things that might help:

Ask your advisors to help you work out a timeline for graduating in 6 years (or whatever number of years -- just make it fixed). That way you will have clear milestones and deadlines to work towards. It can change later, but write something down now.

Try to take concrete action towards developing a proposal. I find it strange that they don't let you propose by the end of the fourth year; we actually can't advance past it without proposing. It does take some time to pick a topic and build related experience, but in theory, a proposal is what you will do. Is there something intermediate -- like a 1 page outline of the proposal, or a list of three proposal pitches, or a plan for preliminary experiments -- that you can work with them on? (the equipment you're building ostensibly has a purpose). Particularly now, that you can't fully run your experiments, it seems like a good time to take stock and figure out a direction of what will happen, so that you can run with it as soon as things normalize.

Why can't you publish your review paper? Try to understand if this is just a recommendation or a firm no. Is there something you can improve? Is there something you can salvage from it (e.g. an intro chapter of the thesis?) If you're not working on anything else, you might as well be trying to get this out. It's possible that they think it's not good enough for a top publication, but it might help motivate you to have one publication through the pipeline, even if not the most competitive.

Try to find a support community. I have found that meeting other students through summer schools or conferences has helped me a lot. You might be able to undertake some related collaborations to help motivate you, and as a bonus publish that way. For experimental work, maybe you could try to find a lab that you could visit or intern with (CERN? DOE? I am not a physicist) -- joining existing experiments might enable you to publish without setting up from scratch.

Take some time off. If you are burnt out and experiments aren't running, maybe just block off a week or two for complete rest and no physics.

It sounds like your advisor might be thinking longer-term than you are -- for him the priority is probably setting up the lab, rather than graduating you. Hopefully, once the equipment is set up, you'll be first in the queue (and get credited on the publications of the other younger students), but I can see that it would be hard to guarantee this in advance and you risk being taken advantage of. For now, I'd try to be clear that you're having a hard time and need some sort of framework or plan for moving forward. Hopefully that will take the focus back to what you want -- an end goal.
I haven't commented on your outside offer because I think that's really a personal choice. But it sounds like you want to take it because you are having trouble with the PhD, so I tried to think of ideas to solve that. The fact that you're asking this question suggests that you're not quite ready to give up on PhD...?

Thanks for your thoughts. Truthfully I think I might be ready to just leave. I don't want to stay in academia anymore and I'm just miserable here. I love actually doing research when I'm allowed to, but those times are few and far between. I'd probably be better suited for an engineering type role somewhere. Not as fun, but I wouldn't be on the brink of a mental breakdown all the time.

At the end of the day, you should do what's best for you and your mental health, and it seems like this conversation has clarified what that is, so that's great. As I said, I don't think there's a clear right or a wrong answer...Looking back, I just try to think: if I was convinced that I made the best choice I could given the information/situation/etc at the time, then there is no point in having regrets!

Both your advisors seems to be doing an unacceptably poor job of advising (though, of course, I'm basing this solely on your description). In addition, your program doesn't seem to be doing a good job for its students, in terms of advice or supporting timely completion. From what you've written, there doesn't seem to be a driving passion for the research topic that would be strong enough to outweigh the first two issues. And finally, you have an excellent job offer -- something plenty of people with a Ph.D. struggle to get. To me the choice would be obvious. The main thing I suggest is to definitely not think of the past four years as wasted, or even to regret them. Life is full of meandering paths, and you've undoubtedly learned or practiced various skills, had interesting experiences, or simply grown in your outlook. Do what is best for yourself; don't worry about the past, or about sunken costs.

Thanks for your thoughts. I finally talked to one of my advisors today(been trying to get a one on one since March) and he said I could propose a thesis next year. Truthfully I don't think I believe him anymore though. It's just very difficult to leave because research is really the only thing I've ever wanted to do with my life.

First step is to figure out why you are studying. What are you hoping to accomplish anyway? You want a PhD, obvious enough, but why do you want one?
Ultimately the purpose of education for most people is to be the foundation of a career. The degree helps you get a job you enjoy, which also earns you $$$, which makes you rich, which lets you have children + send them to college, and retire in comfort. Does this describe you? If not, what does? Think carefully about what you are trying to achieve.
Do you have some idea what kind of job you enjoy? This is a difficult question because you usually won't have an idea until you try it out or see it firsthand. Still, you could get some indication from the things you like doing. For example do you like putting machinery together, gathering data from experiments, analyzing data, and writing patent applications? If you stay in academia, you'll be doing more of that. If you find you don't like doing these things, it's a sign to switch.
Assuming you're talking about USD, $85k a year is a tremendous amount of money. That's more than what some professors earn. Does money matter to you? It might sound shallow, but if you have a spouse to accommodate and/or intend to have children, buy your own house, etc, you'll need money.
Based on your description it's a choice between:

Stay on in your program for an uncertain number of years. Keep doing things like putting machinery together, gathering data from experiments, etc. Probably not be paid very well. Maybe get a PhD in the future (and then what? You need to fill in the blanks of what you are going to do with the PhD).
Leave, start earning a lot more money. You'll probably never get a PhD and feel like a failure as a result (note however that you can stop feeling like a failure when you stop treating "fail to get a PhD" as a bad thing). You'll do something else which you might enjoy more, or might not.

It's a choice only you can make since you're the only one who knows what you want to do with your life. Just remember that the second option is a legit one. You don't have to stay in your program if you're miserable and burnt out. It might be the preferable option if you think the burnout is temporary, that things will get better, that getting a PhD is what you really want to do - but if that's not the case, there's nothing wrong with quitting.

Thanks for your thoughts. I certainly don't really want to leave, but I've seen some grad students here for 9,10, and one at 15 years. I don't want that life. I was told the average here was 5-7 and that's what I committed to. As it is I'm basically a very cheap technician for them. I had an old friend asking why I'm not graduating yet (granted he thought I'd been here for 7 years) and it just felt terrible because he got out in 6. I've been considering leaving for a while now.

It certainly sounds like your advisor has not done you any service, even given their personal life taking their time (justifiably but perhaps overlong). I believe the answer by Allure is exactly the right framework to think through, because getting a PhD really comes down to remembering why you are doing it when it gets difficult.
As far as proposing a thesis, I think it is a good call not to propose yet, because part of the proposal should be grounded in previous research done, and it also sets you up for timely expectations. Many departments intentionally slow this down because it is more important for you to have a solid background before graduating, i.e. having papers and research to set you up well, than it is for you to just fly through it and finish it. The exact amount of research depends a lot on your focus and department, but I would be hesitant to propose without already having knocked out a few papers that lead into that direction.
Another choice you have is to switch advisors, which can be beneficial if yours is not working out. Switching advisors within your school should not delay your progress, but switching schools could add some time, although it may also be shorter than the unknown amount of time it sounds like is going on.
For the job, consider the location as well. $85k sounds great until you realize that $85k in SF is equivalent to $40k in Cleveland OH. Cost of living is important and can vary dramatically in the US.
If you are looking for stability, then a job may be a good choice, especially if you are not sure why you want a PhD anymore. If you are looking to move into a role you can't get without it, then you probably want to consider how to stimulate your progress. I would recommend talking to the other professor and explaining your thoughts and what you are deciding between as well; they tend to be able to understand your perspective if you explain what you are going through.

Thanks. I really don't know why I'm doing this anymore to be honest. Basically a year was wasted on a project that went nowhere and got no publications out of it. I've gotten really good at putting together scientific equipment, but I wanted to be a scientist not a technician. The job is in the same city I'm in now so cost of living is the same.

