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Received an ultimatum from PhD advisor to leave that broke me completely. How to cope emotionally?
I am a PhD student in an American university, on year 4 of a 5-6 year program. Recently (three months ago), my advisor told me to leave the program since he doesn't think this subject is for me (he said this statement exactly). He doesn't think I have it in me to get a PhD because I haven't made enough progress yet. This completely broke me from inside. They gave me some time to come up with an alternate career option along with a deadline to reach up to a certain point in our research.
I see where my advisor is coming from. I am still learning how research works. My work involves a lot of code, and this is not my strong point; it took a while to come up to speed. Communication is difficult since my advisor is mostly online. On the other hand, I did very well in my classes and quals, and I do well in conferences and such. I had asked my advisor for feedback many times, and they told me everything was fine until now.
I actually managed to meet the deadline, and things have improved externally.  We never did discuss alternate career ideas. The advisor now acts like everything is fine. But for me its like pulling a bullet through me and then acting as if I everything is great! I can take criticism but this broke me so much that I constantly feel like crying. I can't talk to anyone. I am scared that if I talk to professors, they will think I am just stupid and really lack what it takes to do PhD.
How do I cope with this emotionally? I do still want a PhD. Finding a new supervisor at this late point would be very difficult due to funding and visa issues.
Clarifications from comments:

My advisor is not a bad person. In fact, he is considered one of the nicest people ever. So I fear if I open up to someone, either I will get ridiculed or will burn bridges for future.
Their attitude changed abruptly when one of my seniors was taking very long to complete a thesis (~2 yrs), that is when I think it hit them that it is taking too long. That is when his behavior changed towards me too.
I am an Indian female, the advisor is American male

Agree that more context on field would be helpful. Esp.: "I can do the work but am not extremely great at coding." What role does coding have in this field? Are you in a CS or informatic type field? Or is it some other science that uses code as a tool?

Does your program award a Master's degree as part of progress toward PhD, or is there a mechanism to apply for such?

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I recommend that any graduate students facing discouragement and fraught advisor relationships make an appointment with the student counseling center. I would especially recommend this route for you because you state in a comment that “Now I am workwise doing fine but internally I am very broken.”
The counselors there are very familiar with the issues students face when dealing with advisors. The counselors can help to coach you through this, in particular helping you to work on not getting stuck in a negative thought pattern and keeping good relations through productive conversations.
More than half of the students in my high-pressure graduate program used these programs and we all found it very useful. They were free/covered by our student health insurance fully.

Thank you for taking the time to read my really long post. I have tried the counseling services provided by the university. Every time I tried then, it really was more of them letting me talk and then saying see you next week. It eventually turned into a rant program but I never got any help from them. I appreciate them listening to me but after a point, I started feeling like this may come across as a joke to them. I tried 2 separate counselors and upon talking to other students, I found out that our uni-provided counseling services are not very helpful overall. private option-out of budget

The counselor would never approach a professor @Trunk. Our counselors were very effective at providing emotional and moral support for the impact of badly behaved advisors. Sorry if this was not your experience.

Ultimately, the advice is to take care of your mental health - perhaps finding a book that is geared toward identifying and changing negative through patterns would be another avenue toward the same goal.

Counsellors aren't going to help.  You have to go to an academic in the system who is in charge of the welfare of PhD students and explain the situation.

There are really two aspects to this, and the way @StudentOfLife wrote about being "broken completely" indicates that the mental health aspect is important. So I'm with Dawn on this one, but still of course also steps to address the situation with the supervisor and in the department make sense. Both things are important, focusing on one of them shouldn't stop her from dealing with the other.

@StudentOfLife If by "them" you mean a single counsellor, it is worth asking for a different counsellor - you need the right one for you as just slight differences in the way they understand what you're saying can make a big difference. You can say you don't feel like you and the current counsellor gel.

I recommend talking with other professors in your program. It may seem like you're stuck with your current advisor and that's your only possible funding source, and you have no other option, but that's not true. Plenty of student-advisor relationships sour over time (you're not going to remain friends with everyone you meet), and students can change advisors. Graduate programs would rather move money around than lose graduate students. I've seen it happen in my own program.
I would review the research areas of the other professors in your program, set up meetings with them to talk about your research, find common ground, and see which professor feels right. When applying to graduate school you just pick a professor to work under and hope it's a right choice. Sometimes it isn't, but that's not the only professor in your program doing interesting research!
Rephrase your situation and realize the opportunity you have. Now you get to have deep research conversations with all of the other professors in your program and really get to know the other professors and see who you really click with. When applying for grad school you only really get a 30 min interview with the two professors they think match your interests. Now you can talk with them all!
In addition to meeting with the other professors in your department, I'd chat with the dean of your department. They want you there, doing research, and if there's a better fit with another advisor that will help you do research better, they can help find the funding for it.
Grad programs can take 7+ years for students to graduate, especially if the person you're forced to have advise you stops doing it (as in the case here, obviously they're not a very good advisor to tell you you're bad at what you're doing and to just quit).
Remember, you really do have other options, you aren't stuck with this terrible advisor. Who cares if it took you X years to graduate instead of Y years. When you get your degree no one asks you how long were you in grad school for, they just say, "Hello, Doctor."

I wouldn't jump so hastily to "they're not a very good advisor to tell you you're bad at what you're doing and to just quit" and "terrible advisor".

@PasserBy No, I think this is entirely the correct amount of haste. In fact the very moment they said a student four years into high investment program like immigrating to get a PhD should quit, they crossed the line into "terrible advisor" and would have an extremely hard time crossing it back.

There are all sorts of legitimate things you can say or do if you think your student is struggling, but "quit" is almost never on the table. I suppose if they, I don't know, suffered horrific brain damage in an account or illness and lost their capacity to think at their old level, maybe. Short of that, though? Not their damn place.

@linkhyrule5 How would you know what specifically was and wasn't said to OP? Do you hold that PhDs be given to anyone after they have spent a certain amount of time? Purely in the hypothetical, if there is a standard to be cleared, and if OP's advisor genuinely think OP is unlikely to clear it, would you rather OP be led along for three more years or find out now?

I'm reminded of the wry joke: "What do you call the guy who graduated with the lowest grade in his doctorate program?" "Doctor."

@PasserBy The fact that the OP was evidently surprised by the advisor saying that and had to ask him to explain why indicates he is, in fact, a terrible advisor. Regardless of whether the advisor is correct or not (and it's by no means clear that he is), he should've given the OP feedback on what to improve on a long time ago. Telling someone the subject isn't for them and they should just quit should be the last step after multiple discussions of how they'd like the OP to improve, and at that point the OP should already have a good idea of why they're saying that.

@EJoshuaS-StandwithUkraine an inability think through implications or to do more than follow directions (as indicated from "my mistakes" on) seems to match up pretty well with not noticing anything less subtle than "Quit now."

@fectin It sounds more like the advisor just wasn't giving feedback at all.

@fectin  Clarifying- I contsnatly have been asking for feedback and was always told good.never hinted at any areas of improvement.  the points I have made is after crticially thinking through everything, things i feel i can work on. I asked many times what made him think i was bad but he seemed very unwilling to say. When i asked is it the subject he said-no, is it the project progress, he said yes. He wouldn’t explain very much other than u r very good at communicating the subject you should try an outreach degree. He wasnt willing to explain details but more focused on pushing me to leave

I am extremely self critical and noticed when the behaviour changed towards me which was extremely subtle. If once, I would even lightly be told that you should focus/ work on, I won't take that lightly, I have a lot to loose. If i told to improve on something, i wouldn't just sit around. I am an international student. The top 3 in my class, I understand the stakes here. So yeah, i am not oblivious to any subtle feedback i can get. Also the mistakes I mentioned are what i think my area of work could be. none of these was told by advisor when asked about the reason i should quit.

@StudentOfLife The first paragraph is the correct answer IMO. As someone who got through a terrible relation with my first advisor, I can say that switching advisors was one of the best life decisions I've made. At the moment everything might seem grim, specially after facing any sort of abuse from your advisor, but know that change is a good thing here. Also, don't be afraid to change the focus of your research, I personally believe that having someone who would like to supervise you and help you flourish is more important than doing fancy stuff. You'll get time for that later on.

