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Should I bring a gift for my supervisor based in a university in Central Europe?
I am an incoming STEM PHD student in a Central European university. I am from South Asia.
I got admission to PhD program in Central Europe. My new supervisor really encouraged me to apply to do a PhD with him. I have had good communication with him over e-mails and 2 times over Zoom. He told me what to study until I am granted a visa to go to Europe. He also very passionately told me about the research area. I am positive that we will get along well.
Should I bring a gift to him from my culture (sweets, clothes or something else) to say thank you for really encouraging me to apply for PhD and guiding me? Since I am coming from far away he might expect me to bring me something from my culture. Or this is considered bad manners in Central Europe?
Should I purchase something to gift him or not?

Avoid any gifts until you have a strong grip on the local culture. You are never doing anything wrong showing up motivated and empty-handed.

Where specifically?  Switzerland, Germany, Hungary, and Serbia have big cultural differences in etiquette. // Relatedly, it would be helpful if answerers could include which countries they’re speaking mainly from experience of.

As a side note, many European counties have restrictions on what can be brought in, particularly anything containing meat, dairy or raw fruit\vegetables. Anything edible should be in air tight packaging, and have the ingredients written on the side in the language for that country, or if not possible then at least in English. Alcohol may also be subject to heavy taxation. culturally relevant crafted goods may be easiest. Such as decorations associated with a local festival.

@xLeitix "until you have a strong grip on the local culture" - this sentence alone is missing from many responses below. I recommend making it into a response.

The regulations in our place are very strict. While there is a perfectly reasonable acceptance threshold before it needs to be returned or donated, all gifts, no matter how small, are to be reported. I therefore refuse categorically all gifts, as I really do not feel like filling 15-20 minutes of forms about value, origin, reason etc. and submitting them for each trinket, as well-intentioned as it was. To me, a gift is a punishment, not a pleasure. I can only highlight @xLeitix first-rate comment: the greatest gift you can bring to a supervisor is motivation.

Which country do you go to?

@CaptainEmacs Very sorry, due to my own privacy I can't be that precise.

@DVI Fair enough, I understand. It makes it harder to answer, but I guess then the fuzzyness of the responses comes with the territory.

PhD students giving gifts to their supervisors is not a part of (central) European academic culture. Thus, there should be no expectation that you bring anything.
Giving a gift with substantial monetary value (eg > €20) falls under anti-bribery regulations, and your supervisor would be obligated to reject and/or report the gift.

I agree with @Arno and @Marianne013's answers, but - if you're joining a research team, you could consider some kind of a mass token-gift. For example: Some confection/candy from your country which has many pieces, and then when you first arrive, you can bring that as a gift to the group, so that each person has one or two pieces. You could on that occasion offer your new supervisor the first piece, and thank them personally. That way, you're expressing the sentiment you want, but it's not a gift of any significant value, and there is no chance of perceived impropriety.
... of course that suggestion doesn't really work if it's, say, just the supervisor and another supervisee you rarely even see.

This. Bringing any kind of local food/candy/tea/coffee to the department/lab (as opposed to gifting them to a specific person) is always appreciated and avoids any kind of awkwardness that is associated with giving gifts to your supervisor.

In Germany, bringing along some food and/or drinks during your first or second week, and having a small gathering with the entire group, is so common, that there even is a word for this: "Einstand". (Typically not on your first day, if you don't know how many people to expect.) Not sure about other countries, though.

The short answer is no, you shouldn't.
The slightly longer answer is that it is not uncommon for students to bring their supervisors token gifts (e.g. tea, sweets etc) from their home countries at the end of their course/degree/studies. At this point they usually a) know their supervisor well enough to know how such a gift would be received and b) it cannot be mistaken by either the supervisor or university administration as an attempt at bribery.

Personal gifts have different meanings in different cultures.
In Central Europe, you are not expected to give gifts in this situation. First, to be acceptable, the value of a gift in Central Europe needs to be small and clearly symbolic. Otherwise it would fall under bribery regulations and put the receiver into an embarrassing situation. Even without fear of regulations, giving a gift creates a difficult situation for the recipient. So, giving a gift to a superior or supervisor is just not a good idea.
Second, it is much more common to do something for your new colleagues. If you'd be working in construction, you might be expected to pay for a round of beer for new colleagues, but in Academia, this is not customary at all. So, bringing a box of candy or tea or coffee from your home country, as long as the value is small, for the socializing events that are common (e.g. 10 am coffee, afternoon coffee) is acceptable but not expected. It will make everyone else uncomfortable because they now have to do the same thing, or maybe not, or maybe yes. So, you'd have to make up a story, like your Grandma insisted or you do not like tea and someone gave it to you, ...
Since you have to pack and since the only way for a mitbringsel to be acceptable is something small and personal, that you can describe as purely coincidental, I would not bother.
Once you have established relationships, things are slightly different. For example, if you have a home visit, you can ask whether you should bring something and your professor can pay for it. It is more acceptable but still not appropriate for the superior in the relationship to give a token gift to the inferior.
People in Academia are used to traveling and know about cultural differences. So, if you were to give a gift, they can probably handle it and will not hold it against you. Usually, you will find colleagues that are willing to help you navigate culture. Once you arrived, ask them what the customs are. In Central Europe, there is a sense of solidarity among co-workers that need to stick together.

"So, you'd have to make up a story, like your Grandma insisted or you do not like tea and someone gave it to you, ..." This seems like a stretch from my Czech perspective.

That's because I am German and no longer living in Germany.

Do not bring it to your supervisor specifically, but to the research group. I have visited and stayed with several research groups during the past few years and I always brought sweets (pre-packaged, not home-made) from my home or residential country. They were always devoured pretty quickly by grateful students (and the PI). A good way to start in a new place ;)
Good luck with your new position!

look up what you can acutally take with you... don't make a big fuss about it.
just bring something small, like 2 bars of chocolate and a big bag of candy that you liked as a kid or something.
Bring something that you enjoy very much and that you want to share.
Something of importance to you our your culture... as a gesture. Whatever you think fits best... maybe something historical, something from your research field, a funny qirk...

What are you basing this on?

being german, having been in academia (media and arts mainly), knowing quirky nerds, knowing german law and habits... beeing a basic human being.. what else? :)

Contrary to a lot of the answers above, I would advise against food gifts (including sweets, snacks, food speciaties, etc.) for dietary restrictions. If there are any food poisoning, you're liable. Expensive gifts could be turned down because the advisor might want to avoid conflict of interest (i.e. other people thinking that you bribed the advisor). Gifts that are too personal might not be a good idea, because you just knew this advisor in a professional setting.
You can definitely write your advisor a thank you card though, and maybe a self-made card if you are good at arts and crafts. That would be very thoughtful without possibly violating anything, and your advisor will know your gratitude. This is my go-to gift when showing gratitude in professional relationships in academia.

"You can definitely write your advisor a thank you card though, and maybe a self-made card if you are good at arts and crafts." Very nice advice IMO!

So are you advising against giving food gifts in general, at any occasion? Seems an exaggeration.

@user1079505 Unless you are familiar with their dietary restrictions (i.e. have asked directly what they can or cannot eat), yes. I would want to avoid any awkwardness in case the advisor turns down the food or suffers from any food poisoning.


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One of my postdocs elegantly solved a problem another postdoc had been working on for years. I have no idea how to navigate this delicate situation
I run a lab in an applied computational field (e.g. computational biology/chemistry/physics etc.)
One of my postdocs (“A”) has been working on a problem for the last two years. They have made good progress, but the accuracy of their solution is not quite where we want it.
A new postdoc (“B”) joined my lab a month ago. Recently, B told me that they had given some thought to A’s problem and realized it was amenable to a specific computational method that neither A nor I were familiar with. B then showed me that, over the course of an afternoon, they had adapted said method to solve A’s problem. B’s approach is far superior to anything A and I had come up with in every possible way—accuracy, speed, interpretability, etc.
A does not yet know what B has done; B came to me first because they did not know how to break the news to A. To tell you the truth, neither do I. Knowing A’s personality, I think they will be extremely upset about this, and I have no idea how to navigate this delicate situation.
(To give an idea of how much better B’s method is: imagine spending months trying to come up with a good numerical approximation to a fiendish differential equation or integral, only to be told that there’s an obscure closed form analytic solution, obtained using techniques from a completely unfamiliar subfield of mathematics.)