And I completely agree it would be premature to propose a thesis right now. I'd planned on just taking data earlier this year and proposing this summer after I could get a paper out for review. COVID kind of messed that up. Labs were shut down from March-June. I'm going back now but it'll probably be shut down again very soon.


text:
Do academic reviewers have a duty to critique authors who submit questionable research?
I recently reviewed a paper that made some very strong claims that were not supported by the data. However, it was much more than that. These claims were so extreme that that were actively misleading: e.g., "The present results represent the most important findings in personality psychology to date." (Not as bad as this example, but not too far off..)
I wrestled with two options in my review.
A.) I could respond in a scientifically disinterested manner: e.g., "These strong claims are not supported by the data. Please revise them."
OR
B.) I could go beyond that and politely "critique" the authors for their questionable practice: e.g., "These strong claims are not supported by the data. In fact, they represent such an "overselling" of the manuscript's findings that they are actively misleading. Please revise them and we urge the authors to avoid such hyperbolic claims in the future."
In the end, I went with something like option B.) because I think that there is inherent value in stating firmly that these kinds of practices are not okay. As a scientific peer, I did not at all appreciate these obvious efforts to oversell the results for the sake of "a top publication." As reviewers, we are the guardians of scientific literatures, and when appropriate, perhaps we should scold our fellow researchers for questionable scientific practices to deter them against such behaviors in the future.
This begs the intriguing question: Do academic reviewers bear a responsibility to critique authors for engaging in questionable practices that undermine the validity of scientific literatures?
Very interested to hear the views of others!
Edit: "Reviewer" is intended to refer to one's role as a reviewer of publication submissions for journals.

By "reviewer" you mean what?  "A paper in a top journal" suggests that the paper is already published?

As I see it, your only duty is to give the editor your honest and well-reasoned opinion as to whether or not the manuscript should be published.  Anything else is your own preferences.

Strictly rejecting and calling out bad substandard manuscripts that contain for example overreaching scientifically unfounded claims is important to prevent junk science from taking over ... Or at least from becoming too widespread.

I'm afraid this is a textbook example of a question that is "primarily opinion-based". (That probably everyone here does have an opinion on this does not change the fact.) StackExchange is not well suited to soliciting or discussing opinions. Voted to close. Discussions like these could be conducted in chat.

@StephanKolassa no, this is an important issue for academics and it therefore should discussed here.Leave open.

@Dilaton: many important topics are nevertheless opinion-based. StackExchange aims at providing correct answers. It is not well suited to discussions. Forums or chat are a better venue for this. I cast one vote for closure, five are required - we will see whether four others agree with me, and then the question can still be re-opened. Or we could discuss this specific case on Meta.

My feeling is that rather than explicitly telling the authors what to do in a context other than the present submission, it would be better to explain your objection to their present submission in a way which would make clear to any moderately receptive party that the advice would apply more generally.  E.g. something like

In my opinion, the authors overestimate the significance of their work to a degree that becomes actively misleading: virtually no work in the field has the level of significance claimed by the authors here.   In general, work which is described in such hyperbolic terms can be hard to take seriously.  Those who do make major breakthroughs tend to describe the advances in more sober, factual ways.

This is plenty heavy-handed.  Anyone who is listening will get the message not only to tone down the language in this submission but that such language is never appropriate.  Still, you aren't telling them what to do, but only giving your (expert) opinion on the consequences of their actions.

Be a professional, and be helpful.  What's the point of chastising the authors? will they think you are 'smarter' than them? No, to them, you'll sound clueless or/and arrogant.  Hence, it is a waste of your time and frankly, doesn't help  the editor because he/she will think you have some axe to grind.  Your ONLY job is to help the editor make a decision, and if you are kind, provide constructive comments to the authors.

I respectfully disagree that one's "ONLY job is to help the editor make a decision." It goes beyond that. One is a representative of the field at large and every review shapes its practices.
And no, they certainly won't think the reviewer is "smarter than them." But that's not at all the point. The point, articulated by the commenter above, is to "prevent junk science from taking over." Which, to a disconcerting extent, it has.

No -1: the purpose of the review process is keeping up the level and scientific standards.

@ATJ you assume the authors will listen to reviewers.  I doubt that very much if you are not professional in your comments -- the operative work is chastise, which the questioner is advocating.  Ask yourself, are your more incline to listen if your parents berate you or when they talk to you kindly?

@Dilaton Yes, to review and help the editor reject poor papers.  In other words, ensure papers with questionable claims do not see the light of day.

Perhaps "chastize" was the wrong word. I feel like that carries with it a negativity I did not intend, and I've changed it. And authors do listen to reviewers--whether consciously or implicitly in future behavior. That is certain.

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Psychology Science degree
My brother did a Bachelor of Science degree, Psychology Major, at the University of Manitoba.
I am curious if it is common for Psychology to be offered through Science and Arts faculties as opposed to just Arts. Do most Universities offer this?

I don't understand what you're asking. What faculty would you expect psychology to be part of?

Just the faculty of arts.

In the US, Psychology is rarely considered part of the arts, and is generally called a "social science", with most degrees being offered as "bachelor's of science". Oddly, psychology is often excluded from "STEM" designations, where it is often not considered under the umbrella of either "science" or "technology". For more info on this, see the American Psychological Association's article on Psychology as a Core Science.
Regardless, at least in the US, Psychology is generally not classified as an art. It's a field in kind of a weird place, classification-wise. There often is some flexibility in degree classification here, as many Universities allow you to get a "bachelor or science" (BS) or "bachelor of arts" (BA) in nearly any field (even something like Physics or Math). The BS vs BA classification often is just a question of what other classes you take, such as in language (BA's usually require foreign languages and more classes in humanities). Just in case things aren't quite confusing enough for you.
Psychology's position as "social science" is something in-between the humanities and science-proper, with some areas clearly being heavily related to the arts (such as dance psychology), while some are actually housed within engineering schools (human factors, psychology of engineering, etc). Still other fields - or descendants - of psychology are hosted in schools of technology like computer science (human computer interaction, for instance). So the field of psychology, perhaps more than most fields, tends to defy easy classification and every institution has their own unique interpretations and departmental history.

+1. Plus things like neuroscience, which is (IMO) obviously science, as in "natural". Clinical psychology is close to medicine. Biological psychology is very close to biology and biochemistry. Now please excuse me while I go and review a manuscript on immunological alterations in post-traumatic stress disorder.

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How to defend plagiarism in master's thesis
I am an Indian student and studying in the USA away from home and family.
I am writing my master's thesis in a private University and we were two weeks away to submit the final version to the committee and I was about to start my PhD in a public state university. I was working in math and proved some original result with some different proofs and I also read a paper and elaborate the proofs in my own language. I admit that I took the statement of the theorems word by word and some discussions as well.
I was unaware of this serious plagiarism before as in my undergrad I didn't have idea of writing a thesis.
I first wrote my understandings on paper and then tried to type this in overleaf. I am pretty bad at reading pdf files from computer screen and can't do it for longer and after typing a bit I went to another state to my relative's house and got stuck in Covid19 and I lost some major details of my paper. I was panicked because of family's health and my health. I also consulted with doctors as I have anxiety and insomnia problems which includes some short time memory loss. I don't know how to express this that I forgot to put a citation of that corresponding paper. I cited a ton of other papers in my thesis and even other papers of those corresponding authors. I even thanked some of my friends and my students whom I give private tutions with whom I discussed in my papers. I also said my advisor that I am reading one paper and elaborating it and asked whether it is okay or not and his reply was it is ok if you give proper citation and still I missed that particular paper. Now my advisor has taken an academic dishonesty action against me as last week we were discussing about one definition and suddenly I recalled that I wrote a particular section of my thesis from a paper and although we were out two weeks away from my submitting it he complained against me.
I have an anxiety feeling and guilty feeling because what is happening with me these days. I am student with good academic understanding. I never wanted to make this happened with me and I want to confess when I am now reading about plagiarism I feel that it is a plagiarism but I was unaware of this fact before this severe consequences. I remember I asked my professor whether my thesis will be published or not and he said that it won't be published. I have few questions:

How severe the consequence of plagiarism in masters thesis if it won't get published?
Can I appeal to make changes as I have one week now in hand?
Should I say the reasoning or rather accept my guilt and say that I have done this willingly because in one article it is written that accepting is a better solution.
How should I defend myself? I have my defence on Monday. I am the first scholar in my family so I don't have any guidance on how to say it precisely. I can also have paid guidance if someone wants to guide me. I can't afford much I think I should have one. Moreover, I often feel that I am a Bengali so my English is the very weak to express what I feel and the committee members or the teachers sometimes get bored with what I say. Partially this is because of nerve problem as well.