I'd like to respond to a few of the things here.
First, your advisor's claim that you haven't made enough progress yet isn't particularly specific of feedback. It would be helpful to get more details from him about what he was expecting you to have achieved by now that you haven't. Right now, it seems like you're going off of what you assume that your advisor thinks your problems are, which may be quite different than what he actually thinks the problems are.
In my opinion, the fact that you don't already know that is a failure on your advisor's part. If he felt you weren't making adequate progress, he should've given you feedback on what he thought you needed to work on much sooner. It seems quite strange to go straight to "this subject isn't for you, quit the program" without ever having given feedback on what to work on. That kind of a discussion should never come as a surprise.

"I didn't understand how to do research" - isn't that why people do PhD programs in the first place?
"I can do the work but am not extremely great at coding. I am working on getting better." If this is a serious impediment to you completing your work in a timely manner, there are courses available on Coursera, Udemy, and other platforms. Don't be afraid to use resources other than the ones that your professors "officially" require/recommend. Personally, I used supplemental textbooks in most of my math coursework after I got to calculus (which was the first math class I genuinely found difficult), and I was able to complete a math degree with good grades as a direct result.
"I am scared that if I talk to professors, they will think I am just stupid and really lack what it takes to do PhD." Are you sure that they'll react that way? What evidence do you have for or against that? It's really hard to predict whether they will or won't. I'm guessing that there'll be other professors who are more willing to work with you than your current advisor appears to be. If you don't ask, however, it'll have the same effect as if they really do think that. Also, even if they do think that, you won't be in a worse situation than you're in with your current advisor.
"I got stuck at a point due to a misunderstanding in a concept for a long time. It took away around 6-8 months for me to know the problem." From your other statements, it seems like you may be extremely concerned about appearing stupid/ignorant/etc. This mentality could be hurting you here, as talking through the problem with other people can help you get "unstuck." I've often found that even attempting to describe the problem in detail to someone else helps me get unstuck.One trivial example: a few years ago, I was writing a Stack Overflow question on a problem I was stuck on. When I was adding steps to reproduce, I noticed that the error message suggested an article to read - and I hadn't read it. I decided that I'd better read it (or people would ask why I hadn't). It turned out that it described my problem exactly and its recommended solution worked right away. If I hadn't gone to describe the problem in detail to other people, I likely would've continued to gloss over the link for much longer than I did.
"Advisor have only been available through online meetings and emails. Communicating sometimes was challenging." If the way you and your advisor are doing things isn't working for you, don't be afraid to ask for what you need. If asking for what you need is difficult for you, I'd encourage you to read a book on assertiveness (or speak to a counselor to help you become more assertive).
"I have been taught to keep professors in very high regard." It's good to respect experience and expertise, but be sure that you're not discounting your own experience, needs, and opinions in the process. The mere fact that someone's an expert in the area doesn't automatically mean that they're right. For example, the mere fact that your advisor thinks that the subject isn't for you doesn't automatically mean that it isn't - they could be wrong. You're not obligated to uncritically accept everything your professors tell you; in fact, not doing so is an important part of being independent (which is one of the areas you mention struggling in). Again, being able to express disagreement may not come naturally at first; this is another area where assertiveness training could help you.

Hopefully, there are at least a few things in here that will help you. The biggest points I would like to emphasize: first, you have nothing to lose (and potentially a lot to gain) by talking to other professors. Secondly, it sounds like assertiveness training could be very beneficial to you in this context. This will help you gain more independence and advocate for your needs and opinions more effectively. Third: don't be afraid to take advantage of outside help or resources if you need them.

-Thank you taking the time to respond. You points are extremely helpful to help me look at this with a different perspective. As for the coding, i can code everything, i will have 5 lines instead of 2, but they work. As I mentioned in some comments, the advisor was not very willing to discuss the issues they thought i had but more focused on giving me other career i should try. I was never communicated that i was not doing well. That is why it came as a shock to me. These problems are identified by me, not him. your response is very helpful for me to work on. TY

@StudentOfLife Yeah, sorry you're going through this - it seems like your advisor isn't doing his job. If he felt that you weren't making enough progress, he should have given you feedback on ways to improve a long time ago, not ambush you with "this subject's not for you, quit the program" completely out of the blue. After all, the job of an advisor is to, well, advise, and it sounds like he hasn't been doing that.

What does your advisor mean when they say you haven't made enough progress yet? Did you ask them? In my field, I would expect my students to have written a couple papers by this point, but I am extremely hands-on for the first paper or two (learning to write papers is very hard for most students). I have to sit with them and outline the paper and then later sit with them in several sessions where we basically rewrite nearly every sentence. I get the idea that your advisor is somewhat hands-off. Have you made progress on any manuscripts? Is your advisor helping you with this? Do they expect you to begin having your own project ideas? Do you have any ideas of how to extend your project or take the methods that you've learned to another problem?
You shouldn't take a single person's opinion of your potential for a career in research or academia as the word of god. Should you take what they say seriously? Yes, but you should also consider it as one data point.
It sounds to me like your advisor is very hands-off, which may not be a good fit for you. Maybe your advisor is waiting for you to take the initiative and if you take the initiative and if you ask them they will give you the support you need? Maybe your advisor is a nice person but not a good advisor and unwilling or unable to give you the support you need. However, year 4 is rather late to be changing advisors unless you there is someone in your department with very similar research where you could make use of what you have learned so far.
If you want to continue in academic research, producing some papers during your PhD is essential. It will be hard to find a postdoc without some evidence of productivity. If you haven't published yet, you have two years, which is plenty of time. But you need to to start now. You will need help. Perhaps if you are assertive about asking for help in organizing the paper from your advisor they will help. If they are a negligent advisor, you will have to be assertive in finding help from other resources (other faculty, postdocs, other graduate students).
The reasons you give for "delays" in your project all make sense. Research is hard and most students don't understand how to do research at first. It takes years to learn. I'm not sure what you field is, but unless you are a computer scientist, it is probably okay to be not very good at coding. Have you taken any classes on data structures and algorithms? Many scientists are not very good at coding, yet use it often in their work. Even as a PI, it takes me 6–8 months to start really making progress when I start a new project. Most students are not independent when they start. When I was a graduate student, I just did what my advisor told me to do for the first 2 years. It wasn't until my 4th year that I started suggesting my own ideas for projects. However, I think at the 4th year you should be ready to start coming up with your own ideas and be able to plan and organize a paper yourself (although still with comments from your advisor).
What is your plan for the future? Do you want to continue in research? Do you want to continue in academia but are okay with a mostly teaching focused appointment? There are many academic jobs with primary teaching appointments, where you might do a little research or collaborate with other researchers. Does this interest you? Are their jobs in industry in your field?

"If you want to continue in academic research, producing some papers during your PhD is essential" this is certainly not always true. I didn't publish in my PhD and got a good post doc, tenure track etc. It's hugely dependence on the field, country etc.

@user438383 what field is this? In which country?

Genetics in a Western  European country

@watermolecule Thank you for your time and response. Here are some of the details- i have 3 papers right now. I am in stem field so coding is not the degree but important. I can code but i will write 5 lines instead of one. I adked many times what made him think i was bad but he seemed very unwilling to say. When i asked is it the subject he said no, when i aked is it the project progress, he said yes. He wouldn’t explain very much other than u r very good at communicating the subject you should try an outreach degree. He wasnt willing to explain details but more focused on pushing me to leave

Sounds like this person is trying to get rid of you for reasons unrelated to your work – perhaps funding, lowering his staff count, doesn't like working with you personally. Could be anything. I would not accept his comments as direction on how to proceed, but I would try to get a new adviser.  He probably doesn't have the ability to fire you explicitly, so is trying to demoralize you into quitting

@user438383 this is in USA, I am in stem field. I have 3 papers, one in nature. will have a few more.

@RC_23 this is a very interesting observation. Thank you for bringing this to my attention. You are correct, the only reasons an advisor can fire a student is extreme underperformance. This has happened in my dept. but the cases were not similar to mine. Students got fired, none had completed their proposal and weren't in the field for this long. the chair was formally informed and the chair took the responsibilty of relocating them to a new advisor.
my case- this conversation is only b/w me & advisor. Formally no one is involved. based on my performance record, I can't be directly fired.

Incidentally, the OP implied that their advisor uses male pronouns in the question.

@StudentOfLife "I have 3 papers, one in nature." Are any of these first author papers? If you have at least one first author paper, you are doing fine. Start looking for a postdoc as you finish up your PhD.

@EJoshuaS-StandwithUkraine Are you suggesting that I should have used "he" instead of "they"? Isn't using "they" as a generic pronoun, especially for a person unknown to the speaker, always acceptable? I generally use "they" for people I don't know well and have unconsciously for decades.