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Could you clarify if B looked at A's approaches/attempts at a solution at all? Or did B merely hear the initial problem statement and then come up with a solution without additional info? I ask this because it seems quite possible that B's recognition that A's current approach wasn't working was itself important to the solution - otherwise B might've tried going on the same (or a different) path, and reached their solution later/never. If B might've benefited from A's work indirectly (even if it was just realizing "A's approach probably won't work"), a joint paper really makes sense.

I wish all the world were as generous as the situation and solution described in the answer by Moishe Kohan.
However, before you do anything, you need to verify the solution of B to be sure that it holds up. But, assuming it does, there is no real solution but to "bite the bullet" and deal with A. It should be your task, not B's to break the news to A. You will probably also have some responsibility to A to get them to a success point.
But talk to B first to explore their position.
I don't think that A has an automatic authorship position here, given your description, but I also don't think it would be exactly a "gift" to include them.
But, if B insists on sole authorship, as is probably valid, then you need to sit down with A to break the news. You can then explore how much is salvageable from the work already done by A.
And, don't try to pressure B on a joint publication. (Caveat, a somewhat different scenario might call for a very different solution.)
One option in a joint paper is to describe both approaches and why the one is superior. That would make joint authorship valid by anyone's (I hope) definition.

A has worked on the problem for a year. They almost certainly have a lot of insight, tests, and comparison data that would be very useful for a paper. It would almost certainly clear the bar for "intellectual contribution" to work on a paper together. The paper might be better by describing the failed attempts because it highlights the quality of the solution described in the paper.

@WolfgangBangerth Of course! A has certainly done enough work on the problem irrespective of the method used to ultimately solve it to warrant a co-first authorship. However, the publication would still be a methods paper first and foremost, and the method showcased therein would certainly be B's.

It would be B's method, but the readers won't know this. For all anyone can infer from the paper, it's a group effort.

If B insists on sole authorship, B must not include any conceptual or writing contribution from A in their paper. B learned about the problem from A, and it would be easy to accidentally include an insight from A in the paper that B assumes is trivial or well-known, but is actually novel, and an intellectual contribution warranting co-authorship. Given A has worked on this problem for so long, this is quite likely. The safest option for B is to offer co-authorship. This also will lead to a faster publication because A is probably more familiar with the literature than B.

@WetlabStudent, the OP has described it as independent work. I based the answer on that, not assuming otherwise. But, yes, a sole author publication can't include IP from others. Learning of a problem, however is not sufficient. You have a lot of speculation in your comment, actually.

@WolfgangBangerth : indeed, and in such a situation it might well happen that B's solution only works within certain limits or given certain assumptions, while A's work can still be used to study how the system works outside of those constraints.

Everyone here seems to assume a pure maths approach where authorship order doesn't matter but the OP talks about an applied field and in most applied fields order does matter. In this case B would have nothing to lose from having A as co-author since the contribution of the first author isn't watered down by having an extra author. The OP could explain this to B and ask if they would be happy with this arrangement, also explaining the advantages of having A as co-author (e.g. that they can more easily than B write the introduction and literature review, etc)

@buffy actually the OP has described nothing about the interaction between A and B at all. Both your answer and my comment are the same level of speculative, but at least my comment is a conditional statement: if X then make sure Y. Since the OP has said nothing about whether Y is true, it is fair to recommend they make sure they have done their due diligence to make sure Y is the case.  It is also speculative to assume B had not benefited at all from intellectual knowledge from A, even if indirectly through the supervisor. All I am doing is making the assumptions explicit.

Given that A have not solved the problem for 2 years, B's solution should be ran through every failed test from A's experiments to confirm its validity. At minimum, A would know a lot about why his results didn't work, and this is extremely non-trivial knowledge.

Another way of framing it is that everyone got lucky. B got lucky, because a bit of knowledge they had happened to be the key to a lock someone else had constructed, and they're getting a free paper out of it; A got lucky in that they finally have an outlet for all the knowledge and tests and reading they now have, and can stop banging their head against a wall; and you got lucky, in having the good taste to recruit a new postdoc, B, from (by the sound of it) a slightly different background, who managed to unblock a logjam. Drinks all round, when you knock out the paper!

This is a tough one.
I am a pure mathematician. Early in my career I was in a situation akin to the  one of Postdoc B. (Except I was still a master student and the person in the role the postdoc A already had a permanent position. He worked on a problem for a year but had only an incorrect proof. One more thing to add here: I have learned a lot of research-level math from A as an undergraduate student.) Here is how my advisor (who was also a former advisor of A) handled the situation:
He first talked to me and said something along the following lines:
"Moishe, you are brilliant. We all know this. In your future math life you will prove many remarkable theorems. [At the time I felt embarrassed by all this undeserved flattery. In retrospect, my advisor used the right approach here by “smoothing my feathers” first.] You solved easily a problem that A was working for a year.  What do you think of publishing the result as a joint paper (with A)? To you it probably will not mean much, but to A it will mean a lot."
He was right, I said yes and published the result together with A. I did not resent my advisor's advice; I also do not regret following it.
Will this strategy work in your situation? I do not know, but, I think, it is worth trying.

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Dilemma appreciated. I'm a sw developer (40 years) who has worked with many scientists & done a lot of collaborative design in different fields, with oft-touchy people.
Further to the excellent answer by Moishe Kohan is the question of framing - would B have thought about A's problem in the same manner if they didn't know:

A had explored a lot of approaches
a nearly-acceptable answer had been found but accuracy of their solution is not quite where we want it?

That context of A's work as a preface to B's insight is further reason for a joint paper.

I am not sure A's work is a preface. The solution by B is analytical so it does not really matter what A did before (this is not to lower A's work, which could be excellent in the computational world, but is is orthogonal to B's work)

@WoJ Analytical? OP writes B showed the problem is "amenable to a specific computational method that neither A nor I were familiar with". It does seem to be a bit of an assumption to claim the two approaches are orthogonal.

@Anyon, ah, you are right. I was misled by " (...) only to be told that there’s an obscure closed form analytic solution, obtained using techniques from a completely unfamiliar subfield of mathematics"

This scenario reminded me of a Billy Corgan (of Smashing Pumpkins) interview.  Essentially, he says he would have been more successful and faced less drama if he had shared his writing credits.
Based on this logic, if "A" contributed to "B's" idea, B will have more success AND an ally by sharing the credit with A.
Billy Corgan Interview:
https://youtu.be/GLvqzWSRwnA?t=307
The interview contains some swearing.

My gut feeling in computational mathematics is that every method has place to shine, given the right circumstances.
Method X may work very well in situation ABC, but might not generalize beyond that setting (in theory or practice). Method Y might not work as well in situation ABC, but may apply to situations DEF, GHI, and JKL much easier than X.
If your example is anywhere close to the scientific setting

(To give an idea of how much better B’s method is: imagine spending
months trying to come up with a good numerical approximation to a
fiendish differential equation or integral, only to be told that
there’s an obscure closed form analytic solution, obtained using
techniques from a completely unfamiliar subfield of mathematics.)

then would guess that B's method works in specific setting but A's method may work still once you change the specific problem a little bit (stuff like: nonlinearity, wild material coefficients, etc., can work wonders to derail good methods).

Given the fact that B had the presence of mind to consult you before approaching A, I would echo the sentiments of several posters here to impress upon B how the terrain mapping of A framed the problem in an efficient way. Knowing where not to go has huge value and often comes at a high cost of time and effort.

This is in fact very good news, and is one of the best reasons why we discuss our research with our peers. Yes, it is a situation that must be navigated with care, but really this is a win-win. Clearly the three of you should share authorship of this result, as it was cultivated in your laboratory through an ideas-sharing process. Culture of authorship order differs by field and should be navigated accordingly; you need only to be sure that everyone gets credit, including the credit for working at this problem for more than a year.

This answer is to this question, but moved into an industrial environment rather than academic.
It seems that the "delicate situation", at least as referenced by the other answers, relates to who gets to publish the results, and (I presume) get a career boost.  I re-read the question, and "publishing" is never mentioned.
Even within a lab, many problems are solved and advances are made that aren't directly published.  A lab itself is a small industrial culture which solves many problems, some big, some small, some publishable, some patentable, and some that are keep secret until they need to be revealed.  I would claim that given the OP's problem statement, this may have much in common with an industrial setting.
In an industrial setting, person A may have been working on a problem for a year and made good, but not complete, progress.  Person B has a new idea for how to solve it.
My job as the manager is to put persons A and B together to talk about the problem, and the progress B has made.
If the problem was important, chances are that A was my best pick for someone to work on it.  If I had a preferred outcome, it would be that A continues his work with B's ideas, and finishes the problem.  If the problem was not important, it could mean that A isn't important to the organization.  I should think about that.
Several outcomes are possible.  No matter what, I would publicly note A's long-term progress and B's breakthrough.
I would also look for other problems to slide past B.
It is important that I be part of their first meeting to judge the vibe, and then follow up with guiding an outcome based on the responses of the individuals.  I would also keep an eye on interactions between them after the meeting, looking for signs of collaboration or obstruction.