Clarifications / details / updates:

I did find the citation in the bibliography, so the only problem was the lack of an inline citation.
My advisor and I discovered the issue during a final review. I mentioned in the discussion that a citation was missing. The next day, he canceled a meeting with me and I was informed that a misconduct hearing had been scheduled.
In addition to the mental health issues, I also have some physical health issues that could be relevant (B12 deficiency, etc.)

Further edit
As suggested I am confused with some comments as some people are claiming that I can't have oral defence before submission.
Let me add timeline details:
17th of April: I have mentioned all the citation of the corresponding paper and after that, we have almost met 30 times on reviewing the thesis. Most of the discussions were till section 5 and I overlooked that I missed the citation on section 6 and was the major citation that I am realising.
12th of July: I have sent my thesis for review to the thesis committee.
16th of July: One committee member made some comments on half portion of my thesis and asked me to correct it( didn't have any information regarding plagiarism) but stated that in this current format the thesis is unacceptable.
17th of July: My defence scheduled on 24 by my advisor.
17th of July: Another committee member made some comments on one third portion of my thesis and asked me to correct it( didn't have any information regarding plagiarism). Some comments were common with the first committee member.
17th of July: My advisor emailed me that we need substantial improvement in the clarity of the
writing to accept the thesis for graduation. Committee members
will get comments to me by early next week. I should go through the
comments as a high priority and send to me a new version. He will go
through that new version again and mark any places that still need
improvement. We will then go through those places together until
they are acceptable. This final version will be returned to the
committee for a final look. My advisor is away August 4-9, so this must be
completed before he is out of communication.
This does not all need to be completed before the defence but does need
to be completed before the format meeting with the graduate school. Note
that the latest version you sent still has overruns into the margin
which will cause the graduate school to reject your thesis.  ( didn't have any information regarding plagiarism).
20th July: I was done with the part one comments of the 2nd committee member.
21st July: We had a meeting regarding defense.
24th July: Defended my thesis and did it successfully but was informed that current state of thesis is still concerning. Plan is to sit next week every day for hours and fix it and return it to the committee at the end of the week and upon satisfactory re-read the recommendation for conferral degree would be submitted.
27th July: Done with most of the comments of all committee members.
27th July: We first discover the citation problem in the thesis and my advisor told me that he will inform on how to fix it next day once he will read the other paper.
28th of July: My advisor cancelled the meeting stating that he will be in touch with me. By that night, I didn't hear back from him and asked whether he is ok or not! I was worried about pandemic going on in the states.
29th of July: I heard from my instructor that academic dishonesty report has been filed against me. I was also advised to inform the counselling centre as the proceedings will be very stressful.
30th of July: I have heard from the departmental head about my hearing is on Monday.
Is it called submission that I have done on 12 th of July because the committee sent me several comments to improve and I was improving that?
Further edited:(Missed one comment)
My thesis has 6 sections in the first 5 sections I have given some new proofs of some known result and the last section I actually discussed someone's paper entirely. I did copy-paste the definitions the statement of the theorems, lemma and corollary directly like a verbatim in my undergrad I was advised to remember the theorems, lemma et all exactly and I tried to write the proofs in my own language.
**I am also wondering one thing that I completed my writing with a citation by 17th of April. Does any advisor check for plagiarism after that as we were doing grammatical and mathical corrections after that. Now after being reported I found that in see **

"I have one week now in hand" - does this mean you have yet to submit? If so, now is the time to get off SE and start fixing your thesis!

Protecting, as this question has attracted a number of unkind answers and comments. While it is natural to be outraged at academic misconduct, please recall our be nice policy and keep this constructive.

Hi,
I have edited with timeline deadline. The health part if that is unnecessary then can be ignored as some of you advised me to ignore that.

Comments are not for extended discussion; this conversation has been moved to chat.

Also - your question is far too long. I don't think your "further edit" section is necessary, and suggest deletion. The judges in your case may benefit from your hour-by-hour timeline, but this forum requires/allows a brief summary only.

Ok, I won't add more. I can't decide which part to delete. So I leave the case to you all who are more experienced.

@Ri-Li Finally, what did you do?

I admitted my fault. No matter what is the reason, I did that mistake. Even after my pleading and statement that I made a crime but not being well aware I was not given a chance to rewrite my thesis but I can't blame anyone but myself. If I would be given a chace then that would be one sign of mercy. I got my masters degree with course work but my dream of writing an MA thesis got shattered. Probably this is a lesson for me and for the upcoming generation as well. I gave myself condolences that I should deserve the punishment. Hopefully that will give me some peace.

Probably the bigger punishment is my self-regret, repentance and nightmares. I also think we should also be open about our mental problems. One more things that I am learning is acceptance because it was the hardest part to forgive myself for the mistake I made as I have only one life to live. I hope that it will not affect my future to a great extent. Nowaday we have seen bigger problems which are larger than a micro-life. So being from a 3rd world country also haunts me for being in a job insecurity. I pray that everything will go well.

This answer does not respond to subsequent edits to the question.
If you submitted a thesis with plagiarism, the typical consequence would be expulsion.  You would not get a degree.  The good news is you didn't submit it yet, so there might be no consequences.
Can you still change your thesis?  You need to ask your supervisor.
You have admitted there was plagiarism in the draft.  Stick to that.  Just make sure there is no plagiarism in the final version.  Your defense should that you did the wrong thing in the draft and have fixed it; the final version does not contain plagiarism.  You will still look bad, but I think avoid punishment.
Health problems are never a defense against charges of plagiarism.  Continue to get treatment from health professionals.

"Health problems are never a defense against charges of plagiarism." I think that's something for the university's disability office to decide, since it would potentially open them up to lawsuits for ADA violations.

@nick012000 No.  There is no disability that causes people to plagiarize a master's thesis.

What I don't understand is why did his/her advisor didn't just resolve this with him/her and filed a claim? The advisor is equally responsible.

Comments are not for extended discussion; this conversation (about health as an excuse for plagiarism) has been moved to chat, and new information from the OP has been edited into the question.

Hi,
I have edited with timeline deadline. The health part if that is unnecessary then can be ignored as some of you advice me to ignore that.

I do not have any further advice for you.

This answer does not respond to subsequent edits to the question.
Have you submitted your paper yet?
If you have not yet submitted then you haven't done anything wrong (yet!) and you have time to change it. If required you may have the option to ask for a deadline extension, given the current exceptional circumstances and your own health issues.
Reading your question I'm not 100% clear what you've actually done or how much of your thesis could be considered plagarism.

If you've failed to attribute a couple of theorem definitions then this should be easy to fix; either re-write them in your own words, or quote them, and cite all sources properly*.
If you've copied (even in translation) large portions of discussion and analysis then you'll have more work to do, but it's essentially the same job as you've had throughout your thesis: You need to express these ideas in your own words and convey your understanding of them.
If the writing is your own, but you are worried that the ideas are not as original as you have portrayed then you may not have such an issue. Provided you are submitting your own work, then a masters thesis does necessarily not need to contain entirely "new" proofs or results. If this is your concern you should talk to your supervisor and understand their expectations (and the marking rubric) for a thesis, if they have read your draft and are broadly happy then you may not need to do anything further.

