text:
How to not feel guilty when reporting possible misconduct during exam/coursework as a teacher?
I am teaching a small class in my university. This is my first time, and as I am still a PhD student and the university was missing a teacher, I ended being selected to present it.
It is a programming class. During my first coursework marking, I found one answer to be suspicious, coming from a student. I checked online and found the exact same answer on Stack Overflow. It doesn't mean anything by itself, as it is a rather simple and short answer, but other small details led me to believe the student may have copied it online (which from the university guidance given to them is not authorised).
I raised my concern to my course leader, who told me to look at the misconduct guidance. I contacted the contact in the Discipline Committee in my school, and they told me to file a report to the Student Conduct Office which will investigate the matter, as staff and teacher should not investigate themselves.
I had to contact the student to inform them, and I now feel very bad about this whole thing.
It is only one question on the coursework and there is no clear evidence, only suspicions. The student had mitigating circumstances for the last few years and just returned to university this semester. I'm afraid that if they didn't cheat, I will make them very stressed.
I am aware that I am "simply following the procedure", and that as a PhD student I feel like I have even less margin of action than a regular teacher. But I can't stop this feeling that I am not doing something correct.
How do you justify possibly wrongly reporting a student for cheating/plagiarising/etc and causing them more stress other than the simple ethic that cheating is not correct?
Alternatively, was it even the correct choice?

"I had to contact the student to inform them, and I now feel very bad about this whole thing." Your brain is wrongly conflating "I made someone feel bad" and "I did something wrong". That's literally all there is to it.

@AdamPřenosil it sounds so simple and easy when you put it like that. Thanks still, it helps a lot reflecting on it

As an academic teacher your responsibility is to teach people and confirm that they have learned what they should have and not "make them feel good". Making people feel good (or, in particular, not feeling bad) seems to be a priority nowadays for a lot of people, which does much more harm than good.
What I would do is to stress to the student that this is "a suspicion", then that "you are formally obliged to raise an investigation" and that "if he did not cheat, then he will not suffer in any way". Ensure (within your power) that the investigation is fair and that's all.

It doesn't matter if you feel bad. What if the student had an arrogant personality that made you not feel so bad? This is why policies exist, so they are fair to all.

@GregoryCurrie well look, I am human. It's easy to say "it could be like this, and it would be different". It's not. And it does matter to me if I feel bad or not

If you trust your university's processes, it doesn't matter if you reported them 'possibly wrongly' -- it will be investigated and decided. On the other hand, you may have taught this student a lesson that will save them from plagiarism or cheating later, with way worse consequences. You are not just teaching the subject.

@SakariCajanus it's not just about investigating and finding they did something or not. It's about the stress it may generates and adds up on a student that had long mitigating circumstances which made them leave uni for a while. Stress is often not logical (just like my guilty response here may not be logical) and I don't want to aggravate their condition. Thanks for highlighting the lesson I'm also showing them, and the "prevention" it is doing

You have been told exactly what to do, namely to follow procedures. This protects academic integrity, the student, and you as the "whistle blower". At most universities, convictions are only obtained with an overabundance of evidence, so that you do not need to be too concerned about your student. The student has ample chances to protest their innocence and will not need an advocate.
I understand that you are feeling bad because you are imagining scenarios where your accusation is false. But that is not quite true. You in fact did not make an accusation, you just noticed something that objectively would be seen as suspicious.
Since you accepting the teaching job, you accepted the responsibilities that go with it. This includes reporting occurrences like that. It is now too late to have second thoughts about these responsibilities.
On a human level, you need to stop taking responsibilities that are not yours. This will take time to learn, but if you do not learn it, you will not be a very effective member of society and of academia.

Thanks for the answer, and the last paragraph. Felt a bit harsh on the first read, but resonate with the experience I have

+1 especially for the last paragraph. It's common in student/youth culture that if you do something wrong, get discovered, and suffer bad consequences, then it's not you who are at fault for those bad consequences, but the one who discovered your misdeeds. But people have to grow out of this way of thinking, or it will make it very difficult to become successful in the next stages of life.

@vsz 'Steelman' take on that mindset: when there is a relatively haphazard link between effort and reward, people become more attuned to questions of moral luck and the illusory nature of certain rules. You can see this in the way that people in the higher echelons of power frequently take risks and break rules: they do so not just because they tautologically have power to begin with, but because they understand that rules are relative to power and that it's anarchy at the top.