A career math's challenge is like a romantic partner: if they get unexpectedly wed to a competitor, jealousy can ensue, even revenge. If you hint the news to him and he starts to splutter and even cry, don't unleash the full force of the news. Use subtilty: Scientists are temperamental, unstable, you potentially stand in the way of causing A to become depressed, feel like a failure, belittled in his field and workplace. You and B can conspire to announce it gently to him over a period of months and years, not necessarily all in one shocking destabilizing revelation... Say that news has come of a potential solution for the problem, using said analytic system, and let A find the solution for himself and feel positively about it.
Solving the maths problem using broad general knowledge is a very laudable feat (is that OK english?) You can agree with B to not break A's heart and belittle him if you feel that it is the professional way of dealing with it, depending on A's mental stability.
Once he is over the entire quandary, a few months down the line, perhaps years, you can start to break the news to him... "Oh! it was student B that told me that said analytic method could solve the mystery". Some months later, say that B even "started to demonstrate the solution, so you told him not to give A chance to solve his beloved maths problem". see how he reacts, if he starts to cry, leave it.
Various tactics can be used to lessen the danger of emotional destabilization.
Academia and depression are often closely bound, and there is no need to raise the risk of a student's depression. Perhaps now is a good time to research instances of madness and nervous breakdowns of scientists in relation to academic theories.

Announcing this over months or years does not seem practical; B presumably wants to publish now. Moreover, I agree that a certain degree of tact is called for, but I see no need to "conspire" to avoid a "nervous breakdown"; A can presumably handle their disappointment appropriately.

scientists can be spectrum autistic (i.e. Elon ) and hyper nervous in a weird social combo which lends me to consider that mental health is not enough valued in favored answers, I know folk that have had major depressions from phd's and sometimes it put them off that career choice completely and they change fields.

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Can failed research become the objective of research?
I am working on a paper on social conditions during the pandemic, and have been using mixed methods. Unfortunately, the qualitative data collection process has been a disaster as I was unable to conduct any interviews. The reasons given for declining interviews were mostly due to pandemic disruptions. As such, I am now wondering if it's possible to do a reflective analysis instead, by arguing that the failure to collect qualitative data is in fact an indication of the real-time state of affairs?
I haven't quite been able to find relevant precedence and am unsure if there's an established methodology for this sort of "reflective analysis"? If anyone could point me in the right direction, that would be greatly appreciated!

Every paper ends up with an analysis of the study's success and analyses, doesn't it? So I think this is really just a normal part of presenting your conclusions.  I wrote a paper once about open source applications and ran into a ton of tech trouble with the open source application I was evaluating for the paper.  So I turned that into a big part of the paper -- here's the problem with open source applications!  I know you asked for specifics; my suggestion is look for papers that either didn't prove what they set out to prove or that proved something else instead.

What would the research question be on this new meta-project?

Meta-science/meta-research is the discipline that deals with studies that use the research methods to study research itself. Its currently quite en vogue, I don't know if you could make your study fit into this category.
Personally my two most successful papers are about what would have been quite mundane studies but anomalies in the analysis lead me to identify problems with the way data was commonly analysed across the whole field.

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Where can I find statistics about papers (length, writers, etc.)
Different fields have different writing culture. Some fields prefer single author papers, and others prefer group efforts. Some fields prefer a short paper with a survey of a new results, and others prefer longer and more technical papers.
Specifically I'm interested in mathematics (and its subfields, if such breakdown exists). Is there any way to obtain some sort of statistics as to how many papers were published, how long they are, and how many writers were involved? Some statistical analysis and trend-changes would also be very interesting to me.
Do these statistics exist for other fields? I'd be interested in also knowing how different is the publishing culture in mathematics compared to other fields (STEM, social and humanities).

If this question is inappropriate, I apologize in advance. I was also a bit uncertain regarding the tags.

Related: in the past @PiotrMigdal has been actively interested in similar data analysis projects; see for instance https://meta.mathoverflow.net/questions/2363/arxiv-vs-mathoverflow-popularity-of-disciplines, https://academia.stackexchange.com/questions/38969/getting-a-dump-of-arxiv-metadata, https://meta.mathoverflow.net/questions/2139/an-interactive-graph-of-mathoverflow-tags.

For math, see the links in this answer for papers about this: http://academia.stackexchange.com/a/41279/19607

Scopus can provide you with a statistical analysis of publications that it has recorded that match a query. It's behind a paywall I think, but your organization might have a login.
Using it is pretty straightforward;

If you want more information on the query format;

Then;

It can give you results over time or various filters etc.

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Updating the arXiv version of paper after it is published in ACM proceedings
Before submitting my paper to one of ACM's conferences, I uploaded the earlier version of the paper on arXiv. The paper has now been accepted and published in ACM proceedings. I plan to update the arXiv version of the paper with the final version of the paper that has been published in ACM proceedings. I wanted to ask if:
1) Am I allowed to do this?
2) Do I have to make any changes to the format of the draft. i.e the paper contains a copyright block from ACM now.
When granting licence to ACM, I did NOT opt for open-access. Also the paper was published in 2018.

According to the ACM Copyright Transfer Agreement, you are allowed to

Post the Accepted Version of the  Work on (1) the Author’s home page,  (2) the Owner’s institutional repository, or (3) any repository legally mandated by an agency funding the research on which the Work is based, and (4) any non-commercial repository or aggregation that does not duplicate ACM tables of contents, i.e., whose  patterns of links do not substantially duplicate an ACM-copyrighted volume  or issue. Non-commercial repositories  are here understood as repositories  owned by nonprofit organizations that  do not charge a fee for accessing deposited articles and that do not sell advertising or otherwise profit from serving articles.

So, yes, you can update your manuscript on arXiv with the accepted version but you should not use the published version (version of record), i.e. the one with the ACM copyright. Remove the ACM style by, e.g. using another style sheet in LaTeX.

So "accepted version" = including final edits after receiving peer review comments?


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What is considered appropriate men's attire for a PhD interview at a Max Planck institute?
During this winter, will it be alright to wear a shirt-jeans and a jacket for the PhD interview at Max Plack Institute?

Please be more clear about country, gender, research field, ... see, e.g. http://academia.stackexchange.com/questions/85117/what-is-considered-appropriate-womens-attire-for-a-phd-interview-in-germany.

You are about to have a PhD interview. Please make sure you spell their name right.

(Physicist here, experience with PhD admissions at British and German universities, including one Max Planck institute). In my field, I have never come across an actual dress code for PhD interviews. Nonetheless, if you dress too casually, especially older faculty members might get the impression that you are not taking it seriously enough. On the other hand, with suit & tie some people might perceive you as overdressed and maybe a bit stuffy. So being somewhere in the middle, e.g. jeans, shirt & jacket as you suggest, is a good approach.
I strongly assume that it is similar for other STEM fields (which account for most of the Max Planck institutes), but it can be completely different in other fields that tend to value formal attire (e.g. law).

I think you can do better than just jeans without going overboard with a suit and tie, there are a lot of things in between.

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Was forced out of PhD for academic/health reasons, need advice on what to do next
I was accepted into a PhD in maths at a fairly highly ranked school in 2017. My supervisor was known for being quite demanding, but I wanted this because I wanted to push myself, and he is quite well known in the field I was interested in, which is algebraic geometry.
During the first year I was doing background work and developed my maths up to the point where I could start actually doing research. This involved going through textbooks and exercises and generally learning maths at a high level. Each week he was unhappy with my work, and would find holes in the proofs and logic, and holes in my understanding. After this happened over months, he began to suggest that maybe maths wasn't for me. Eventually he basically explicitly said this, and said that I wasn't understanding the material and wasn't able to think mathematically. He suggested that I drop out and "do something else with my life".
The other issue here is that I was suffering from depression, and was fairly burned out from my undergrad, and I blame that in large part for not being able to study efficiently and think clearly. I did end up leaving the program late 2018, and I got a medical certificate to document the depression.
The thing is, I am determined to succeed. I know for a fact that a PhD in maths is what I want to do, and I am not willing to give up on that. I am certain I have the ability, and am putting my failure down to the above mentioned issues. I am still doing maths every day to keep my skill level up and increase my understanding. At some point I want to reenter a PhD program. That is where my question comes in.
What is the best way to get back into a PhD? How much will my past dismissal (technically I left voluntarily) affect my chances? Given that my supervisor has said flat out that he doesn't think I am cut out for maths research, how would I go about getting an academic reference for any future application? Any other advice is appreciated.