@WaterMolecule Just pointing out that either is acceptable in this case, since the gender of the person in question is definitively known.

@StudentOfLife You have a paper in Nature? Like, the journal Nature itself? Or some other journal that Nature publishes or with the Nature brand? Nothing wrong with publishing in the latter, but if you actually have a paper in the singular journal called "Nature" it would be extraordinarily bizarre for anyone to criticize your progress; that's an achievement that many full professors do not obtain in their career. In any case, your progress sounds very good, especially if these are first-author papers. If they are not first-author papers, your progress may still be good.

So, your supervisor set for you a deadline to reach up to a certain point lest you would have to leave the programme. After working with that deadline, you finally reached the point you had been supposed to. Now things have progressed and you feel that you doing fine.
First, I wish to congratulate you on your victory. Probably, for the first time in your life you came across a really difficult situation in which you had to count mainly on yourself because your communication with your supervisor was, as you said, challenging. You did great. Things are now on track.
Now, please ask yourself if you really have any reason to be "completely broken from inside". Is this how a winner should feel? -- No way.
This was a difficult battle -- which you have won. And you have acquired good trophies: strength and experience, not to mention a progress towards you future degree. So, please, do not be shy of your victory: feel proud.
Whether you choose to stay with your present supervisor is to be your decision. My only recommendation would be to base your choice on expedience, not on emotions. (Expedience, though, comprises many parameters, including your psychological comfort, and your trust in your advisor -- or lack of trust.)
Good luck with you research and your PhD thesis! You have proven to yourself that you can do it.

@Micheal_1812, it sure as hell doesn't feel like a victory but your response definitely gives me a positive perspective. Thank you for giving me something positive to think about and pushing me to stop sabotaging myself over this. I got so badly affected that I just lost the strength to stand up and own any small things I achieved. Your response made me step back and realize that maybe if I can do this, I can do the rest too! I guess I needed that! Thank you so much for taking the time and responding! I really really appreciate your time and advice! May god bless you! <3

@StudentOfLife I like your wording: stop sabotaging yourself. Once I was watching the Olympics and saw a runner who won a Marathon -- and who almost fell on the ground after finishing first. He could barely stand on the pedestal when receiving the medal. So keep on with your Marathon. Looks like you are up for a gold.

My Answer comes from the graduate student point of view. I am currently in a somewhat comparable situation and can only tell what helped me.
First of all my situation is "a bit" easier, as I studied in my home country, so I don't have a lot of the things you are struggling with. But after a long time of competing with irreproducable results and thus lacking paper acceptance, I came to the point where I haven't had enough work done, another reject reached me, contract was expiring and additional funding was declined. That also left me in a pretty dark place.
The thing is, we are all humans, your professors to. So it is quite possible, that there was just a resolvable or temporal problem he did not identify as such. You describe that your work is still going good since your ultimatum, so you would have enough to show that "you are not as bad as he thought". So what I did is talk to my professor about these problems, it was a very unpleasant meeting for both parties, but just because of the topic, not because of ill behaviour. I would say, this helped me a lot, even if just in understanding the problems better, and we were able to work out a way which, although still very stressful, can leave me with a PhD in the end.
From your description I take that you can still professionally respect your supervisor and that he appeared to be a good person in general (apart from the changes you mentioned). Your case also seems to have a bit more flexibility, as the funding seems to exist and you basically only have to come to terms with your professor. After all, what helped me making this decision, is also "what if this meeting  does not end well?", well so what, you will be in exactly the same position as you are now. But the prospects of such a meeting are just to good. First of all you can help him understand your situation (regarding you work, lack of which and progress of which). It could also help you in seeing things differently, maybe there are problems in your work, you are not seeing yourself, since your view is blocked by other things, maybe your assessment of your progress is faulty, that is difficult to pinpoint from a single view, especially if you are struggling with emotional problems (It was for me).
Of course this depends highly on the general relationship to your supervisor before this and I can only hope that this helps you and is applicable to your case. Keep in mind that your assesment of his "feelings" towards you, are very likely skewed due to your emotional state, and is not necessarily as bad as you think. What would be important either way, is that you don't start this meeting with any demand, but as a discussion to help you understand what you did wrong, even compared to other students which can continue (or did so in the past).
Good Luck

I am not a professor but I just got out of a situation just like this. I had to go to a psychological counselor to deal with my burnout, which did not resolve my issue. I was miserable, I wasn't nice to myself, my friends, or my family. After a lot of contemplation, I took some steps that turned my life around. I can't say with absolute certainty that how I handled my situation will suit your case perfectly but I can lend my experience so you can make a more educated decision.
First things first, you have done an excellent job explaining your situation and acknowledging your own shortcomings in an honest and forthcoming manner - I really appreciate it.
Let me deconstruct your situation a bit and in doing so, I will try to get your hopes and confidence up. Think of it this way:

Your supervisor asked you to "voluntarily" leave the program. He didn't enforce it, he merely suggested it.
When you asked for a reason, he gave you his opinion and in his opinion, you haven't made enough progress yet - which is nothing but his opinion.

Now, I am putting myself in your shoes. I understand that you feel like there is too much at stake here and getting your degree solely depends on your supervisor's whim. You probably have been dreaming of your Ph.D. from a very early stage of your life and the person holding your destiny thinks that you don't have it in you. Here is why I think you are overthinking it.
Most immigrant students (like myself) who come to North America for thesis-based Master's and/or Ph.D. programs depend solely on the funds provided by the professors. Most of the time (around 95%), the professors' funding is the only source of income for immigrant students, who are not allowed to work off-campus in the USA. As a result, the students gradually become submissive and subservient to their professors. And thus, the mere opinions of the supervising professor can make or break the graduate students' spirit. Things are even more complicated for Asian or South Asian students, where people regard teachers at the same level as (or higher than) their parents. I remember one of my fellow graduate students saying, "I don't believe I will amount to anything without my supervisor's blessing", which is, I won't deny, a great gesture to have about the teachers but such deification can be quite detrimental for the students (especially adult graduate students) in many ways. When such students find their teacher standing between them and their dreams, they either lose confidence in themselves or start to vilify the teacher.
If you belong to the first cluster (I believe you do), please consider the option of focusing less on your professor's authority. Deal with this situation as you'd deal with your peers. Yes, your supervisor is ahead of you by a couple of years (let that be 50) in academia but that doesn't mean they have the right to intimidate you out of your program. A supervisor who oversees a graduate student’s work should share the same level of responsibility and accountability for the quality and outcome of the student’s degree as the student themselves. "I don't think you have it in you" or "You don't have much progress" are vague and do not carry much value as far as the feedbacks go.
From what I understand, your supervisor had some expectations in mind that he thinks you did not fulfill. You can take the following steps to mitigate the situation:

Confront your supervisor about his remarks and let him know that quitting is not an option for you.

Don't be afraid to share that you struggled because he was not as on-hand at the beginning of your journey as you'd expected and you didn't get a chance to start fresh (You had to assimilate yourself with other's work, which can be quite daunting).

Share your discomfort about feeling inferior when he is around. You mentioned you can put together a well-rounded presentation in front of others when your professor is not around and you mess up when he is around you. According to my psych counselor, a healthy adult and independent person's behavior should never be affected this much (I was in the same boat for a while) by the mere presence of another person. "Do not become too susceptible to others' opinions, no matter how superior you deem them to be." - that's what she said.

Do NOT underestimate yourself. Remember, you have fought your way into the program. The supervisor/university recruited you because they thought you have it in you to finish the program expectations.

Discuss what is expected of you in the next 2 years of your study and set an expectation that you both can agree upon. Negotiate with your supervisor and find a realistic goal that works for both of you.

If you can come to terms with your supervisor and agree upon certain goals that you need to achieve to get your degree, work towards it - slowly and steadily. Keep your professor in the loop - send three progress reports on a daily basis, 5 days a week (at 12 PM, 5 PM, and 9 PM), no matter how trivial the progress is. I am sure your supervisor will appreciate the effort and resilience.
On the other hand, if you can't agree upon some acceptable terms, if you and your supervisor have different opinions or goals that you cannot reconcile, or if the chasm of your supervisor's expectation is too deep for you to fill, it's better to approach your department with these concerns. I am pretty sure you have to report your annual progress to some sort of supervisory committee, which comprises multiple professors from your department. Go to them, be honest, explain your situation, and do not sell yourself short. They have the authority and they can intervene on your behalf. Sometimes they tend to make decisions or judgments based on what the majority of the committee members think (due to group-thinking bias), rather than depending on their own independent analysis or evidence. This can lead them to show favoritism toward the people who belong to their group (i.e. your supervisor). If that happens, you can resort to your dean's office for help.
Remember, "You haven't come this far, to only get this far"

thank you for taking the time and giving such positive insights. I agree i do hold profs to such a high regard that it may be toxic. Thank you for your critical observations on my post! I recently read a paper on why having such disproportionate respect for the authority can hurt for phd students. Its very relatable and definitely something I am focusing to work on! Really appreciate your inputs and time! Very helpful! Thank you so much for your response and belief in me. I’m struggling but I’ll get through! For sure!