If your thesis has been recently submitted then you should talk to your supervisor as soon as possible and explain clearly what has happened. It may still be possible to retract you thesis and further you may be able to talk to your academic institution and arrange for an extension and re-submission date when you can submit a plagiarism-free version. This will be a discussion between you, your supervisor, and your academic institution, the outcome of this will depend on the precise details of what has happened at what stages.
If your thesis has been submitted and plagiarism has subsequently been found during the marking process.
This is a very different situation from the above. You should read up on the policy of your department and the broader institution. You may wish to edit your question/ask a new one in order to get more specific advice, you will need to provide further details as to how much was plagiarised and how exactly it was copied (short phrases with minor changes or entire paragraphs etc.).
General advice on discussing health and it's impact on your work
Current issues surrounding COVID and your personal health are not an excuse for plagiarism, but they may be a valid reason for delaying a submission until you can remove the plagiarism and submit a legitimate thesis.
*Edited for clarity, you should always cite sources properly, not just when quoting!

"either re-write them in your own words, or quote them and cite them properly"—the source likely should still be cited if you're rewriting them in your own words. Especially given the circumstances here, it would probably best to get advice, preferably in writing, before deciding that a paraphrase of something doesn't need a citation (e.g. that the theorem is common knowledge).

Citing a source is nothing bad. I've got the impression that he may think you need to do more original work by rewriting the theorem. This is not needed and the theorem will not be original work. On the other hand, it is probably not required to have the theorem to be original work, when it is only a perquisite for other parts of the thesis. Most the time you'll rewrite it a bit when using it and cite the original source, sometimes you'll take it as is (maybe changing the formatting a bit) and add something like "we'll use theorem X from work Y: (theorem here)"

And with most advisors, good work does not mean complicated work. An easy result does not mean you didn't work enough, but that you're able to express the idea and result in simple terms, what is a good thing. One doesn't need to add complicated own theorems like the one that was not cited correctly to impress anyone. Most works are not about quantity or having many complicated formulas. (Disclaimer: One may have an advisor who thinks otherwise. But this is a problem with the advisor).

It hasn't got published or submitted yet but in the oral defence talk, I haven't mentioned their paper while taking portions from their work, I blindly followed what I have written in the thesis. The problem is I asked my professor that I am reading a paper and elaborating it. He said it is ok in master's thesis but you have to cite that. I have thanked my friends and put many other citations and mentioned the name of that particular paper in reference but I don't know how I skipped putting \cite.

Then we were doing a final review and I said that I made a mistake and a citation is skipped. He said we will meet tomorrow and then he cancelled the meeting and said that I am charged of plagiarism under section B and I have to face a departmental and academic hearing. I have taken the statement of the theorems and example from that paper and tried to write all the proofs in my own word. I am willing to rectify all the work and I could have done it in the mean time when I have to face two hearings and time is running away.

I was supposed to get my degree in mid-august and start my PhD by the end of August. I am so upset for all this. I never wanted to put a question mark on my academic career. On my laptop I can only see a portion of the thesis and I missed that point that the citation(\cite) is not there.
I am just confused on what to say. If I say it is all my fault. Will the department chair file a case to the academic committee and what should I say to the academic committee then?

I am worried that if I say anything to defend myself whether my professor would offend and I will not get my degree on time. See if I don't get my degree in August, I have to delay my admission and then I don't know even whether they will accept me in future. Then I will be stuck in the USA with no earning and I have to maintain my family. I am just repenting on what I have done. If I could have figured it out!

@ri-li I'm honestly confused. You're being cited for plagiarism, but you haven't yet submitted your work? You're doing the oral defence before submitting? I'm not sure how that happens, but it sounds like there is some portion of the story that is missing here. I would advise you to clarify your post with a timeline of deadlines and remove the additional details (health, visa, future PhD studies). They are important personal details, but they're making the rest harder to.understsnd and harder to help with.

@zachlipton - you are completely correct. My grammar has let me down. I've added an extra comma to hopefully clarify!

Hi,
I have edited with timeline deadline. The health part if that is unnecessary then can be ignored.

Admitting your mistake is the 2nd step in fixing things (finding the mistake is the 1st), and the 3rd step is making sure the mistake doesn't become a problem by fixing he mistake. There are lots of minor steps (which usually change based on the situation), but I've found these are the 3 major steps to get a situation back on track.
We're all human and can rush through even important things. Use this as a learning experience to prevent doing it again.
You shouldn't defend the plagiarism, just admit the mistake and correct it, which it sounds like you are willing to do, if you haven't fixed the issue already.
The things that caused you to make this mistake can all too often be used maliciously as excuses for bad behavior. Don't fall into that trap. Even if they are true, it'll likely be taken as an excuse, rather than a good reason. We've all been affected by changes in our lives due to Covid-19, so there's a little more leeway for things like this getting in the way, sometimes. But that's still not a good reason for making career ending mistakes.
If you haven't already, you should apologize to your advisor for the mistake and reassure them it won't happen again. You can state that it was unintended, but unless you can somehow prove it, like you said you could with the reference in the appendix, then it likely won't reduce the lost trust.
This is a case of "take your lumps" and learn from it. It'll likely take less time and energy than anything else. You "did the crime" so you should "do the time". Because it done was accidentally (intention often matters in law) and you haven't submitted this as a final draft, your crime isn't as serious as it could be. Defending it would make it more serious, so just don't do it. The "time" usually depends on the severity of the crime, so you've lost trust from your advisor, which is a lighter sentence than another Answer mentioned about expelling you. Just work to regain that trust, even though it might not ever be regained, and try to make sure you don't give them another reason for them to lose trust in you.
Martha Stewart is a good example of this. She was convicted of insider trading and, for the most part, did her time and got over the whole ordeal fairly quickly. She could have made a huge deal of trying to save her fame and fortune by putting up a massive fight, but instead she only did what seems to be a perfunctory fight against the charges. She ended up doing her time in prison fairly inconspicuously, then her home confinement without making a big deal of it. She might not be as big of a deal or as much of a "household name" as she could have been without the problem, but she's still around.
There's plenty of people who have made a huge deal about charges against them, only to make things worse. Don't do this to yourself.
As for your feelings about what happened, well, you'll just have to deal with it. Forgive yourself if you can, understand that it was a mistake that you fixed, and over time, it'll feel less like you've done something "horrendous". It could have been worse, but it was caught before that happened. Again, use this as a learning experience. You are allowed those. I know what I'm saying isn't exactly comforting right now, but that'll just take time to dull the edge of what happened. That's normal.
It's actually a good thing you are reacting like this, even though it doesn't seem like it right now. Your feelings will help prevent you from making the same mistake later, due to "never wanting to feel like that again". Just take some time to calm down. In a few years, you'll look back at this as a lesson learned and pretty much everyone else will have forgotten about it.
Edit:
I'm not saying to not defend yourself, just defend the correct thing. Don't defend the plagiarism, defend that you did it accidentally and are willing/working to fix it.
Edit 2:
Also, when you go to defend your thesis, don't bring up this issue, as it'll simply confuse your defense. The people on the Board/Panel/whatever, will either know the situation and bring it up, or they won't. If they do bring up the plagiarism, stick to defending the accidental nature of it and point out that it's fixed.
You can say that you've learned you lesson and that it'll never happen again, but that can come off as a simple placating gesture, rather than an actual fact. They've probably heard the same thing from others that end up making the same mistake they promised would never happen again. It's possible to make this type of statement sound real, but it has to be said with real conviction, since the tone of your voice and your bodily actions can speak just as loud, or even more loudly, than your words.

Good edit........

@paulgarrett, thanks. When I posted the answer, it felt like I was leaving something out, but I couldn't figure it out right then. It wasn't until after lunch that I realized what I was missing: stating my implied idea explicitly.