What sort of objective assessment of your mathematical skills do you have? Do you have an undergraduate degree in it? GRE? Did you take qualifying exams for your grad program? The two primary questions you should be focusing on are: was your supervisor's assessment accurate, and has your ability changed?

@Acccumulation - I'd say that the biggest question is whether the depression is being adequately treated or not, and if the treatment will withstand the rigorous demands of a math PhD program.

@Acccumulation yes I did a four year undergraduate and finished with first class honours. We don't have the GRE system here. I would say there was improvement, although my supervisor would say that my ability to reason mathematically has not improved. I think that is largely down to my illness, and communication.

Do you want to continue the same work you did before? Because in that case, you could maybe mention this as an advantage when talking to potential supervisors. In the vein of "I will probably be done much sooner than a usual PhD student because I've already started working on this". At least if you think that assessment is correct, and if you think that it is something a potential supervisor would like to hear. (I would love to hear something like this, because it means I don't have to train you.)

Am I correct in guessing that this was a maths PhD program(me), not a math PhD program?

@YemonChoi well, a maths PhD program is how we'd write it in Australia, but yes

Would it be possible to first do a master's? And by all means get another supervisor.

I once worked for a biomedical scientist working on HIV vaccine development. I thought the research was so translational and meaningful. However, my supervisor rarely encouraged his staff scientists and heavily degraded their research presentations, and he walked into the lab saying, "THAT'S NOT THE POINT!!!" Then he would change his mind later and he would not apologize for criticizing us for doing what he told us to do. The postdoc had regret in his eyes and voice! I hated waking up every morning. So went to the Assistant Vice President for Research and said "Help!". My life is MUCH better!

If you want to continue at the same school I'd start by going to talk to the administrators in your department, hopefully as a PhD student they will be familiar with you and your situation. Ask about your options to continue your studies, and possibly seek out a new supervisor.
I'd also make a list of other schools you'd be interested in attending, and find faculty there with similar research interests, ideally you could try setting up a meeting to discuss your shared interests and ask them if they might be willing to supervise you or if they have any projects that might be a good fit for you as a PhD student.

Not “possibly”. Definitely seek out a new supervisor.

Don't choose the project! Choose a good natured supervisor. Your project changes evermore. Yesterday I was doing optical physics. Today my supervisor walks in smiling saying, "Figure out how to grow this algae. It's our new model system for your project." Now you might think that doing plant biology in a biophysics lab is absurd. But it's a highly logical solution to my project.

Given that my supervisor has said flat out that he doesn't think I am cut out for maths research, how would I go about getting an academic reference for any future application?

Who gave you a reference in the first place? I'd suggest going back to them. You don't have to tell them the full details of what happened; you dropped out for health reasons, you're moving to a different supervisor because you didn't work well together, and your supervisor isn't in a position to give you a reference for that reason. It's not unusual for people to be asked for references even a few years after they last saw you.
A word of support, too. Stories of students not getting along with their supervisors certainly aren't unusual. When you say that your supervisor was known for being "demanding", well... sometimes "demanding" is a euphemism. I also suffer from long-term ongoing mental health issues, and they are enough of a barrier in their own right, but during the periods in my university career when it was made clear to me on a regular basis that I was a disappointment, the quality of my academic work plummeted and I completely lost my passion for the subject. In that respect, a patient, understanding supervisor can make all the difference, and I think most academics know that. (Maybe don't rant about this at interview with your new prospective supervisor, though...)

I am generally in favor of finishing the Ph.D., once started, even for weaker students.  At least it is a decent resume bullet, even if you are not top of the heap. If you're halfway through, you might as well get it done and cross it off.
But getting back into another program after not hacking it in a first one?  Seems low reward/risk.  Even in general, starting a Ph.D. should be looked at very skeptically (there is a lot of push to get students, but it is not always the right thing when you look at foregone earnings and issues with jobs after getting out).  But once you have not made it in a first one?  Sure there is the possibility that you hack a second one ore that it is a good use of your time.  But I think you need to adjust your Bayesian prior even lower (after all you have data, the first attempt).
If you really want to just get the Ph.D., the best thing would be to talk to the department where you were.  They may feel some responsibility for you and give you an easier, more agreeable, etc. advisor.
I'm not sure why you have to go for this Ph.D.  You state it like it just makes sense to want one, but you don't clarify why or what will change after you get that particular certification.  Do you think you are a research grade mathematician?  A professor?  I just would seriously consider other areas.  There may well be something else satisfying and that you are good at (even have a differential advantage) versus top tier algebraic geometry.  Note, even if this isn't for sure the answer (do something else), you should at least examine the possibility.  Not just stay wedded to this initial dream.  Just seriously investigate this.

I would have preferred to finish, but my mental health had deteriorated to the point that it wasn't practical. I would prefer a good PhD than a mediocre one that I finished because I had started. My goal is an academic career. I have put some thought into this and I am convinced that maths research is the right path for me. Obviously a PhD is the basic qualification for this. Even outside of career research, I am set on mathematics research. At this stage, earnings are not a concern for me. I am happy to sacrifice that for maths. That was a decision I made when I decided on research.


text:
How to write an abstract of paper mentioning the exhaustiveness with an emphasis on an unexplored case
I want your advice on writing a small portion of the abstract of a paper. Let me introduce the situation first.
There is a large class of objects, and an excellent way to study these objects is through a property, say "Property P." Now, this large class is subdivided into two sub-classes, say, "object of type X" and "object of type Y." Now, the Property P for objects of type X has been well-studied, nowadays classic stuff. Also, the sub-class of the objects of type Y is further divided into finer sub-classes, say "object of type Y_1" and "object of type Y_2".
Though the Property P for objects of type Y_1 is not written in the literature clearly, it is well-known to the experts in this field and also follows from Property P for objects of type X more or less directly.
Now, the Property P for objects of type Y_2 is neither written in literature nor known to experts very well (but they expect it to be true).
For a moment, assume that I am able to show the Property P does hold for the objects of type Y, i.e., I exhaustively studied the Property P for objects of type Y_1 as well as objects of type Y_2. It is expected that I will write an abstract for a paper as "Property P holds for any object of type Y."
Here is my problem: when one says that "any object of type Y," most of the time, people assume that statement is about "any object of type Y_1", as these type of objects appears more naturally, as I stated earlier. So, as a result, one may ignore the whole paper just reading the phrase "Property P holds for any object of type Y" for the obvious reason: what's new? (as this directly follows from property P for the object of type X)

Question: How do I tackle this? Should I mention this way: "Property P
holds for any object of type Y, possibly of the type Y_2". Do you have
a better way of writing this?

If the main and major point of your paper is exactly what you mention, then it deserves an explicit mention that is unambiguous and explores tacit assumptions. All major contributions of your paper acquire space in the abstract corresponding to what you consider to be the importance of that contribution.

We show, for the first time?, that property P holds not just for Y_1 subclass of Y, but also for Y_2. This establihes the previously unclear theorem that P holds for all known Y.

I would advise caution when using "for the first time" if you are not highly certain that it is the case, given your extensive study of the literature. Using a softer tone is always recommended.


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Disadvantage of having only accepted papers but no published papers while applying for a postdoc position
Is there any disadvantage of having only accepted papers but no published papers while applying for a postdoc position? All my papers are in arxiv, where the names of journals where my papers will appear are mentioned. One of the journals has a webpage for upcoming papers, but it seems like the other journal has nothing such.
My research area is in geometry and topology.

I mean, what are you gonna do about it?

Honestly, when choosing postdocs I mainly look at reference letters and the arXiv preprints. Everyone understands that publication takes time.

It doesn't matter, for papers "to appear" and a fixed publication are equally valuable on your CV.
Sometimes in academia there can be bureaucratic reasons where "accepted" and "published" can make a small difference. But in the context of applying for postdocs it doesn't matter.