No worries! Keep your head high and move forward! You will endure and succeed in your life.

TLDR: Focus on graduating as soon as possible, only use your advisor for things directly related to that goal. Do not use them for emotional support.

The current top answers focus on seeking counseling* and exploring other professors** in the department. Those are reasonable options, but I think miss the mark a bit.
Your advisor has stated he "doesn't think the subject is for you," and that you haven't made enough progress, but has offered no evidence to support that. You provide evidence that your progress is sufficient (possibly even more than sufficient), and other than normal temporary setbacks you don't identify any major obstacles to completing your thesis.
First, other than severe lack of progress, it's not your advisor's decision whether to continue your program. As long as you're progressing, that decision is yours alone, and you should only leave the program if that is what you want. It doesn't sound from your comments like that is what you want, so I'll assume for this answer that your goal is to complete your degree.
As others have pointed out, your progression sounds on-track for this point in your degree. Advancing to candidacy and having an approved research plan are major accomplishments that you should be proud of, and are direct evidence of your progress. You describe in other comments that you've authored 3 papers, with one in Nature. If any of these are first-author papers they are also major accomplishments.***
Unfortunately, your advisor's discouraging words, and the difficulty communicating with him, signal to me that he is not, and is not going to be, your enthusiastic supporter. This is understandably very discouraging and an emotional blow.
It is understandable to hold professors in high regard as a graduate student. Keep in mind, though, that being a professor is only evidence that they are a subject matter expert. Simply knowing someone is a professor does not tell you if they are a good manager, communicator, or advisor. It also doesn't mean they're any good at knowing who "has it in them" to accomplish a goal.
You have evidence that your advisor's assertions about your progress are not true. In fact, you don't need your advisor to affirm that you are making progress, you can check that for yourself. You have a research plan that was (presumably) approved by your advisor and committee. This is your progress guide. If you are advancing on your research plan, you are advancing.
With this in mind, my recommendation is to acknowledge that your advisor is not going to have the expanded role most people wish for in the advisor/student relationship. They aren't going to be your cheerleader. They aren't going to give you encouragement. They probably won't give you good career advice.
This is discouraging, but it's not the end of the world (or of your degree). You have a year or two left on progressing your research plan and writing your dissertation. Use your advisor only for the things that are needed to accomplish that. They can (and probably should) advise on experimental setup and analyses. They should be responsive to editing manuscripts and chapters. They should do the paperwork that needs to be done to keep the lab and your position going.
Another answer suggests trying to sit down and making an emotional connection with your advisor. I disagree. I don't think you should spend your energy trying to convince them of anything other than that you are doing dissertation quality work. (This is obviously very personal advice. Only you know your relationship with him, and maybe trying to convince him to be supportive and that you're brilliant is worth it. But at the end of the day all you need is for him to sign off on your thesis, you don't need him to be chummy while doing it.)
You will also need to make sure that he is holding up his responsibilities as an advisor. This means some minimal amount of communication. It means responding to experimental questions and edits in a timely manner. It means acknowledging progress on your research plan. It means providing reasonable lab resources to do your work.
His focus on progress might manifest as a suggestion that the research you've already outlined is not enough for a degree. This is when you pull out your research plan, that everyone signed off on, and ask what has changed to demand more work. Your committee can help with this, too. (My uni had a requirement that committees include a member from a different department to represent the student's interests. If yours has something similar, they can also guard against piling on work.)
Focus on finishing your thesis. Don't take on any extra lab or department duties you don't have to.
Finally, find your allies who will be supportive. Get encouragement and affirmation from your friends, fellow students, and family.

*Counseling is an excellent suggestion, and an appropriate place to work on your emotional needs and get a detached perspective. I see your other comments that you haven't found it very helpful. Consider discussing with your counselor what might help this, and use whatever counseling benefits you have to their maximum.
**Several other answers suggest switching advisors. This might ultimately be needed, but I don't think that's a given, yet. As far along as you are, it might be very difficult to find a new advisor, and you'd spend a lot of time figuring out all the logistical issues in switching, such as funding, space, etc. You might also run into objections from your current advisor (I don't know what their incentives are, maybe a student switching looks worse than one dropping out). You'd have to weigh whether it's worth your time to go through that, compared to putting that effort into your thesis. However, if your advisor begins actively blocking your progress, or essentially abandons you so that you can't progress, by all means, find someone else.
**If all three are first-author papers, you're progress is excellent. If that's the case you should seriously consider how to transform those into the bulk of your thesis. This also may be evidence of actual obstruction from your advisor, because it would be highly inappropriate to suggest that a 4th year student with three papers leave a program.

"it's not your advisor's decision whether to continue your program" - Actually, sometimes it is, or approximately is. Varies by program/field/country, but some ways can include 1) advisor provides funding; if an advisor cuts off funding, student has either a ridiculous tuition bill that no one should ever pay, or they need a new advisor with funding, and 2) although decisions on graduation may be up to a committee, the advisor's word is likely to influence everyone else on the committee and only in extreme circumstances will they override the advisor.

Now, it's certainly possible this is one of those wild, rare cases - some of the descriptions by OP suggest it could be. But it's likely not going to be sufficient for OP to keep their head forward and keep operating at the status quo. Something is going to need to shift/change for them to succeed, either getting their advisor on board for them to graduate, or replacing their advisor's role as a person who has influence on whether they graduate.

It's true that different institutions would have different policies about retaining grad students, but the advisor would likely (though perhaps not technically) need to show some cause for dropping a student. It doesn't sound to me like they're actively trying to kick OP out, they just feel she "doesn't have it in her." My point is that that's not just a feeling, they have an approved plan to compare it against. The reason departments require those plans is to make sure the student's on track, yes, but also to discourage shifting goalposts from the advisor.

As you have already tried the Student Councillors and that hasn't worked, and you have other good answers I thought I'd add my alternative viewpoint.
When I read your post it made me want to reply because I think you have obviously tried very hard over many years, and the feeling you currently have isn't representative of either your progress (which sounds great), or the intense feeling you have (which sounds like it is being in the middle of an explosion).
What I mean is that although you feel in the eye of the storm, you must remember this is not something that will define your whole life. That will sound ridiculous to you now, but if you can step back and look at the bigger picture it might help to give you some perspective.
I did once start an MSc that I gave up half way through (Uni life was NOT for me!).
So, I'd like to be honest and compassionate with you?

I think doing a PhD is not a "job" for everyone. It may be that is the case for you and maybe your advisor has just waited too long for you to "shine" and then it got so late and he is struggling to let you know in a compassionate way (as others have said he's probably just human).

Having said that, I wasn't born good at communicating but knowing it was my destiny to try improve I work at it every day. It's "hard" for me to do, but it is also part of me. What I'm trying to say is that maybe your level is not good enough currently for where you are in the PhD, but if it is your destiny to get one, then maybe you do need to work 2 times as hard to get there, and maybe that means having hard conversations with your advisor (not aggressive, just vulnerable where you are honest about how you feel - more on that later).

It does sound from your description that he is (as someone else put it very politely) hands-off. This means he has no time to actually teach you and expects you to just do it. It sounds like this is not what you need. There are a number of options here but getting an expert second opinion would be useful. If you're struggling to find someone at your university you could "hire" a new advisor to help you focus (they could coach and mentor you through the problem). Use something like Upwork/PeoplePerHour (or something similar where you can find an expert in the field you are in -  I have nothing to do with them but use them regularly to get hold of really specific expertise), you can post a job for someone with the expertise you need and ask them to be a coach and mentor and see what they say. This could be a great way to get another independent viewpoint that helps you decide if your destiny is to carry on or not. Or make changes to your current one.