It hasn't got published or submitted yet but in the oral defence talk, I haven't mentioned their paper while taking portions from their work, I blindly followed what I have written in the thesis. The problem is I asked my professor that I am reading a paper and elaborating it. He said it is ok in master's thesis but you have to cite that. I have thanked my friends and put many other citations and mentioned the name of that particular paper in reference but I don't know how I skipped putting \cite.

Then we were doing a final review and I said that I made a mistake and a citation is skipped. He said we will meet tomorrow and then he cancelled the meeting and said that I am charged of plagiarism under section B and I have to face a departmental and academic hearing. I have taken the statement of the theorems and example from that paper and tried to write all the proofs in my own word. I am willing to rectify all the work and I could have done it in the mean time when I have to face two hearings and time is running away.

I was supposed to get my degree in mid-august and start my PhD by the end of August. I am so upset for all this. I never wanted to put a question mark on my academic career. On my laptop I can only see a portion of the thesis and I missed that point that the citation(\cite) is not there. I am just confused on what to say. If I say it is all my fault. Will the department chair file a case to the academic committee and what should I say to the academic committee then?

I am worried that if I say anything to defend myself whether my professor would offend and I will not get my degree on time. See if I don't get my degree in August, I have to delay my admission and then I don't know even whether they will accept me in future. Then I will be stuck in the USA with no earning and I have to maintain my family. I am just repenting on what I have done. If I could have figured it out!

Martha Stewart was not convicted of insider trading; she was convicted of lying to the SEC, obstruction of justice, and conspiracy to do those things. She probably did not even commit insider trading, let alone be convicted of it.

Talk to the disability office at your university.
The mental health and insomnia issues that you mentioned in the original post would qualify as disabilities, and the university is obligated under the Americans with Disability Act (ADA) to grant you reasonable accommodations. Additional time to correct errors in your thesis paper that arose as a result of your disability would likely qualify.
Of course, you should also take efforts to correct the mistakes now that you've become aware of them, and to let other people in your department know so that you don't publish your thesis prior to the mistakes being corrected.

Suggest you edit this to say "in addition to other actions taken in parallel to handle the problem". OP should not just let things roll ahead while consulting with the disability office.

This answer may be bringing some new points only because, coming late, I've been able to draw from a number of more recent comments, trying to answer (semi-) briefly on select points. Otherwise, as the most relevant points have been discussed in great detail and length, the rest may just approximate some  summarizing. But still...

How to defend plagiarism in master's thesis

Do not defend plagiarism. That is, if your wording of your question title is not just a language thing (no offense meant). Plagiarism in itself is indefensible and, as has been broadly pointed out here and elsewhere, is commonly treated as an inexcusable offense (to a point where some may even seem to stop using their brains and EQ to consider and differentiate circumstances. To be sure, neither do I mean to defend plagiarism or any motivation to plagiarize whatsoever.).
Plagiarism is not (seen as) covered by any health or state of mind issues, either (excluding recklessness, which counts as aggravating). There is simply no acknowledged health issue that is seriously believed to bring about plagiarism. (It has been discussed elsewhere on this site that some rare health issues can bring about unbelievable things (like deliberated murder incomprehensible to the victim-perpetrator), but I don't think that helps here.) So as others have said already, you had better not seem like you were trying to hide behind excuses. (The ADA thing may be valid where applicable but surely not for directly explaining plagiarism, as far as your actions are seen as that.)
Though I might contest the idea that no health issue could contribute to a course of things happening that may lead to an effect that, assessed by the rules, amounts to plagiarism -- but be very careful with that, it could count as a desperate attempt at a cover-up, so unless a seriously qualifying and qualified person (maybe at the counselling center or faculty) advised you explicitly and clearly to mention anything in that quarter (and what), or was going to mention it for you, you may be better sticking to cold facts, not including any of this.
(I think, and hope, it may help you a bit that working this QA has made you summarize the cold facts which may help you work from there. Have that timeline handy in the hearing - things now being where they are, help the committee determine the facts by offering up what facts you have - unless advised otherwise, and use as appropriate.)
As a corollary and general rule (though I guess that's not helping you much now, but for the classical step back and for posterity), if you are facing whatever issues that are a risk to your ability to avoid producing plagiarism, it is a very good idea to deal with them as early as possible, doing whatever is necessary. It helps to start building a habit of absolutely producing complete and sound citations from very early on during your academic progress. And rather citing "too much" than too little so in doubt you'll be erring on the side of caution.
Going from that, can you reasonably mention - only as a side point, of course not as a mainline of defense - that your habits of citing everything (which can be seen in action in all other citations you made - if these are high-quality enough to justify saying so), were insufficiently trained (in terms of the training you allowed yourself, not meaning by your advisor and teachers) as this was the first thesis you had to write ever, or for a long time? Beware though, that could be self-disqualifying, too - I'm actually surprised, if I get that right from what you're writing, that you were never before required to write something that required proper citation practice.

The problem is I asked my professor that I am reading a paper and elaborating it.

Not meaning to overdo taking you literally, but that's not a problem. What's a problem (and a big one) is that you failed to expressly cite the specific paper and passage even after your supervisor expressly said you have to cite here.

27th July: ... 29th of July:

Wondering what caused the sudden change of attitude in your advisor (I really do), I'm imagining he suddenly realized that you seemed to have defied his clear order to cite and fell for the assumption this was intentional as he was so clear about it. (In this case, I'll assume this should be taken like an order -not just advice or guidance- because it is advice about really complying with the most basic rules that should be understood to be taken and complied to far earlier than only in one's graduation thesis)
About this being basic - as hinted, until the time you had to prepare a thesis in earnest, you should have trained your very gut feeling to awake you even from sleeping on Valium, and in the middle of whatever stressful work or distraction, to the slightest trace of an omission of citing any old thing, and then make you calmly and automatically and fully add whatever missing citation.
I do think it may be in your defense unless - see next paragraph that it was you who brought up the missing citation to your advisor, not vice versa. I don't dare give advice on this point in your situation but maybe somebody in the know can advise you about bringing that up in the hearing (unless your advisor will claim it's not a fact?) - it could be clear from here that there was simply nothing bad you were trying to do.
But considering that the oral defense had already happened and you did use that part of your thesis there with the citation missing, after which you brought the missing citation up to your supervisor later, it seems possible that he reacted to this by seeing it as first successfully trying to slide it by the defense audience then cover it all up by fixing it later in the paper. That would be really wrenched and sophisticated misconduct, of course. Again, I don't dare advise if and how you should react to that possibility but if there's still some time between now and your hearing, you may be able to get some advice about it.

have taken the statement of the theorems and example from that paper and tried to write all the proofs in my own word

That's a double-edged sword - it may be what (you think) you do to show that you have understood and thoroughly thought through all of it. Of course, technically it's also the same thing that the ordinary common plagiarizer would do to hide the fact that they are really just copying someone else's work.
A better approach seems to be to make it a habit to always state (if need be, ad nauseum), so-and-so explain this and that and their reasoning goes thus - recounting all of it meticulously with not ever the slightest of change (and not forgetting any of as many footnotes as may be warranted) - then add "I use this as the basics to do X, changing Y, arriving at Z via R, S and T."
(Once you do this perfectly, you may well be at liberty to summarize the work you are citing, where applicable, but always keep the distinction visible.)
Keeping the clearest visible distinction possible between your work and others' work may save you a lot of misunderstandings (and the immense effort of rewording lots of stuff that presumably has been worded well already, so in fact your rewording could not help rendering the same facts in an inferior way, which is clearly not your goal in a thesis.)
And that could be guidance to rework these parts of your thesis if you get the chance, and it seems not entirely impossible that where you are this could be seen (but you better ask the right people there) as a way to also clear up a methodical fallacy ("rewording is good") and produce a remedied version of your thesis that clearly shows your work and what is the work of others.