It is not a big deal, but I have been in situations, where applicants for tenure-track positions listed a lot of work-in progress, forthcoming articles or articles "in the second round" and this does leave mixed impressions, in particular, if there are other candidates that have a similar track record of only published work. In committee discussions, you get members saying "Look this guy has a great pipeline of upcoming works" and others saying "Most of the guys listed works are not even published yet."
However, if you have recently completed your PhD, it is normal and ok if some works are not yet published but "just" accepted


text:
Cover letter and research interest
In postdoctoral application cover letter, is it okay to write, "My research interests are perfectly aligned with Professor X," even though the same professor did not reply when I mailed, expressing my interest in research collaboration?

To build upon Buff's good answer, show, do not tell.
For example, you might write:

My doctoral project on [4-dimensional underwater basketweaving], aligns with Professor X's interests in [multi-dimensional underwater basketweaving]. Furthermore, I would like to further develop or test [the Smith theory multi-dimensional underwater basketweaving].

Basically, list specifically your overlap, relevant experience, and future overlap.

Your statement seems a bit too strong, since you don't have confirmation that the professor agrees. I would recommend softening it.  "perfectly aligned" is a value judgement.
If you write it without "perfectly" and can offer some examples, it would be more "fair and balanced" (not to coin a phrase).


text:
Is there a point in pursuing a PhD outside of top universities?
I graduated with engineering and physics degrees last year, and started a PhD program in theoretical physics. While the program is a good one, it is not top-15 in the US or top-50 in the world. This means that, statistically, there is very little chance of me ever being a professor at a school with a comparable ranking. I get the sense that my program isn't really respected, and that our own professors don't expect us to accomplish anything significant. (At times it even feels like we are mostly here to fulfill the need for teaching assistants.) Since I am not in an applied discipline, I can't really motivate myself with the prospect of a research career outside the academia either. Furthermore, when I look at my peers who got into top programs either in engineering or in physics, I see that they are much more productive than I am. Whether this is because they are smarter/more creative/more motivated/more hardworking than I am matters little. Honestly, I am suffering from a deep inferiority complex due to this coupled with a few more things in my personal life, but that is a separate issue that is not really relevant here.
My question is, what exactly is the point of continuing the program? I suppose I am the one who should have an answer to that, but the best I can come up with is to view this as "entertainment" without tying it to any specific career outcome. Is it better if I just drop out and get a "real job" without delay? The demand for theoretical physicists is already low, and everything seems to indicate that I wouldn't make a good one anyway.

What's wrong with 'entertainment' or 'personal development'?  Yeah grad school is a dumb idea for homo economicus, but we're not homo economicus.  When I last applied for jobs as a professor, my backup plan was becoming a peace activist.  I don't need to explain that there's no money there.

It's more for personal fulfillment, I think. I definitely recommend getting a backup non-academic job while you're in grad school, because it will leave you with more job opportunities in the future.

Did you try checking how former graduates of your department doing? You can get an idea on what to expect after your own graduation based on that. Also, don't forget you can always to some postdocs to significantly boost your credentials.

@AlexanderWoo I find you guilty of writing answers in the comments. Which is frustrating, because that's the answer I want to vote for and I'm too lazy to write it myself. Please make answer?

"This means that, statistically, there is very little chance of me ever being a professor at a school with a comparable ranking." if that were true, it would be an indictment of top-50 universities (academic snobbery preventing them from recognizing research talent outside their group)

As per usual with these questions... With only a few exceptions, nobody cares where you got your degrees. They care about what work you produce and what you do with the skills you've acquired. If you write a top-notch thesis at your local town's uni that nobody has ever heard of, that'll be better than a minimum pass thesis from MIT as far as prospects are concerned.
Also, if you're doing your PhD for any reason other than that you want to for the sake of it, you're going to have a tough time

Based on my experience (computer science in the US), I think it's crucial for PhD students to have a realistic idea of their prospects after graduation.  In my field, jobs (academic or industrial) doing theoretical research are extremely competitive, and as a rule only go to those few students each year who have extremely strong records, usually from the top schools.  Same with good postdocs.  I strongly encourage PhD students who are interested in theoretical work to have a realistic awareness of this, and to have a tolerable backup plan in advance.  Do it if you want, just be aware.

No matter how prestigious your school, statistically, your chances of attaining a professorship at an equally prestigious school are low.  This is simply a function of the number of openings available vs. the number of graduates.  If you will not be satisfied with any other result, then you take a grave risk by continuing.  But that's not to say that you should give up on your aspirations, just that you should come to a realistic view of your prospects, and have a plan B that will still be fulfilling in case plan A doesn't work out.

The likelihood of becoming a professor depends a lot less on your school's ranking and a lot more on your research advisor's reputation in their field.

I think the better question would be is it worth pursuing a PhD at ANY university.

Apart from the job perspectives, I feel there's a lack of motivation from everyone in your department and around you. And this is not an Academic question, this is more of a life question, as we all go through the inferiority complex, once we try to compare our weaknesses to other people's strengths.

Note also that like with most things, the top 50 universities a few decades ago likely don't entire match up with top 50 now, and top 50 in a few decades will likely change some again.  Why?  Because where the education and student quality/effort sparks growth, they will move up, and where they rest on their position, they will slump down.

Is there a point in not being the best? Actually yes, I still think my life is great, I have a decent job, fulfilling tasks, cool team etc. etc.

"Is there a point in pursuing a PhD outside of top universities?" <- This title is rather conceited and disrespectful.

Your post leaves out a key issue: Do you have a passion for theoretical physics? If so then there is a crystal clear answer to your question: Taking into account that there's not actually enough room in the top universities for all those having a passion for theoretical physics, the answer to your question is a clear "yes". If you do not have such a passion, for example if to you it is solely a utilitarian decision, then I'll leave it to you to ponder other advice found in this thread.

You can always try moving into politics after your PhD.

Surely in theoretical physics, if you come up with a brilliant paper, it doesn't matter where you are working? You've heard of this Swiss/German guy who couldn't get a university job and made do in the patent office?

There are so many things wrong with your question :-)

The point of a PhD is not only so that you can become a professor. A PhD is also both an education that opens doors for future jobs in industrial research, and it is a set of letters that open door to promotions that would otherwise be more difficult to achieve (for example, to be the head of a research department in which a substantial number of PhDs are employed). In all of these regards, where exactly you got your PhD does not matter very much. Furthermore, it's not true that only those in "applied" areas are sought after by industry: theoretical physicists have long made a good living in quantitative finance, for example.

Even if your goal is becoming a professor, having your PhD from one of the top universities is neither necessary nor sufficient. It is probably true that the majority of those who are offered assistant professor positions in the top-50 universities of the US are in fact PhD graduates from top-50 universities, but the best people often find ways to move up over the course of their careers and find ways to be hired by top universities even though they were initially employed further down in the rankings, or got their PhDs further down the rankings. And even then, being a professor can be (and often is) a very rewarding career even if you are not employed by a top-50 university -- in fact, maybe even more rewarding than actually being at a top-50 university.

Be aware that there need not be a strong correlation between a good researcher and a top-50 tenure track position. "Science is a wonderful thing if one does not have to earn one's living at it. Only when we do not have to be accountable to anybody can we find joy in scientific endeavour." - Einstein

Note that you don't have to be employed by a "top university" to have a rewarding career in academia and then retire vey comfortably.

@quantum I think if one were to make those notions precise, there would be a strong statistical correlation.  Maybe what you mean is that there are many good researchers who are not tenure track at top 50 schools.

However, "neither necessary nor sufficient" does not cancel the fact that there's still a strong causality. It certainly helps, more or less, to move up your career in academia or a research division in a company if you've got a PhD degree in a decent institute.

+1 due to the first sentence in your answer.

@quantum - and isn't that true of anything? Someone said, "get a job doing what you love and you'll never work a day in your life." Complete horsesh*t, of course, because it doesn't account for how management will suck the joy out of any good pursuit.

I think this is an excellent question that really cuts to the heart of the US university system (and other Anglosphere HE systems, namely UK, Canada, Australia, etc.). A strongly hierarchical HE system that clearly delineates between "top" and "non-top" universities inevitably invites such questions about doing research in "non-top" institutions.
My short answer is this: if you are extremely motivated, you can still make it to a tenure-track position in a good research university. You simply need to work harder than your peers and be more active. Not only this, a person who started at a low-ranking school and ended up in a higher-ranking one, is bound to be one of the strongest researchers around. So the challenge is quite appealing in this sense.