If you are able to have a sit down conversation with your advisor and get an emotional connection with him, letting him know you respect him and that you really need his help and how it is affecting your mentally, this may enable him to tap into some compassion. Also, if you try and do this and he brushes you off it will demonstrate he doesn't really care about your feelings (this might be because he is just interested in results and not emotions).

You must also realise there is a possibility he is under a lot of stress from the university, his wife, his mortgage etc. This is a possibility, but if you have funding this doesn't sound right.

Also there is a possibility he is a bad advisor and he just cares about himself. This means you need to take what he says with some disbelief. Obviously it's hard to know if this is true or not, you need to use your intuition. A lot of people that are "Professors" love to be "famous", this can skew their viewpoint and mean they make the wrong decisions. I would not assume this is the case but it's something to think on.

SO WHAT NEXT? I advise you to do a number of things:
Think deeply if the PhD is right for YOU. Or, do you not care a lot about the PhD but want to stay in the US? If this is your ultimate goal you NEED to find a way to complete the PhD. This could be biting your lip and doing whatever your advisor needs, or finding a new university, or course or advisor (I am saying those realising it is not easy, but if you really want to complete the PhD you need to start working out what the best way forward is).
I would get a second opinion on your abilities and progress. Try and find an "Honest but compassionate PhD advisor" that is an expert in your field and get them to appraise what you've done. This could help you decide if you carry on or try something else. You need someone that will be honest and say if they think your work is at a high enough standard, and if it ever will be.
Slightly left field one here. Take 2 min cold showers daily. A lot of times we are fearful of the truth and we are worried about so many things happening in life it makes us immobile to get on with what we need to do. When you have a cold shower it resets your nervous system, and you can be a bit more rational and less emotional. This may help you see a way through the current pain, especially if you do it daily.
Finally: I believe all the things in life are MEANT to happen to us for a reason. Even if you flunk the PhD (I'm so glad I gave mine up looking back) you might go home back to your country and end up bumping into your future partner and you live happily ever after with them. And that would be much better than slogging on a PhD and not finding "the one" etc.
In reality this is a small part of your life even though it feels like everything now. You need to look a little bit ahead to the future and just try and work out the best way forward for you.
You've come so far. Don't stop, and keep going in the direction you know in your heart is right, just remember it might be slightly different (or even a LOT different) and I'm sure based on what you've said and how hard you try you'll get there eventually.


text:
Is the using same techniques considered plagiarisim?
A geologist used some techniques to investigate certain oil field for his PhD thesis. If another geologist useS the same techniques but for a different oil field can it be considered plagiarism?

Did you read the definition of plagiarism on wikipedia? What do you think? Why would it be plagiarism and why not? We are not going to google for you.

@Louic I have confused. I need a straight answer.

You have received a straight answer. That straight answer is: look at the definition of plagiarism on https://en.wikipedia.org/wiki/Plagiarism

If you cite the early work and explain that you are using the same technique, then no, it isn't plagiarism. But it may not be "novel" enough for publication, though that depends on the details and the judgement of reviewers. And for a thesis, it depends on the judgement of advisors and examiners. The standards there can be different from publication standards.
It might have an economic benefit, of course.
Plagiarism is about claiming ideas of others as your own. If you cite the early work then it isn't plagiarism.

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text:
Is the reviewer the journal manager?
I submitted a manuscript to a journal, and the feedback I received required major revisions. Interestingly, I noticed that the system indicates that one of the reviewers is the journal manager. What does this mean? Previously, this manuscript had been on hold for seven months without finding a reviewer. Was it reviewed by internal journal staff?
What kind of position is a journal manager?

"I noticed that the system indicates that one of the reviewers is the journal manager." No, it does not. It indicates that the report was uploaded by a "journal manager".

"Journal manager" sounds like a member of the journal staff. They are not expected to review the paper. Since they uploaded the report, one of two possibilities suggest themselves:

The reviewer sent the report to them directly (e.g. via email), and they are uploading the report on the reviewer's behalf.
The review originally had some problem which the journal manager fixed, and this requires them to upload a new report. Examples could be, the reviewer forgot something, the report is poorly formatted, the report included identifying information of the reviewer and the journal manager is anonymizing, etc.

In some cases, a journal manager may be an academic as well, and may occasionally review manuscripts.  But (as noted) you cannot make that conclusion from the information shown in the OP.

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


text:
What language is "Solutio problematis ad geometriam situs pertinentis" written in?
The article by Euler titled "Solutio problematis ad geometriam situs pertinentis"(The Seven Bridges of Königsberg) is considered as the first work in both Topology and Graph Theory. However, in the original paper, I am not quite sure what language it was written in. I asked AI, and it told me it's in Latin. I'm a bit unsure because I'm writing a comprehensive article and need to ensure accuracy.
The language doesn't seem to be very common today, and I feel that English shares many similarities with it.

For future reference, e.g. Google Translate's "Detect language" function can be quite useful in these situations. It correctly identifies the title as written in Latin.

It's in Latin. The title is pretty clearly Latin (even with just a little familiarity with Latin, that is clear) but you can also look here which says it was written in Latin. Also, Latin was the language that European people wrote in back then. (Euler also wrote some papers in German, but this clearly isn't German) and he wrote letters in Russian, but probably did not produce any papers in Russian (some were written in German and translated).  In any case, this clearly isn't Russian.

Nice. Thank you. By the way, its English translation version can be seen in the book " Biggs, N.; Lloyd, E.; Wilson, R. (1986), Graph Theory, 1736-1936, Oxford University Press"

"Latin was the language people wrote in back then" Well, I get your meaning, but this is true only for certain parts of the world.

Good point, @Snijderfrey. I will amend my answer.


text:
What to do if I have found a major issue with my model before a conference presentation?
I submitted an abstract to a major conference in my field. I am presenting tomorrow at the virtual conference and the video is already uploaded, no conference proceedings were submitted. However, today, I came across a major issue with the modeling technique used in my research. This might be seriously challenged tomorrow. Also, this might influence the conclusion of the results as well.
How do I answer if the issues with my modeling strategy are questioned during my presentation? I can't remove my talk at the last moment. I am worried that I will be ridiculed tomorrow.
What can I do?

Things like this happen. No one should be ridiculed for honest errors. It's a good thing that you found this one before someone else did.
Your description suggests that some (even much) of your work is still OK, since you say only that the problem  might affect your conclusions.
If you can describe the problem (even with no solution) in advance, you should.
Does the conference format allow you to introduce your talk with some preliminary comments, either via zoom (or some such) or with a short new video upload? Ask the organizers.

No, the video presentation was uploaded 20 days ago. I will be allowed to talk only after the presentation.

Is the presenter allowed to shorten the presentation, point out that a problem was discovered only yesterday, and ask the audience for suggestions?

@AndrewMorton No. The issue is with the fundamental assumprtion used in the simulations. Though the results are basically okay and serves the point I am making, they can be challenged on the basis of physics of the problem

Can you say in the beginning of the Q&A session that you had the following thought XXX after uploading the presentation?


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What's exactly the right way to cite IEEE conference paper?
According to the IEEE reference guide, we should use standard abbreviations for the conference name. However, among academic publications, I have seen at least three different ways of citing a conference paper. For example:

Authors, “Title,” in Proc. of the IEEE Intl. Conf. on Robot. and Autom. IEEE, year, pp. xxx-xxx
Authors, “Title,” in Proceedings of the IEEE International Conference on Robotics and Automation. IEEE, year, pp. xxx-xxx
Authors, “Title,” in 20xx IEEE International Conference on Robotics and Automation (ICRA). IEEE, year, pp. xxx-xxx

My questions are:

what is the right way to cite the conference paper, or doesn't it matter?
when to use in proceedings and when not to?

Unfortunately, there is no consistency on how a conference article is cited.  I use LaTeX, and my references do not come out as you've listed them.  There is no publisher field (the publisher appears in the conference title), and you need to include the address of the conference; e.g., S. Claus, 'How to take care of reindeers?' in IEEE International Conference on Animal Husbandry, North Pole, Aug, 2021, pp1-6.

It will probably depend on the place the document will be published, archived, etc. Check with the authority figures in that place, editor or Dean of the department or whatever. Also, look at how previous authors have done in that journal/archive etc.

In any type of citing issue, it is best to ask the editor/conference head. Another way to go about it is the guides. All journals/conferences have citing guides. You could follow them.