For sure I won't defend plagiarism and I won't defend myself as well. I did copy-paste the definitions the statement of the theorems, lemma and corollary directly like a verbatim and I tried to write the proofs in my own language. I admitted that in the comment. It is ok.

I do admit that I have done wrong but I know that it was unintentional. In my hearing, I will admit my guilt as I believe it as well. May be I am still missing some points that have been raised. I will try to say my words honestly but really thanks a lot for all your help and advice. Pray for me that I won't any mistake in future.

Your edits/clarifications have changed the question substantially, so I'm going to post a second answer as I think the first still holds as general advice
The situation you describe is still confusing to me, I'm not sure I can gauge the extent of the "citation problem". Missing a (single?) in-line citation (which has been put into your own words) is certainly not good practice, but I'm not sure it would usually lead to the reaction you describe. In particular, your advisors rapid transition from "you should probably cite this, let me check the paper" to "This is a case of serious academic dishonesty, I'm escalating it immediately" indicates to me that there is more going on than is given in your post.
Before your department meeting (today!) I would urge you to ask yourself the following:

What does your department policy consider to be plagiarism?

Is this different from what you think plagiarism is? If so, why is it different?

How much of your paper does your department consider to be plagiarism according to their rules?
How much of your previously submitted work contains this kind of plagiarism?

Just to add, I wouldn't expect the reviewers of your thesis to date to have spotted plagiarism, the fact it's been seen by several people doesn't mean that any of them would have been the look-out for plagiarism.
Separately, you seem to have an issue with the overall quality if your thesis "informed that current state of thesis is still concerning". I would put that issue out of your mind as much as you can for now as it's not relevant to a discussion on plagiarism.

A masters thesis in math rarely has any significant original research in it. In fact I know people whos MS thesis in math consisted entirely of citing other peoples results and discussing them in an expository fashion.
As long as you didn't claim an original result from someone else I'm not seeing the problem.

While not entirely untrue, presenting others' results without explicitly giving credit is still plagiarism, even if the claim to have established them yourself is only implicit or ambiguous.

Depends, if the OP states at the start of his thesis that these works aren't original, it's not plagiarism - it's failure to properly cite which isn't the same thing.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Advisor-student collaboration (or lack thereof) and paper authorship in mathematics: how does it work?
In (pure?) mathematics, author order on papers is alphabetical, based on the assumption that all authors contribute equally (e.g. as discussed here and explained in this statement from the AMS).  Moreover, single author papers are quite common, even from students.  Many math PhD students will have few (or no) papers coauthored with their advisor, and when people from the same research group collaborate, the usual practice of alphabetic authorship is followed.
As an outsider from a "related" field (theoretical physics), I'm wondering how this works in practice and what the experience of a PhD student in mathematics is like.  The description of "joint work" from the AMS statement makes sense in describing collaboration between colleagues, but not advisor-student collaborations.
In physics, typically a professor will suggest an idea, and the student(s) will explore the idea, do some calculations, etc.  Then they'll have some discussions, the student(s) will present their results, the professor offers some suggestions, the student(s) do more calculations, and eventually they write a paper.
How does it work in mathematics?  Is it similar to physics, where the advisor offers ideas and direction, but with the convention that the student typically writes up the results as a single-author paper? Or is it the case that mathematics PhD students really are expected to be highly independent, and receive much less help from their advisors compared to graduate students in other fields?
A related question of mine is whether there is any "grunt work", so to speak, in mathematics research.  There are no experiments to do or simulations/computations to run, but is there still a certain amount of calculations or proofs that merely require "routine" work?
For example, I imagine that mathematical research, conducted "physics-style" might look like this: Professor thinks of some theorem to prove, problem to solve, etc, and introduces it to a student.  The student works on it for while, and then brings their results to the professor, who then offers their interpretation and new ideas, and so on.  Over time, they "jointly" work on the project, but the student does the vast majority of the pencil-on-paper work.  Is this style of research (or rather, of advising students) not common in mathematics?

As a preface, which might help explain the phenomena you observe, "grunt work" tends to have low status in mathematics.  A solution to a problem that uses a large amount of "grunt work" and little else might be unpublishable, while a different solution (providing the same answer) to a problem that involves much less "grunt work" might be publishable in a fairly highly regarded journal.  Remember that results in mathematics tend to have less (but not no) extrinsic motivation, so part of the evaluation of a result is the elegance with which it is achieved.  (This general valuation extends to entire subfields - graph theory is a low status field in large part because proofs in graph theory tend to have a high grunt-work-to-insight ratio - for example the proof of the Four Color Theorem involves a fair amount of insight but a gargantuan amount of grunt work, so much that it had to be carried out by computer.)
It's worth noting in this context that a significant fraction of dissertations in math are never published as papers, because the results in them (or rather the manner in which they are achieved) aren't considered interesting enough to be published in a reputable journal.
So - a dissertation in which an advisor provides a problem and the student solves the problem by pure grunt work is unpublishable, and terrible for the career of the student.  Also, if you are looking at this from the outside using the journal publication record, you get a misleading view because the dissertations written in this way are simply never published as papers in journals.
This doesn't mean a student is expected to be completely independent as might be the case in many (other) humanities fields.  There is indeed a cultural norm where many (probably most) mathematicians do not put their names on work of their students even where, if there was not a student-advisor relationship, their contribution would merit co-authorship.  It's quite common for advisors to offer direction and hints at ideas, but the student writes up the work as a solo paper (with an acknowledgement for the help of their advisor).  In general (though not always, and each research community tends to know who the exceptions are), when a paper is jointly authored by an advisor and a student, that actually means the advisor did all the important work and the student contributed only grunt work and no insight.

Thanks, that is interesting.  In this sense math is very different from physics (and probably most fields), where the advisor has a much lower bar for authorship.  Example: a potential project arises in a discussion between A and B.  B is too busy or not interested enough, so A pursues the project.  A and B have a few discussions later on, as A writes the paper.  In physics, I would imagine that B might (though not necessarily will) be on the paper if he were A's advisor, but maybe not if otherwise.

I really do think the cultural prevalence of whether advisors tend to put their name of students' papers is so unclear as to render a speculative "most" very ambitious.

Hnm, I'm wondering a bit about the sentence "It's worth noting in this context that a significant fraction of dissertations in math are never published as papers." I think almost every PhD student I've got to know during the last 10 years or so (in mathematical analysis) published at least a paper or two. Of course usually not in super fancy top reputation journals, but certainly in reasonable journals where people will typically assume to find serious mathematics.

@JochenGlueck The statistics in this answer, averaged over different math fields, indicates a substantial fraction (roughly 50%) are not published or accepted at the time of an exit survey. I suppose the asymptotic value as t→∞ must be lower, but seems unlikely to be negligible.

@JochenGlueck: I work in a department where, apparently, in the entire 50+ history of our PhD program, no pure math student has ever gone on to a research-oriented academic position (not even a postdoc).  That may skew my perception (but in more than half of math PhD programs in the US, less than one student a year goes on to a research-oriented academic position).

@JochenGlueck: I also want to point out that you suffer from selection bias here - other professors are less likely to introduce you to their PhD students whose research is less successful.