You “simply” need to work harder than a peer group that is consists of the most motivated and talented minds of your generation, worldwide, that is. Simple!

@KevinArlin, yes, it is simple. It's just not easy. Actually, it's very hard. But then, even if you're at a top school, it's very hard to get a permanent position at a good research university.

Having a Master's Degree in Engineering, spending much of my career working with other engineers with PHDs, and talking to a few colleagues about the relative merit of a PHD, I believe I can provide some relevant feedback on this question.
First, when it comes to technical degrees, the school you went to has much less importance than it does for a liberal arts degree. It all comes down to where the rubber meets the road: what do you know and how well can you apply it. I got my undergrad degree from University that is not especially known as a top engineering school, but when we competed in a national engineering design competition, we placed very high (4th place) among our peers (over 100 other major schools), yet some very famous "top-tier" engineering colleges only placed in the middle of the pack. I later found out through a good friend who took a couple graduate level courses at one of those "top-tier" schools that those students were actually being short-changed because they were exposed to a lot of different glitzy programs but didn't get a very thorough exposure to those topics. On the other hand, our "mid-level" engineering programs, with much smaller budgets, focused heavily on the fundamentals with examples of practical applications, so we were well prepared to apply what we learned.
The next point has to do with how a PHD is viewed by the rest of the world. Those 3 letters tell people that you had the determination and endurance to go through a prolonged and intense program of study and see it through to the end. It opens doors, oftentimes without questions from those in non-technical fields, and even technical types will recognize what it took to get that degree, even if it wasn't from a "top-tier" school. In other words, the degree itself has value no matter where you got it from.
Third, there are lots of places where an advanced degree in a theoretical field is not only desired, it's necessary. Several colleagues of mine with PHDs are looking at how to do things and build devices that haven't been built before. Major corporations trying to solve some big problems need people that know the theoretical side of things to come up with new materials, new processes, or new applications for existing devices. For example, take some of the work that's being done in the areas of superconductors and other electronics, high temperature tolerant materials for aviation and space applications (think propulsion, heat shields, electronics, etc.), and more. The people doing the work in those fields are mostly PHDs. Another advantage of working in industry is that they usually have much bigger budgets than universities, even when accounting for government funding and research grants. And several of those colleagues I mentioned earlier have transitioned to university positions at prestigious institutions primarily because of their experience (and accomplishments) in industry.
Finally, the process of getting the advanced degree itself has value. I was an officer in the military, and I was told point-blank that even having a bachelor's degree demonstrated that I have the capacity to learn. Having an advance degree shows that you have an even bigger capacity to learn, and a greater capacity to conceive of big new ideas and (hopefully) be able to find solutions to big problems.
That pretty summarizes my experiences, but of course, your mileage may vary.

A “theoretical field” like applied physics, perhaps. Somebody with a phd in theoretical physics won’t have the foggiest idea how to actually design any physical device, in general.

Focusing on the career reasons here (i.e. not academic ones like "you learn things"):

PhDs enable new career options. If you go to your local jobs portal, chances are you'll find results that specifically ask for a PhD degree. That means completing the PhD lets you do jobs you won't be able to do with a Bachelor's or Masters degree. This applies regardless of which university you did your PhD at.
You could still be the biggest fish in your local pond even if you are not the biggest fish in the ocean. For example if you're in Kenya, then the "best" university is the University of Nairobi. If you have a degree from that university then you're good in Kenya, even if your international prospects aren't that good. The same goes if you have a degree from a top-100 university in the US, since even the rank 100 university in the US is more highly ranked than the University of Nairobi.

I’m looking at my jobs portal, and I see exactly no jobs that want “a PhD, even if it’s not in a directly relevant field.” There are essentially no jobs that a theoretical physics PhD can get that a master’s holder can’t, other than college professor or researcher at a handful of national labs.

@KevinArlin Counterexample.

alright, alright, there are still a few quant firms hiring for “any quantitative PhD.” Of course you’re much more attractive to such a firm if you have a degree involving more coding and working with data, rather than just drawing Feynman diagrams on a whiteboard. For instance, I’ve seen similar ads that specifically exclude pure math as not quantitative enough.

@KevinArlin Another counterexample. Also, I would think most theoretical physicists can code and work with data, rather than just drawing Feynman diagrams on a whiteboard.

Really? Surely the difference between applied and theoretical physics breaks down almost precisely at the need to use substantial real data. I did a lot of math adjacent to theoretical physics, and at least a substantial chunk of the field is just like pure math, i.e. no data is ever seen. It's possible that theoretical fluid dynamicists are more useful to GM than string theorists, I'm not honestly sure...(EDIT) Just based on glancing at some random Quora answers, it does like some theoretical physicists will get enough experience with data experience to be useful to GM, though not all.

But again, if you actually read that whole job description, what they really want is somebody with a PhD and/or corporate experience in machine learning and NLP, they're just not insisting on that off the bat. If you want to be a data scientist, why not just do data science in grad school? I really see no jobs at all except for a narrow band of quantitative finance where they really just hire "anybody, we don't care about your experience, just that you have a Ph.D. [and come across as overwhelmingly smart in the interview]."

@KevinArlin Surely the difference between applied and theoretical physics breaks down almost precisely at the need to use substantial real data. That's not the case. For example "here is a bunch of LHC data, find a model that explains it" is a theoretical physics problem. You could do theoretical physics without having to use real data, of course, but simulated data is still data, and there's a good chance you need to tie your results to observables in any case.

@KevinArlin If you want to be a data scientist, why not just do data science in grad school? You could. Or you could do theoretical physics and transfer later. I don't know how many more counterexamples you need to the idea "there are no jobs at all" either - here is another one.

@KevinArlin and another, more, etc.

actual snort Um, did you notice one of those jobs starts at $26,000 annually? At that rate, why not just work part-time at Starbucks? At least then you won’t be actively contributing to concealing academic knowledge from the world…Another one of those requires quantum computing expertise. Technically possible in a physics degree, but like virtually all actual jobs requiring a PhD, best gotten in a CS department. (Such as the other suggestions, all of which require deep CS expertise.)

@KevinArlin conveniently ignoring the other jobs? I guess it's a good way to preserve your worldview in the face of the counterexamples. I am done, you are giving every sense that you cannot be convinced so it's a waste of time for me to try.

I’ve since edited in a response to the rest of that list of jobs for machine learning experts. It is probably true that I cannot be convinced that a theoretical physics PhD opens many professional doors, because that is not true. PhD’s are a ticket to academic jobs. For the great majority of PhD’s, that’s basically it, and they’re not very good tickets. It’s completely irrational to pursue them for professional reasons, though it may be worth it for personal reasons. And I wish people would stop lying to impressionable 20-year-olds about this. It does harm.

@MorganRodgers On ArXiv and SciHub, of course!

The university you get hired at will depend significantly less on the university you graduate from than it will on the quality of your research and the "prestige" of your publications.
That said, the advisors that you will have access to at "top" schools are often engaged in prestigious research and have access to large pools of money that provide resources and collaborators for quality research.  Science costs money and takes time, and doing research with 6 other grad students who are as ambitious and bright as you, and having access to all the data, computational power and equipment you might need will prove invaluable as you do research.  This is more important in some fields than others.... some areas of physics are notable outliers where a lot of research is a worldwide collaborative effort, and not the cloistered race for antecedence that often marks some trending fields.
In short, the thing that you should really be considering here is "will attending so-and-so university give me access to the resources and collaborations I need to fulfill my research ambitions?"  It is possible that a university's prestige leads you to suspect that you will find just these sorts of resources and collaborations there.  If your peers seem to be finding those things at other universities, and you aren't finding them here, perhaps you should consider a transfer.

I don't normally ever answer here, as I am not an Academic, and in fact, hold no higher degrees at all. This answer has to do with non-academic employment.
A little background of myself, first.
I went to a community college and got an Associates. I was then in the military for 23 years as an electronics technician and ended up a senior non-commissioned officer.
Leaving the Army, I then changed fields completely and began my next career as a systems administrator in IT.
Now for my point.
Many times during my current career I have applied for a new job or position with a company. Every single time the position included the requirements of a Master's or PhD, or equivalent experience.
Now, as I am approaching retirement age, I have 21 years of experience in IT. Sounds like a lot. If I cared to enter management, my years of experience might get me a position at the lowest level. But advancing in the management track would require me to go back to school, to get a Bachelor's, Master's, etc. That is just the way it is.
Let's say you make it through your schooling and are granted your PhD. You would have zero experience, and yet with that PhD, would immediately meet the requirements of jobs I am distinctly uneducated for. There is a mid-level management position available within my company right now, and looking at the requirements I see Masters, or PhD, and nothing about experience. If you and I were up for that position, I am unqualified while you would be.
Nowhere have I discussed from where you may have received your degree. The requirements for many positions are: have a PhD, not have a PhD from a top-tier university.