Google scholar has great bibtex as well.


text:
How to cite a table that has been significantly modified (see example)?
Based on what I have read, the options are to say something is either reprinted or adapted. But "adapted" seems to suggest, according to a college website I was looking at, mere aesthetic changes. I'm dealing with much more significant changes.
What I am doing is this: First, there is a psychology article with a table. I'm taking about half of the info in the table (12 of 20 statements), mixing some of it together (e.g., Number 1 and 3 are now mixed together into Number 1) so they become 8 statements overall, and then adding my own 12 statements (e.g., Numbers 2, 3, 6, 9, 10, 11, 13, 14, 16, 17, 18, 20) are mine.
You might suggest I separate my statements and put them in another table but I can't because I'm basically filling in the gap in the information from the original table. To give an example, imagine the writer talks about issues people have in different age groups, and the info is presented in a random order and with only some age groups. What I'm doing is putting them in order and filling in missing age groups with my own knowledge.
Would "adapted from" suffice in such a case?

What you do is create your own table, and not display an existing one in modified form. Thus, I would cite the contents taken from the other publication just like any other source you refer to.
I would suggest the following: indicate the rows of the table taken from the source in any way (e.g. put an asterisk at the end of the rows, make those rows a different color, ...) and at the end of the table add a footnote stating: "information in marked rows taken from [cite source]."

Right. Each entry in a table can have its reference like indexes a b c.... Caption can then have linea such a: ref#. b: ref# and so on.


text:
How can one make a persuasive argument using numerics?
I am currently a physics undergraduate, but I will be pursuing a physics PhD next fall.
One part of the current research I am doing is to build up evidence for a mathematical "if and only if" theorem. One direction is provable. The other direction is difficult to genuinely prove, and I was advised to build up numerical evidence for the statement instead.
This made me wonder: how can numerical data for this situation ever be persuasive?

Persuasive to whom?

@Trunk Physicists, especially mathematical physicists, can definitely find themselves trying to prove such conjectures.

@Trunk I don't know how to address whether they "have to" do that as the only possible path to making progress, since it would presumably depend a lot on the circumstances. But it's hardly unheard of for theoretical physicists to define some mathematical object, study its properties, and in so doing, prove statements that may be of the "iff" variety. Physics journals routinely publish theorems, but I have no sense of what proportion would be "iff theorems".

A conjecture without a proof is always a conjecture, but you can establish evidence for the conjecture without a proof. Take for example elementary number theory and something like the Goldbach conjecture. We do not have a proof, but we know that the smallest counterexample would have to exceed 4*10^18.
This makes a theorem of the following type interesting:

If the Goldbach conjecture is true then this interesting fact is
true.

Historically, there were conjectures (such as about Mersenne primes) that were shown to be false with an explicit counter-example, though believed to be true previously. The counter-example I have in mind was just within the reach of calculation by hand.
What your advisor is asking you to do is to make certain that there are no simple counter-example.


text:
How to fill 'knowledge of major field' whilst applying for a PhD scholarship
I am currently applying for a PhD scholarship and one of the required fields is knowledge of major field.
I have searched online and can't find what this means. I tried to fill in my educational background but I'm guessing it's more than this because there's another field for that. I also tried adding my relevant work experience and research but they also have their respective fields on the application site.
I don't know if I'm missing something and would really love the help of this community in understanding what this means.
Asking the university directly may not help as previous emails are yet to be replied for months.

Could this not just mean your major?

@Sursula I'll try that... Maybe I should state how my major qualifies me for the research project?

This situation strikes me as strange. The only place where I've been asked to fill out "knowledge of major field" is on the forms that I (as a professor) had to fill out when recommending students for graduate programs.


text:
What are the requirements to have a program accredited as a Bachelor’s degree?
I have found this document about European standards for higher education: https://www.enqa.eu/wp-content/uploads/2015/11/ESG_2015.pdf
The criteria are not as strict as I maybe expected, a lot of it sounds pretty reasonable like “you should have qualified staff” and “you should provide clear information”.
Does that mean a program gets certified as a Bachelor’s degree subjectively, by a reviewer observing its plan and execution, or is there a neater formula for what gets approved or not? For example, how do they decide that the curriculum is acceptable? What’s an example of an unacceptable curriculum and which guideline for certification does it violate?

Keep in mind that, in order to be broadly adopted, these European standards have to be reasonably compatible with a range of different systems of higher education. I suspect that you'll find more specific/strict criteria at the level of the registered regional and national agencies.

Accreditation is something happening at the national level, or in some countries even below that. So to answer your question you need to tell us which country or federal state you are interested in.

Right from this document:

The ESG are not standards for quality, nor do they prescribe how the
quality assurance processes are implemented, but they provide
guidance, covering the areas which are vital for successful quality
provision and learning environments in higher education.

There is no Compliance Committee (unlike something such as USB-IF). If a signatory goes rogue and starts claiming everyone there has a BSc now, they quickly lose credibility. ESG is there to help them build and maintain it, but the actual responsibility for proper implementation lies solemnly with whoever provides accreditation.


text:
How to proceed with a postdoc research idea (in the UK)?
I am a UK-based PhD candidate with viva scheduled in a few weeks' time. I have a research idea that I would like to work on post-graduation, and I have also identified an organisation (in the UK) and a potential PI, whom I'd like to propose my project to. However, being a first-gen academic, I don't know how to go about these things, and I don't really have anyone I could ask for advice on this matter. So, what would be the 'correct' way to start moving things forward, considering that I don't currently have any funding or affiliations; should I approach the potential PI directly to enquire whether they would be interested in the project/hosting me/collaborating in funding applications, or should I try to secure funding first? Also, if approaching directly, should I present a full research proposal at the first contact or, initially, just a short email with a brief summary of my idea? Do I need to be worried about being 'scooped' in case they were not interested in collaboration?
Any advice would be greatly appreciated!

"I don't really have anyone I could ask for advice on this matter" - what about your PhD advisor? I think it's fine to ask the question here, too, but this is the sort of thing your advisor is for.

I agree that would be the ideal source for this type of information, but our relationship is somewhat complicated, so I don't feel comfortable initiating this conversation with them.

Remarkable that you see a difference bc you are a fisrt-gen academic. Do you mean in terms of parents or more in general terms?

Yes exactly, as in my family or other relatives won't be able to advise me on this.

Since you are approaching a potential postdoc mentor you don't know particularly well (otherwise you'd be having this conversation with them) and have your own research project, the first step would be to identify where the money might be coming from. You'd be looking for a Postdoctoral Fellowship.
For fresh PhD, the Leverhulme Trust or the relevant research council (eg EPSRC for mathematics or computer science) are funders offering postdoc fellowships. Look up the relevant funding scheme. If a funder offers something like "80% of the full economic costs", the university hosting you would make money on it, and it thus shouldn't be too difficult to get supported*. But eg the Leverhulme Trust is afaik only paying for half of your costs, and the host would need pay for the rest. Now you know what you are asking for, what the time frame is, and roughly what is needed for the application.
You can then send an email with the key bits of information together with a short description of what you want to do to your chosen mentor. I would expect that you'll need support in putting together an outstanding application. Both the prospective mentor or a specialized team at the host institution might be available to help.
[*] Even if the university doesn't have to put money towards your fellowship, they may still restrict how many applications they are willing to support. For example, EPSRC is asking universities to do a preselection of some sorts. If the university offers extensive application mentoring, they'll be particularly keen to focus on the most promising candidates.
As a final comment, you need to be aware that these fellowship schemes all tend to have rather low successrates. (If it is in the two digits, it is rather high for a fellowship scheme.) So definitely don't count on this working out.

Thank you, this was extremely helpful!

@DanielHatton I've only listed fellowships that don't have a minimum post-PhD duration (as that is what the OP is looking for). So the Royal Society is out.

You might also be eligible for the human frontiers science program  (HSPF) fellowships, and Marie Curie (if you can find a partner in another EU country).


text:
Graduate application writing sample plagiarism
How likely the graduate admission committee will use plagiarism check software to check the writing sample submitted? I am just afraid something accidentally might pop up, like some sentence or something, which was not done on purpose.

If you didn't plagiarise, there is no reason to worry.

Sure, but I am just asking, you seem like a real professor haha

No, I am surely not a professor. You really flattered me. Similarity checker really does not tell you much about plagiarism. Assume that your writing sample was published in a pre-print server,  the similarity index will be really high. That does not mean that you plagiarised.

True, that's a valid point.