Just as another anecdotal data-point: (in the U.S., in math, at an R1) I view my job as PhD thesis advisor to be that of coach/mentor/educator/protector.
The "protector" part of my responsibility is to shield my students from working on things that I myself know full well I could not accomplish (despite being fairly clever, having decades of experience, and reading lots of other peoples' work).
So I suggest/encourage projects that I'm fairly confident will work out, and will be interesting, but ... hopefully ... are not so immediately on other peoples' radar that more experienced people will "scoop" my students.
Then I coach my students in such projects. Yes, I do give lots of specific technical commentary... and editing advice on documents ... but my students do the literal work.
On another hand, no, definitely, there is no "grunt work" that I need done to further my own research projects. I suppose this is wildly different from more lab-oriented things. My own main benefit from coaching beginners is motivation to re-think things myself. A large benefit, in the end. :)
I do understand that there are wildly varying authorship criteria... I take the viewpoint that I am a more senior person who happens to be still-alive, giving advice in person, as opposed to the many good mathematicians who've written useful things, but now can only communicate by their writings. I do make a point of citing historically significant (and, stimulating/helpful-to-me) documents... but I hesitate to give co-authorship to deceased people, no matter how much they've contributed to my thinking. :)

So, in the situation you describe (you suggesting the topic, and offering advice and editing) your contribution would not warrant authorship?  I guess that really is a difference between fields, because in physics the advisor would definitely be an author even when the students did the "literal work" (and that's where the author order comes in)

@Aqualone, yes, I guess it's a cultural difference... I think that, in math, everyone knows that the advisor (at best!) would indeed be very helpful to their students, but not claim co-authorship. Nowadays, yes, I do see some people claiming co-authorship with their students on thesis-related work. Understandable, I guess...

Your last paragraph is interesting. In biomedical, I think the distinction would be published versus unpublished work. You wouldn't give coauthorship to someone for contributions which were already published in some fashion (you'd cite instead), but you would (potentially) for contributions which couldn't be found by independent third parties. Posthumous authorship isn't common, but is completely warranted if they've provided a unique (unpublished) contribution to the work.

In pure math and some parts of CS there is a parallel, but the "do some calculations" part is, perhaps, more challenging than you describe. If an advisor suggests a problem (not a calculation problem, but a question as to the potential truth of some idea) then the student needs to do a lot of work to prove or disprove the hypothesis. It is non trivial. Along the way, there may be consultations and suggestions made. But if the student is able to provide the crux of the solution then it is usually the case that the advisor will let them take sole credit, though people understand that they didn't work in a vacuum as an independent researcher.
The opposite case can also occur, though less frequently in the student-advisor relationship. One mathematician can be working in a problem long and hard without getting the main insight (the crux). A five minute conversation with a colleague might provide that insight, in which case co-authorship is usually given.
Advisors (good ones) should be able to steer students away from dead-ends. This takes a lot of experience to have a sense about what is do-able with the current state of the art in a field and what is probably beyond reach in a year or so if deep thought. I worked on three different problems. The first (if I remember correctly) was too easy and I got results every day. It was "cute" but didn't have enough substance. The second was too hard and a month of work left me with no insight at all. It seemed intractable at the time. The third was just right. Hard and deep, but progress could be made building the needed parts and putting them together.
So, your last paragraph seems pretty close to the mark, but it isn't "pencil and paper" work. It is deep-thought and a search for insight that can be captured in proofs of meaningful statements (theorems).
I think it is often the case that the professor giving out an idea for a problem could do it on their own and may already even know how. But they leave it to the student to work through to the insight needed. I suspected that this was the case with my dissertation, as my advisor was a superstar. But he let me thrash through to the required end and it was a good result. It was my work, but he wasn't surprised as to where I got to. It wasn't a "collaboration", so I was sole author.
The reason for alphabetical listings when there is a collaboration is that the insight might, perhaps often, result from joint discussions where the crux emerges from the conversation and it is impossible to assign priority. These are true collaborations on ideas, not just dividing up a bunch of work into independent chunks. Collaboration in math is often just a search for "attack vectors" that can be applied to crack a thorny problem. One goes at it from many angles but discussions can provide new angles that may prove fruitful or not.
I would guess that in theoretical physics it could work the same, since it is often insight (the crux) that is the key and an advisor could sit back letting the student get there with some general guidance to keep them from going off the rails. I've read a discussion of Einstein and Special Relativity and the ten year quest for insight. That is a lot like what goes on in math. Not "calculations" or "pencil and paper stuff", but key insight and finding ways to express it formally.

As a theoretical physics professor, but with a Ph.D. applied mathematics, I can say that the fields are pretty different with respect to the degree of importance of insight versus calculation. I have had papers with graduate students where the students were first authors, because they did the majority of the work, even though the deeper insights may have come almost entirely from me. It's not an easy problem to figure out the right angle to take to solve a hard physics problem, but it is often even more work (and not intellectually trivial work, either) to apply that method and get the answer.

@Buzz: As I hint at in my answer, I don't actually think that mathematical problems inherently require a higher insight-to-calculation ratio - it's just that, in mathematics, problems that are solved by a lot of calculation are devalued because a lot of calculation is done to solve the problem.

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What does last authorship mean in various fields?
Author order has been discussed extensively on this site, e.g. here, but these typically focus on the first author.  I'm curious as to the meaning of the last author in various fields.
In (theoretical, non high-energy) physics, the last author is typically the one who conceived and directed the project, but may not have done the actual work of performing experiments/simulations/calculations (that would be the first author).  The last author usually is someone more senior, but is not necesarily the PI or the most senior author.  In fact, one often sees physics papers with a postdoc as the last author and the PI as a middle author.  In fields with this convention (which I'll call "last=project leader"), last authorship is as coveted as first authorship, and it is desired for people at the postdoc/early faculty stage of their career to produce last-author papers, as it demonstrates leadership and ability to come up with ideas.
It seems that there are also other conventions.  For example, my impression is that there exists a similar but distinct convention: the "last=PI" convention, where the last author is by default the PI, and doesn't come with any connotation of level of intellectual contribution, or the same strong significance attached to the first author position.
As a (possible) example of the difference between these conventions: in physics (or fields with the same convention) a junior person who performed a major leadership role might be "promoted" to last author, while in fields with the "last=PI" convention, they might be promoted to first or co-first author instead.
And (in some fields?) there is the "decreasing-contribution" system, where authors are simply arranged in order of level of contribution and hence the last position would just be the least important one.
So, among fields where author order is non-alphabetical, which follow the "last=project leader" vs "last=PI" vs "decreasing contribution" conventions? Are there possibilities other than these?

There are probably as many conventions as fields, and more papers that use an individual style than follow the rule.

While the title of your linked question mentions first authorship only, most of the answers also address the other author slots, including last author. So, this may be a duplicate of the linked question.

@cag51 I did not find the information I wanted from the other question, and given that that is an old question, it is highly unlikely that such information will emerge in the future. Yes, there is some slight overlap, but the new question highlights a deemphasized aspect of the old question.  Questions such as this are a useful way of generating new knowledge.

@Ben I am just curious in general, and I hope that this question can also be useful for others who are also curious. I imagine that as an answer, one can write about their own field and any adjacent fields that they are aware of.

@WolfgangBangerth There are certainly not as many conventions as there are fields.  At least there would be a few broad patterns which many fields would fit into one of. And as for unique styles in individual papers, that is very rare and arguably wrong/unethical when it happens, see here

Meta discussion about this question: https://academia.meta.stackexchange.com/q/5463/17254

Per the above-linked meta discussion, I am marking this as a duplicate of the above-linked question. If anyone posted an answer below that is not already covered on the linked question, we encourage you to repost it there. (Otherwise, we may re-post it for you as community wiki.)

In (pure) mathematics it means that the last name of the author comes last when sorted alphabetically.

As a statistician, I have worked in a few fields and, as a statistical reviewer, I've reviewed in more fields. I haven't really got a great answer for field by field, but I've seen:
1a. Alphabetical list of authors
1b. Random order
2a. First author most important, then alphabetical
2b. Same only with random order

Last author 2nd most important

Last author = PI, or the person who got the grant money, or the most senior

But each of this seems to happen in all the fields I've worked in (psychology, epidemiology, general medicine, neurology,  neonatology, social networks, education, …).  I'd say there is more variation within field (often by journal) than across fields, but maybe some fields do have a standard --- there are tons of fields I haven't worked in!