No.
It depends somewhat on what you hope to get out of it, but in general the answer is no.
You could decide that my answer is blunt, abrasive and horrible, but two, three decades down the line you will come to understand why the answer to your question is quite simply: no.

Can you elaborate or explain your answer ?

I believe that the quality of the school is correlated to the quality of the students. But there are outliers... that is, good students at bad schools and bad students at good schools.
You can certainly still make a name for yourself. The only thing holding you back is you, not the school.
FWIW... I went to a community college before becoming a professor at a big German university.

I should add... There are certainly fields which may be impossible to break into at a small university if, for instance, the small university cannot fund the required equipment to be successful in a certain field.

Your question is a great one, but it's also in a sense wider in scope than academia. And it's also one that may get biased answers on Academia StackExchange. You need to first ask and answer the wider question of what would make you happy career-wise, then you'll have a simpler question: how to spend the next years of your life to optimize the chances that you reach those goals.
Regarding the first question, ideally you want something at the intersection of what you're good at, what you're passionate about, and what you can get decently and reliably paid to do. Would you make a better engineer or theoretical physicist? How passionate are you about theoretical physics (setting aside your other concerns)? (This is important, because if you want an academic career, you'll be competing with people who are really passionate about it.) Are there other things you are or might become passionate about? Regarding income, you already know the answer to the last question (prospects are not good, with little location flexibility), though potentially you could develop mathematical and statistical skills in your PhD that are lucrative in finance, for example.
Once you've answered the above questions, it'll hopefully be easier to determine whether to spend the next years finishing your PhD vs embarking on an industry career.

Statistically speaking, one is a lot less likely to find a good faculty position if they graduate from a weaker school. It's down to luck and how you exploit your fewer chances when they show up. And they always do, even if you start from a much crappier place than the weakest American PhD school.
But, knowing a lot of people who overcame the odds, I always wondered what was exactly they did that helped. And that thing is that they made a lot of good connections. In addition, they worked hard on good problems and believed in their chance.
To give an example. One of my people I worked for as a postdoc, graduated from a very small school. He went as a postdoc to a stronger school, working with someone very famous. He found there a few strong colleagues to collaborate with, and, to the best of my knowledge, they still collaborate. This helped so much, that after that first postdoc, he had enough good results to show for and get hired as an assistant professor.
Not so long after he got the position, he worked with some of his collaborators on a problem which made him famous in the physics community. Then he found another problem of that kind and another and eventually he became full professor and lives happily ever after, or so he should, but he's too much of a workaholic. More than half of his former students and postdocs are themselves professors and researchers in strong places, and I don't know of any of them who left science after working with him.
To conclude, your chances are slimmer, but there is a recipe for success, and you can learn it from the people who are successful. If your goal is to be a faculty, better start building your network of collaborators, start learning to create good research projects, and don't underestimate how much you can do even from a weaker school. I myself had colleagues whom I thought they would never graduate, and some of them are now at top 10 schools in the world.
Now that you're in graduate school you may not see much beyond the course work, and the research projects you work on with your colleagues and/or adviser. But, opportunities will come, sooner or later, and you need to be ready and in a proper mental shape to recognize them for what they are and seize them.

"how you exploit your fewer chances when they show up. And they always do" I think that this is probably survival bias. Just because you've gotten chances, doesn't mean that everyone who finishes a PhD does.

@nick012000 If you ever get admitted in a PhD program in STEM, in US or any of the EU countries and start bemoaning your lack of chances, it means you're not paying attention, or not willing to take them.

Furthermore, when I look at my peers who got into top programs either in engineering or in physics, I see that they are much more productive than I am. Whether this is because they are smarter/more creative/more motivated/more hardworking than I am matters little. Honestly, I am suffering from a deep inferiority complex due to this coupled with a few more things in my personal life, but that is a separate issue that is not really relevant here.

This is absolutely relevant to finishing anything you start. It's also better known as "imposter syndrome".

To put it simply, imposter syndrome is the experience of feeling like a phony—you feel as though at any moment you are going to be found out as a fraud—like you don't belong where you are, and you only got there through dumb luck. It can affect anyone no matter their social status, work background, skill level, or degree of expertise.

https://www.verywellmind.com/imposter-syndrome-and-social-anxiety-disorder-4156469
If you don't have the drive to finish something because you are (falsely) comparing  yourself to others you see as better than you, then it doesn't really matter what logic, statistics, job availability, or anything else say. Without that drive, you simply won't finish or, if you do finish, you'll likely resent finishing. The flip side is that if you don't finish your degree, you'll likely regret that decision, but your imposter syndrome will convince you that it is "proper", since "you wouldn't have been any good at it anyway".
Of course, that "logic" is all a load of bull.

Some of the common signs of imposter syndrome include:

An inability to realistically assess your competence and skills
Attributing your success to external factors
Berating your performance
Fear that you won't live up to expectations
Overachieving
Sabotaging your own success
Self-doubt
Setting very challenging goals
and feeling disappointed when you fall short

That list comes from the same article I listed above. I see a lot of that in your question. The fact is that you are doing better than you think you are. The simple fact that you got into a PhD program shows that you have more drive and intelligence than most people.
You are simply having a moment (or more) of self-doubt and probably some burn-out. This is natural, especially when people push themselves as hard as you are for as long as you likely have been.
Often, people with imposter syndrome will try to overcorrect by boasting about how well they are doing in public, then feel like crud in private. So the people you see as "smarter/more creative/more motivated/more hardworking" are likely also suffering the same problem you are.
There's also the opposite of imposter syndrome, which is the Dunning-Kruger effect, which says that people will over estimate their own importance, intelligence, or smarts in a topic when they are actually ignorant in the field. Those people who boast about how good they are might not actually be any good at all. This effect also states that people who are very informed about a subject will know better how much they don't know, so will underestimate their skills.
The bright side is that you can recover from imposter syndrome and the Dunning-Kruger effect to build your self-image back up to where it needs to be. There are a lot of online resources as well as going to therapy, or simply talking to your friends and colleagues about it. Likely, they'll remind you about how well you are doing, even when you get negative feedback from advisors, professors, and whomever else is in a authoritative role over you. Even talking to some of them may help you find out that they are simply trying to push you to do better, since they may believe you can do better. They may just be pushing too hard or in the wrong way without realizing it.

My question is, what exactly is the point of continuing the program?

Why did you get into the program in the first place? Did you look at employment opportunities beforehand? I'm sure you did. I'm sure you got into it because you enjoy the subject. Not many people get into a PhD program just because they were told to. You just need to find those reasons again and they'll be your answer.
Also, you will want to finish your program to avoid the regret of not finishing it and the resentment of paying all money & spending all that time to waste it by not finishing. I have regret and resentment about not finishing my bachelors degree. I can't imagine how bad it would be to not finish a higher degree, so do yourself a favor and avoid that problem.
All of this stress, imposter syndrome, Dunning-Kruger effect, burn out, and negativity can lead to depression, and depression can lead to worsening depression. You need to get help with this. Society seems to make people think they need to handle everything without help, yet a common phrase is that "it takes a village". Generally, this is referred to when talking about raising a child, but really it's about anything. People help each other do many things. Farmers help others when they are sick and can't plant or harvest their fields. Neighbors help with performing house repairs or loaning tools, or simply watching their house when they are away.
We've lost a lot of that sharing responsibility in the past few decades, but there are plenty of people who still volunteer. What I'm trying to say is that we were never intended to "handle everything" by ourselves. This is why we live in communities, so we can share responsibilities as well as resources. We need the help of others to do our jobs, live our lives, or do anything, really. We shouldn't be pressured to deal with mental health issues on our own, either.
So yes, talk to you friends, colleagues, family, a therapist, get into group therapy, find a hobby, something to help you deal with the stress and insecurities of your life. They can help show you that you are doing better than you have convinced yourself you are. They will help you remember why you are doing what you are doing.
The people you love and respect, who love and respect you, will help you answer your questions far better than random anonymous people online are going to.