I doubt that very many people on an admissions committee would do that except in very rare cases in which something else triggers it.
It may be, however, that the job is getting a bit harder these days with AI based text generators. But in the US, at least, graduate admissions are based on a broad reading of an applicant's materials with many factors. I'd guess that a lot of writing samples get only a cursory reading in any case.
I also doubt that plagiarism checkers such as turnitin have a large enough comparison base to catch much in such a case. They are limited to what publishers permit them to index/archive.
And, as mentioned in a comment, if you haven't plagiarized, then a checker will only turn up a few phrases common to a field. And they will miss so much, via paraphrasing, that their use would have little real value.


text:
Is academic letter of recommendation necessary for MS admissions through GRE?
Recently I have been thinking about doing MS. For most of the universities, the admission is based on GRE General score among other things. I think a few letters of recommendation are a must in admission in almost all of the universities. I have been in employment in corporate sector for a few years now and the mentors (two of them) under whom I had done my projects/research in the university have left the university now and moved somewhere else. Will I still be able to get admission in MS without an academic letter of recommendation or with an employer's/colleagues' letter of recommendation?

What country are you referring to?

@Buffy I was thinking about the US specifically. But you can answer for any university in general so I will get an idea.

mentors (two of them) under whom I had done my projects/research in the university have left the university --- Have you tried contacting them to ask them? Do you think they would remember you sufficiently well to write a letter now? I've written several letters for former students after leaving where they were my students, including after leaving academia entirely, although I knew these fairly well (a former undergraduate T.A. for me, another my most promising student at a particular university, another who did an independent study course under me, etc.) and none more than 4 years later.

I doubt that any place in the US with competitive admissions will admit a student based only on GRE general test scores. In fact, that is starting to disappear as a requirement (COVID among other things).
There are places that will accept nearly all applicants, but that may not be your goal. For the most part letters of recommendation rank fairly highly in the analysis of graduate applications in the US.
Admissions are generally broad based, with GPA, letters, your own statement of purpose, etc. being considered as a whole looking for indicators of success. If any piece is missing, the others become more important to the analysis unless the process requires the missing piece.
Academic letters are best for academic programs, of course, and you may be able to get one or two if you are remembered at your former university and/or by former mentors, or can re-establish contact there. Letters from employers might be fine, depending on the program and what your employment was.
But presenting no letters at all would probably indicate a weak application in most cases. Not having any academic letters is a negative, though perhaps not fatal if other things strongly indicate success.


text:
Can you contact a professor whom you have never met to inquire about a RA opportunity?
Is it considered ok to proactively ask a professor from a different university that you never met in person about some potential research assistant internship? Or is something like that considered impolite or is it a complete waste of time due to zero probability of getting it?

Is your question specific to Italy? There would be little point of this in the US unless you'd already been accepted into a program.

You can contact whomever you want about whatever you want whenever you want. Just be polite.

@ScottishTapWater we should make that one of our canonical answers.

Perfectly fine. I got internships this way.

@ScottSeidman - Well... I tried https://academia.stackexchange.com/a/192371/72211

@ScottishTapWater unless there's a restraining order involved.

@DawoodibnKareem - Of course, I'd somewhat hope that goes without saying

All of us get such emails all the time -- I get about 1-2 per week. Anecdotally, most professors just delete these answers, whereas some (myself included) at least cursorily look at the usually attached CV to realize that there is little overlap in research area between the person asking and myself, upon which I then write back and advise the student to apply to the graduate program of my department rather than myself.
So, just going by empirical evidence, it is ok for you to write such an email. But it's unlikely that you will get many responses and even more unlikely that you will actually get an RA position this way.

This depends a lot on the department and grad program. In some, writing to individual profs can't do much for your application (admissions is by committee); in others, it's nearly essential to make contact first. Annoyingly, both can be true at the same school!

While @WolfgangBangerth's answer rings true, you can frequently "stand out from the crowd" of emails by paying careful attention to the subject line of the email and your first sentence.

Research the professor's current work.
Isolate what it is you find particularly interesting about their current work that genuinely captures your interest.
Construct a subject line that honestly represents your question about potentially working for them, and simultaneously includes research terms you suspect will catch their eye. Perhaps of the form "Looking for research assistantship in the History of Molecular Psychology Tensors".

Then make sure your first sentence fits the same rules (honest and simultaneously academically catchy).
This demonstrates that you are not using a shotgun approach sending generic letters to dozens or hundreds of professor. You find them interesting, you find them special, and you'd really be interested in the possibility of working for them in particular.
Just make sure that you mean it and are being sincere.

to the general reader, to be more precise: you have to be sincere and you have to take in consideration that the detailed research theme of a professor covers at best one chapter of one book you had to use during one of your exams. If you are speaking with lower level minions (PhDs, Postdocs): research will encompass a couple of formulas of said book (but ideally they have to master all the surrounding knowledge and potential implications).

@EarlGrey I'd never think of anyone as a minion, and while your description of contribution might hold for an ensemble average, there are plenty of professors who write multiple books and still have more to say.

those professore are the one that will desk-reject an email from a random person without even reading the title. You still have to find a way to them through the minions of research.
BTW: I say minions just because of the working conditions and because of some affinity with the famous characters from the animated movie. I imply no moral judgement: we all have been there!

@EarlGrey One chapter of one book?  One paragraph of one chapter rather.  At most.  One line in the reports by the International Panel on Climate Change (IPCC) can be a career research topic, and the IPCC reports are more detailed on current research than a typical textbook.

@gerrit I wanted to avoid being too realist. And you know there is a reason why textbooks are textbooks, while IPCC reports are ... the Bible that can be understood for a small elite (and usually misunderstood by the masses)

You need to also be absolutely sure who you are writing to. When I was a RA at a university in Germany I oftentimes got spammy email applications that adressed me as "Professor X".

Of course, you can email the professor.  You can email anyone at any time for (almost) any reason.  The worst that can reasonably happen if you send a single polite email is that you will be ignored.
I don't agree with Wolfgang Bangerth in the assessment that it is necessarily a waste of time.  Not every professor is flooded with such emails; someone relatively early in their career might not be.  But you will need to have something to offer.
A junior professor needs papers.  Either from research they do themselves, or from research they supervise.  If they get a good assistant who writes a paper with relatively little supervision, that's great.  If they get someone who needs a lot of supervision but won't succeed in producing research and writing a paper, then they might not find it worth their time.  Sure, supervising is experience too, but they probably have enough people closer-by if that's all they need.  Papers count.  Supervised n students resulting in 0 papers not so much.
Are you someone who can produce research and a paper with relatively little supervision?  Can you convince the professor that this is the case?  This is the tricky bit.  Not many very early career scientists can do this.  Writing a well-crafted (short!) email is good (see uhohs answer), but not enough.  You'll need something to show.  Have you done any really successful student projects, preferably related to their field of interest?  Can someone more senior, preferably someone they already know, introduce you, perhaps write the email for you?  Either of these will strongly increase your chances.  Your email might be ignored.  An email from their collaborator, I have this really great student who would love to work with you, would you have a moment to talk to them?, might not be.  Of course that works only if you are great, otherwise asking for such an introduction may be awkward.
I was a research assistant during both Bachelor and Master.  The Bachelor work helped prepare a paper where I became co-author, and the Master work in a paper I authored myself.  Although I was at the same university in both cases, I didn't really know the professor at that point.  At least for the Master, I don't think he was flooded with emails from student projects.


text:
Accepting An Academic Gift From Supervisor
I have developed a good working relationship with my supervisor and I have expressed my interest in wanting to pursue a PhD in the field that I am working in for my masters degree. I have expressed interest in a textbook from another author in a complementary field that I would want to hold in my collection as a PhD student, and if things work out, as a professor. As well, I am my supervisors first student that they have had under direct supervision after their own PhD, as are they my first research supervisor. So there is a unique 2-way relationship as well for the sake of context.
My supervisor has told me that she would be willing to purchase this book for me and I think that my supervisor would be doing this because they actually want me to have it for my future and in part as a gift to me. Personally speaking, I do not see any ethical concerns with this, but I suspect that I might not have a complete perspective on this type of exchange. Do you think that there are any ethical concerns that I should be cautious about?

There is no issue at all in such an offer. Thank them and accept the offer. This is an entirely appropriate sort of thing to do. Especially from an advisor to their first student.
Gifts in the other direction have ethical considerations, of course. Gifts to supervisors can be misinterpreted.
But, as you suggest, it is a gesture of support for your studies and your future.
I would only suggest otherwise if the relationship had some sort of creepy element generally or you thought the supervisor had other than academic interests. You give no suggestion of that, so dismiss the idea, though it may be relevant to others.
Hmmm. I'm reminded by this that I've done the same, though it was a copy of my own book.