In biology is say its both last author=PI AND last author is project leader. Project leader IS the PI, almost always. In fact,  PI is short for principal investigator.  PIs are usually, but not always, the head of a research group,  so the head of the research group is usually the last author. But not always. If a postdoc conceived of, planned,  got authorisation and funding for a study.  That is,  if they were legally responsible for it.  If it would be then in the dock if the data were fake, or ethical rules were not followed,  then that postdoc would be the PI and the last author.  I believe this situation is more common in physics than biology.
The last author is also usually the corresponding author.  This is the author most likely to be contactable at the same address and able to answer questions across the total content of the paper in 10 years time.

I generally agree with this pattern in my experience with biology, but corresponding author can also be the first author. Some PIs/advisors have their subordinates/students do the legwork of submitting, others, prefer to be the corresponding author.

@RichardErickson I think you may be confusing the author who submits the article with the "corresponding author" who is going to be responsible for the work and future correspondence. You can submit on behalf of the corresponding author, and I often have my senior graduate students do this. That is not to "pawn off work", it is actually an important skill they have to learn if they intend to remain in academia.

@R1NaNo No. I am not. I know that the corresponding author is listed as the person to contact with questions and students are transient. I've also seen people view this as a badge of honor. Also, by historic convention, this person was also the submitting author. Personally, my advisor had me list myself and him as the corresponding author and let me do the uploading. However, other advisors in my graduate department do all of the correspondence with the journal, either because they micromanaged or had legit concerns about the student messing up the process.

@RichardErickson, yes,  I've also seen this happen.  I've also seen people use corresponding author to mark "joint last author" type situations. But last author being corresponding is most common.

Mind that the term corresponding author is used in two distinct ways in different fields. It can refer to the author who handles the submission or to the author who handles correspondence after submission. For details see this question of mine. (CC @RichardErickson)

@IanSudbery What about "small" projects? That is, involving only a few people, and using only existing lab equipment and therefore not needing its own dedicated funding/grant. In such cases the PI/professor may only be minimally involved, and the leader of the small project might be a junior person, so the PI and "project leader" are not the same person in this case.  but perhaps this is less common in biology?

@Wrzlprmft thank you for sharing your question. That helps clarify a lot.

@aqualone I'd say it probably is less common. Most biology project need ongoing reagent costs beyond equipment. Plus the biggest cost is salary. That doesn't mean people should get authorship just for funding. But generally the person getting the funding has official responsibility for the conduct of people on the project. Still, this is one of the situation is one a postdoc would be the PI for a particular project.

@aqualone and Ian Sudbery See this formal attempt to define authorship contributions https://credit.niso.org/

@RichardErickson I'm aware of CRedIT. Its a good idea, but I'm mostly describing here is what does happen, rather than what I think should.

In chemistry/nanoscience/materials science/applied physics, last author with * is the corresponding author and main-PI. You can have multiple PIs with * for collaborative works, and they appear typically in order of contribution at the end of the author list (the last being the project leader). This goes out the window when people do alphabetical which is less common but still done.

Applied physics is not really a field with a homogeneous culture. I have published many papers in what can be considered applied physics where this did not apply: I was the first author, not the PI, had an asterisk next to my name, and was the corresponding author in both senses of that term.

If there is one default convention in condensed matter physics*, it is that the (main) PI is the last author. Many projects may involve multiple PIs, who then tend to collectively be at the end of the author list. In those cases, the precise order can be a matter of politics, or done according to level of involvement. If a postdoc is listed as last author (which seems to happen most often from European research groups?), I would expect them to have had some kind of supervisory role. Last authorships can indeed count more depending on career status, making them more desirable for some authors.
As for who conceived of the project, it is highly variable and cannot be reliably deduced from the author list. For big-budget projects it's most often the PI, but for specific papers it can often be a student or postdoc who had a specific idea for further investigation. Perhaps that is particularly prevalent in theory work. Or it could be that another PI had the idea, but not the expertise**, time or resources to carry out the project. In such cases, depending on the distribution of work, the idea-haver might go anywhere in the author list (or even the acknowledgments). That said, junior people are often motivated to work on their own research ideas so it could well be that the first or second author is the one who was actually driving the project.

*Especially mathematical physics work in the condensed matter context sometimes uses alphabetical order, which is ignored here.
**Commonly seen in experiment-theory collaborations, for example.

We use the ordering of authors to denote contribution. The first author did the lion's share of the work and is the communicating author. From there it's declining contribution or specialist contribution (such as preparation of maps... I'm a Geographer). The last author contributed the least relative to the others. By least, I don't mean of little importance. Everyone plays an important role hence they are acknowledged. It is just that these roles and their contribution to the publication are different. In this model there are no freeloaders who are named without contributing. Having discussions at the outset of the writing is critical as this sets the stage for who does what and how people will be acknowledged etc. If roles change, we discuss this openly. Typically, we share responsibilities and hence where people are acknowledged across a series of outputs. I'll lead this one while you do other things... You lead this one while I do other things etc. This model is particularly good when co-publishing with PHD candidates as it provides a framework for them to understand their role and what they have to deliver while socialising them in an open and collegial publishing approach. I hope this helps you

In medical research, there are guidelines by the International Committee of Medical Journal Editors for what are the responsibilities and meaning of authorship
Basically, it agrees with some of the descriptions already in the answers above: The one who contributed the most for the realization of the research presented in the paper goes in front, while the PI or postdoc (little PI ;-) ) is at the end. Usually the last author conceptualized the research developed and presented in the paper.
About the discussion with the corresponding author: This is the person that will answer ANY question regarding the research presented, including files used for images, code for data analysis, ethics grant documentation for animal or human research, etc.
I hope this helps you to see the variability in fields.

I am in the social sciences, and from what I have seen - and experienced myself - thus far, the last author of a lab-driven project/paper tends to be the lab P.I.


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Resigning from tenure-track position after sabbatical for industry -- how little research can I do before I leave?
I'm on tenure-track and going to go on sabbatical in the fall for one semester. When I return from my sabbatical, I plan on giving a year's notice and switching to teaching part-time while I take over family business. Research is not for me, but I like and respect my colleagues and I want to do "right by them." My question is, how little research-related work can I do during my sabbatical and in the following year without jeopardizing my prospects for being hired as an adjunct afterwards and my relations with the department in general. I should mention that I am much liked as a teacher and coordinate a huge part of the undergraduate curriculum, so I trust that the department will want me to stick around...

Doing right by them. depends upon your own values and ethics.

How do sabbaticals work where you are?  Where I am, you have to have a proposal as to what you are going to do during the sabbatical.  Typically this includes research, but I don't know what you had proposed.  If you said you were going to do research, I think it would be unethical not to make a good-faith effort towards that.

I feel that for this question, internet academics who do not know you at all will not give as good an answer as friends or mentors within your university or department.  As @Nate Eldredge points out, expectations for what happens on the sabbatical can vary considerably from institution to institution, for one thing.  For another, the answer seems to depend crucially on the balance between research and teaching in your department...and even your own balance between research and teaching.  Since you're planning to quit no matter what, I advise you to ask these questions within your department.

I don't get it.  Why do you want to teach and run the family business when you could do just one?


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How do I reference a conference paper that is due to be published later this year
I am writing a paper that builds on a previous work. The previous work has been accepted at a conference and will be published as part of the proceedings, but it hasn't been published yet. Do I just reference it using the standard format for referencing unpublished works or not?

Interesting question - with a journal article usually it's either "in review", "in press" (very brief these days) or out there... but with a conference paper that's accepted and waiting for the proceedings to come out... I'm curious as to the answers.

Either "Accepted for Intl. Conf. on Whatever, 2018", or
"To appear in Proc. Intl. Conf. on Whatever, 2018", or
"Intl. Conf. on Whatever, 2018, to appear".