My question is, what exactly is the point of continuing the program?

If you feel you are doing meaningful research, which will advance human knowledge or have useful consequences/applications (or itself is a useful application); and if you draw satisfaction from doing your research work, at least most of the time - then those are the points of continuing your research work. Hopefully there will be a Ph.D. in it for you, but the title is really not the point.

There are already pretty good answers out there, so I would not add much so just take some time to read along.
Well there are two main issues that should be addressed separately. First the school you go to and your motivation, and I think they are or should be mutually exclusive.
Talking about the school, there are hundreds of schools in the USA alone where PhD level research is being done. And in the current times, most of the PhDs are based on some industrial projects so you get a chance to enhance your practical knowledge while expanding your professional network. And that is what counts during PhD that how significant and practically relevant is your topic. Theoretical PhDs are boring!
Regarding the motivation, yes you said it right that you should be the one who could answer the best. But yes it is lifetime learning experience where you can independently do research and present it to the outside world. And as someone said PhD is difficult in start, messy in the middle and rewarding in the end. So, I hope the same would be in your case as well.
Good Luck!

As a pure mathematician with a Ph.D. in pure mathematics, I find your claim "Theoretical PhDs are boring!" offensive :) But speaking seriously, a theoretical Ph.D. can be just as fascinating as an applied one.

@Gary I think sometimes applied folk somehow miss the incredible frequency by which some mathemagical sleight of hand reveals deep and practical truths about the empirical universe.  Applying the equations is so often an all-trees and no-forest sort of thing.

@Him can you give one example of when that happened this century?

@user1271772 Obviously your mileage may vary, but, for example, I suspect that the recent replicability crises in various fields may be exacerbated in part by folks sometimes pushing numbers through a statistics software package that they don't fully understand the inner workings of.  Of course, nobody can fault one for being a [subject]ologist instead of a Statistician, I suppose.

So you switch from saying there's an "incredible frequency by which some mathemagical sleight of hand reveals deep and practical truths about the empirical universe" to "YMMV... I suspect... I suppose". I was the one who upvoted you for your effort by the way, so the downvote isn't related to my comment.

@user1271772 sorry, I had gotten the impression that your "give one example" comment was with respect to "applied folk somehow miss", as opposed to the "incredibly frequency" part.

A few examples from statistics are the various probabilistic bounds and limit theorems on distributions.  The fact that the distribution of the sample mean approaches a normal distribution for most distributions that don't have super weird pathologies is kinda shocking... deductive metrics for strength of inductive statements is pretty amazing.  The proof of the CLT usually involves representing the distribution in some kind of alternate basis (such as MGFs).  Bases of function spaces (such as MGFs and Fourier Series) are another example of this sort of slight of hand.  Complex numbers, also.

Central limit theorem wasn't proven this century.


text:
Can I present the results of my published article at a conference if another author previously presented it?
I am considering presenting a paper I coauthored (with equal contribution) and am corresponding author at an upcoming conference. The paper has already been published, but theresults were presented by another coauthor at a conference before the publication.
I would like to know:

Is it acceptable to present the published work again at a conference?

Should I take consent or inform other coauthors before proceeding, or
is this typically understood to be permissible if I clearly mention
all information like joint work, publication and presentation?

I want to ensure there are no ethical concerns or misunderstandings
when presenting our work. Any advice or experiences on this matter
would be greatly appreciated.

I think you need to provide more information about it. What is your field? Are these two conferences in the same field? Usually, it is frowned upon to present work from another conference; you should only present the findings of your current submission and use other publications as a comparison or motivation to your current work.

My area of research is Mathematics. Previously the results are presented in the confrence which focuses on algebra, analysis, and now the Conference is related to borader area of mathematics with artificial intelligence.

In my experience this is done all the time in pure maths. Sometimes it also happens that the same person is presenting the same results at multiple different conferences.

Actually, I am scared because of my advisor's misguidance. One time, he told me there would be no problem with presenting, but when I was ready, he blocked it say that it will not create any problem when you have to include it in your thesis. Now he is claiming that I have not presented it any conference yet

Do you have more recent results that haven't been published or presented?

Yes sir. For other set of matrices I have obtained new results which aligns with previous published results.

To go through you questions one-by-one:

Is it acceptable to present the published work again at a conference?

It depends upon the specific context and norms of your field. In my field, the life sciences, this is typically okay as long as it is not the same meeting and there are different target audiences. In fact, sometimes, coauthors and I will reuse and share parts of presentations to reach broader audiences. For example, author A might present at the Underwater Basketweaving International Meeting, author B might present at the Basketweaving National Meeting, and author c might present at the State Weaving International Meeting.
Also, if author A presented at the Underwater Basketweaving International Meeting 2023, you should typically should not present at the Underwater Basketweaving International Meeting 2024 unless you have major changes to your results and conclusions.

Should I take consent or inform other coauthors before proceeding, or is this typically understood to be permissible if I clearly mention all information like joint work, publication and presentation?

Yes, open communication with all coauthors is key.
If any disagree, you should not present the work.
Your coauthors will also know the norms and expectations of your field.

I want to ensure there are no ethical concerns or misunderstandings when presenting our work. Any advice or experiences on this matter would be greatly appreciated.

My number one piece of advice would to have open communication with your coauthors.

Actually, I am scared because of my advisor's misguidance. In the initial stage when I opposed that I will present the results then he told me that show your big heart and let your junior to present the work you will not get any trouble when you have to include it in your thesis.But When it's time for my Phd submission he is telling that since you have not presented the results you cannot include in your thesis.  To include it in your thesis you should present it first. Should I only inform or take written consent prior to presentation. Please guide me properly.

Sorry to hear that you're having conflict with your advisor. I think that is actually your bigger problem. Please consider rewording your question to reflect your situation. BTW, there are several questions on this site already about advisor-mentee conflict. Perhaps some of those questions will help your situation.

@Rst Unless math is very different, you need your coauthors' permission to submit an application to present, which they should clearly be an author on.

@AzorAhai-him- maths is very different. In my experience the expectation in maths is that all coauthors are responsible for the whole paper and "own" all the results. Often the "application to present" is submitting an abstract where the coauthors are typically mentioned by "This is joint work with ...".

@Christian You do not need your coauthor's permission to submit an abstract in math? I will leave my comment with the caveat because sometimes people who aren't in math do come to this site.

@AzorAhai-him- No formal permission in any case. And I think that it is expected that everybody is happy when the joint work is advertised. Discussions whether it is okay to present typically happen if coauthors want to present at the same event - so they make sure that they do not talk about the same thing. I always ask my coauthors if they are fine with me presenting joint work but I think it is not something that is universally expected in maths.

@Christian Interesting. At least in my areas, submitting without approval would be a faux pas, although really only an issue if it was a persistent habit.

@AzorAhai-him- I think the key is if there's conference proceedings. In cases where there are none, I've never been asked. In the case there are archival proceedings, then approval is needed like a paper.

@user71659 Ah, good to know. I don't have conference proceedings.

There are two (at least) considerations. The first is what the conference committee permits for such things. Conferences in some fields, and some conferences, perhaps, in many others, will permit such talks as a way of spreading recent results, even if they have been presented or published elsewhere. Others will not, requiring some key "innovation" in presentations. So, ask the committee (or program) chair.
The second consideration is the opinions of your co-authors, but I'd find it hard to think they would be an obstacle, so long as you present it as joint work, listing everyone with an authorship position. Among other things, you should probably point attendees in some fashion, perhaps a slide, to the earlier published and presented work.
EDIT: Given some comments and additions, let me suggest that a better alternative would be to focus any presentation on new results and to name the presentation accordingly. Indicate that the talk is a follow up to the earlier one. This will make attendees and, I hope, your advisor happier.

Yes the conference committee permits. I talked to them they state that write the email we will allow. If I will give the presentation with the aim to promote the work then it's fine or should I add some more work and then present it with new title?

That is your choice, just be sure to give credit so as to avoid any hint of plagiarism.

If I present results that have already been published and presented, what should I do about the title of the presentation? Is it necessary to keep the title the same as the one used for the published article?

I doubt it, but your co-authors might have suggestions, as might the program chair. As long as you have a way to cite the earlier presentations and publications, the title itself is less important. Don't present it as new work, however, unless it is. People might actually be confused if the titles are the same if either presentation is cited in the future.