So there is one consideration that I think might be overlooked and I would like to see if your opinion changes. Do you think that if the Department Chair found out that my supervisor gave me a text PRIOR to my defense that it could be frowned upon? An alternative option would be to accept the gift from my supervisor,  but inform her that it be on the condition after my defense?

No, I don't think that is any consideration at all. As I said, it is a perfectly valid thing to do. And congratulations.


text:
How to deal with math problems if there is no solution book and no helpful teachers?
Since a short time ago, I refuse to try solving math questions of which there is no solution available, unless I'm working on an own/open problem in my thesis. In subjects however, I refuse, because it is frustrating to get stuck for days and knowing that a solution exists. So knowing that I miss some important way of thinking.
Now you might think Why? If you can't solve it, just look at the course material and if that doesn't help then ask the teacher. Yes I tried that. By both mouth and mail. Unfortunately a lot of them don't like to get disturbed by students, because they are actually not real teachers, but very busy researchers who hardly have time for anything else. I also tried google, mathstack and asking students, but without a solution book it seems like it is always possible that nothing helps and you thus stay where you are: stuck.
Having said this, is there a way to learn without solution books but with the guarantee that you can always get access to the solution for the problem you work on? Maybe I do something wrong with the ways already tried?

This seems mostly to be a rant. I would suggest that self-assembled student study groups are often a good option, and many online-learning platforms have ways to do that.

Not every problem that exists has been solved yet. You may need to work at finding solutions...

@SolarMike For open problems I of course understand that there are no solutions. But I think there is a difference between doing research and learning a math subject.

So, research is about working things out... Learning comes from effort...

Yes, but I think effort is not all. We can also learn by looking at answers after we first try the exercise by ourself for, let's say, hours and don't manage. Then we not only see what we should have thought about to solve it, but I also discovered e.g. that thinking out-of-box is in general better than thinking in (sub-ways of) the same way.

You do know that actual mathematicians sometimes work for years on a problem and never get anywhere, right?

@AlexanderWoo Yes. Moreover, if I would be such a mathematician I would be fine with that, because nobody withholds a solution to learn from (because that's impossible). Maybe these researchers had more success if they had the guarantee described above, so better training in bachelor and master.

If the only way you can solve problems are to follow a method that others have already found, you will be replaced by a computer or a robot in the workforce.  The only people who will get jobs in the future are those who can figure out how to do things that no one knows how to do yet and people don't even know if they can be done.  Start practicing now.

To clarify the sentence "nobody withholds a solution to learn from": I did not mean that they give it to me so that I can follow a method that others have found. I meant that it is impossible to give or withhold it, because a solution is not known. Exercises however are always relatively easily solvable, so then it leads to bad self-confidence if I don't manage and can't even discover which think way is missing.

You should find someone who is willing to spend enough time helping you get unstuck. The generic answer is: asking classmates, asking professors, asking on MathStackexchange and MathOverflow. Of course when you ask a question you should have thought about what you really don't understand. Do you know the definitions? Are there similar examples in the book? Can you ask a simpler question that you don't know the answer to? If you spend some time with your book and you're not making progress then you should ask for help if there's no solutions manual.

is there a way to learn without solution books but with the guarantee that you can always get access to the solution for the problem you work on?

No. Ask people for help and hope that things will get resolved.

frustrating to get stuck for days and knowing that a solution exists.
  So knowing that I miss some important way of thinking.

So your solution to missing some important way of thinking is ... to not think at all?
If you try hard to solve a problem, you are learning. You learn what doesn't work and why. That's a valuable lesson, and it's how you get better. In fact, I'd venture to say if it takes you 4 days to solve a problem, then even if you don't end up solving it, you probably learned more than the person who solved it in 1 hour.
In mathematics, knowing the exact solution of some made-up problem usually isn't the key. After all, the exercise question tells you the conclusion of the solution. You already know the result from the onset. You just have to prove it, and it is the things you learn from proving it that are important, and that's my point: even if you don't manage to prove it, you still did worked with the details and learned similar concepts to the person who did manage to prove it. You just learned it slighty differently, e.g. somebody who proved it learned "okay, this technique works in this case", while you learned "okay, this technique doesn't work in this case". Both are equally valuable.

Ok, I agree that one can also learn by just trying and that only knowing the solution does not make your brain better. But don't we learn even more if we first try for hours (not days) a problem by ourself and if we can't solve it look at the answer? In this way, a building block (a think way you did not have before) can be added to our brain, isn't it?

You say "Both are equally valuable": is this also if his technique is more complicated and thus lead to the solution?

Actually, you will learn more without the hints provided by a solution, provided that you can find a way to get some feedback on your attempts. Perhaps your professor or someone else can provide that.
But you should investigate the Moore Method of teaching mathematics, created by Robert Lee Moore and used by some of his successors. It is, roughly, a discovery method of learning higher math with few hints (hmmm, no hints). Some of Moore's students have become outstanding mathematicians and educators.
The method sounds a bit brutal, of course.
However, if you are in a graduate program, you need to understand that being able to re-prove things that are already known is a lower level skill than true mathematics. Even being able to prove things never proven before, but having been given a good statement of the problem requires only a lower level of insight. But you have to achieve at least that before you can reach the highest level of insight - having a good idea of what might be proven and thus worthy of exploration.
I suggest you press on. But also that you find some way to get feedback. If you go wrong somewhere it is good to know where and why so that you don't develop misconceptions.
However, to avoid frustration, it is also useful to put hard problems aside for a while as you work on other things - or even just take a break. Trying to run your brain on "nitro" all the time leads to burn out and poor results. Give yourself a break in general, and specifically a break from any problem that is eluding you at the moment. Insight will likely come, but it can't be scheduled or forced.

For what it's worth, I don't think I had the "higher levels" of insight into mathematics until I'd completed by doctorate.

I certainly did not get the impression that the OP was a graduate student. More likely an undergrad doing a bachelor's thesis. But, I usually am wrong...

@JonCuster, Never too early to start working on insight, I guess.


text:
Connection with professor
I have applied for an integrated MS and PhD program. I have sent am email for that purpose. The professor had an interview of me via skype. Then he sent me 6 of his papers and told me read those. At the same time, he told me to apply for scholarship via the general admission process of his university.  I am now reading those papers.
But I am confused that whether he is positive to me or not. What should I do at this stage?

I would guess that he is a bit positive and a bit neutral. I hope he knows a bit about you from your earlier contact. Otherwise he has no reason for anything but neutrality.
Read the papers. Make notes. If you are interested in that subject matter you could then ask one or two questions based on those papers. Even questions about things you don't (yet) understand can be valuable at this stage. But you might just get pointed to more papers. But if you work with this person, there will be papers and papers.
But it is likely a mistake to flood him with questions (or emails). Start the long term relationship gradually. But don't be shy about expressing interest if you really have it.
But, for any future conversation, even by email, make sure you are informed about his interests and research direction.

The fact that the professor followed up to your interview in any way is at least a mild positive; if they had no interest in you they likely would not have had any more interaction with you.
However, depending on where you are applying, the professor may have little influence on your application success; in North America at least, graduate admissions is often kept separate from individual professor's preferences. So even if the professor is positive, telling you to apply to the general process may be all they can do at the moment.
Do as the professor suggests, and good luck with your application.

It sounds generally positive to me: after an interview it's hard to know how good a student is, so the professor probably came out of it cautiously optimistic, and waiting for further indications that you're good.
Other relevant points: the question mentions "applying for scholarship", which to me implies admission + funding.
Regarding admission, as iayork's answer says, graduate admissions are usually separate from the professors' preferences, so you have to go through that process. Typically you might identify a prospective supervisor somewhere in the application, and they will be consulted -- it doesn't guarantee anything, but it means that the student will probably have someone to do his/her research with. So here it's good that you talked to this professor ahead of the application process, and I would guess that he'll have a positive recommendation, otherwise he would probably have discouraged you from applying.
Also note that after admission you have a fair bit of coursework and general training ahead of you, so during that time you probably won't be working too closely with the professor. But if he gave you those papers, it's also a way of pointing you in the right direction to get familiar with the research area.
As for funding, if I understand correctly he's asking you to look for funding elsewhere, but this doesn't imply that he doesn't want to hire / pay you. Ideally, you can get other funding, which is a win-win: it's good for your CV, and for him it means he can hire you with less strain on his research grant.