Likewise, a student might come to understand how playing the game truly relates to building a successful life and might reject the idea of academic rules for their own sake. In other words, some students might get caught and others not, but it's not a storybook world where applying or failing to apply the moral rules you are given results in reward or punishment. Note that this is distinct from the student reaction of just blaming the world for their sloppiness.

I agree with the vast majority of @ThomasSchwarz answer on a factual level,  but actually,  what a most disagree with is the last paragraph.
Feeling bad is a sign of compassion for your student.  In a world where compassion is often not enough in evidence,  compassion in an educator is a superpower. It might make you do and think about why this student did this.  Are there any changes to the course design you could suggest that might have made it less likely?
In 10 years of teaching I have not stopped feeling bad when I have to flag students for investigation. Particularly if that student has had a hard time.  But i do still flag people - that bad feeling is just part of being an educator.
Instead of trying to avoid this feeling by trying to learn that it's not your responsibility, sit with the feeling and reflect on what it says about you as an educator, and what it would mean if you stopped caring about the fact that a young person going through a hard time will now face the consequences of a bad decision.

I understand what you are saying. I think I am taking away points from both your answers. I think compassion is good, and I know myself enough, it is not going to go away. But I do think on some level what ThomasSchwarz said is right, and I have to draw a line somewhere, so I can act responsibly. But I join you on what you said, which is I have some responsibilities as an educator.

'that bad denning is just post off being an educator' should read 'that bad feeling is just part of being an educator'??

As well, there is nothing to stop you reaching out to the student and saying "the discipline thing is out of my hands now, but hey, if you're going through something that led you to some shortcuts, perhaps you need some extra help? We can spend some time on the stuff you're finding difficult... "

@RichN , yes.  Sorry writing in a phone first thing in the morning,  in a rush while I wait for my porridge to cook, with added dyspraxia is a naff combination.

You could add, (if you agree) that this is a moment where the student may be experiencing powerful emotions also which should clarify for the student how serious academic integrity is. For better or worse, even the appearance of impropriety can have consequences, and now the student should be aware of that. So the student should have learned from this experience and perhaps remembering that can be some comfort to the educators involved.

I think indeed there are two sides on this that each needs to be handled, just like the story of a young ruler who found that his father is found guilty, had to judge him and deliver the guilty verdict, but then take his punishment in his stead as his son (let's assume the law in the story allows for taking other's punishment). The comment by Kate is spot on. We need to both do "you are guilty" and "I'm here for you"

This is a great answer. It is rare to read.on this side that feelings or compassion are real.

In the interests of making you feel less guilty I'm going to point to all the other students in the class who (almost definitely!) did the coursework themselves without any visible potential academic misconduct. On behalf of them, I will say "Thank you" for upholding the value of their work. Some of them will also be facing difficult circumstances. Think about how they'd feel if they knew some people obtained the same qualification as they did not by doing the work but by just copying stuff off the internet. You did the right thing for your part of the procedure and the institution's policies (enacted by people more experienced than you) should be robust enough to take care of the rest.
You probably still feel bad about the possible negative consequences. If it helps, look up your institution's policy (the academic misconduct procedure will be laid out very clearly so that students who are subject to it know exactly what is going to happen). The actual consequences might be a lot less impactful than you're imagining.

For a conscientious instructor, handling academic integrity cases will probably always remain something of a pain point, and rightfully probably should.
Simply getting more experience will give some perspective. I've dealt with a lot of cases at this point, and I'm not so troubled as I was initially.
(For the following, note that the process at my institution is quite different than the OP's or many other institutions. E.g., at my university, the faculty are required to investigate and cycle with the student before filing a report. While there is a formal disciplinary process, the administration is broadly supportive of faculty handling the whole issue themselves to taste, with consent of the student.)

Part of experience reducing tension comes from getting familiar with the process. I've become aware of exactly what will happen, how considerate the Academic Integrity Officer is to everyone, and how broadly unlikely it is for really harsh punishments to be meted out.

Another helpful element is that I've developed my own flowchart/FAQ/template for email interactions at various steps with students in question. When an issue arises, I log it in a spreadsheet, and paste the appropriate email notification. This reduces time spent, and in a case where I might be a bit emotional or uncertain, I get confidence that I've previously thought out my responses and process at a quieter moment, and they've been battle-tested over time.

Also, I've come to see that in my context there's a very limited number of denials I get from students (really just two or three primary ones), and they almost always follow the same pattern of flipping when I present hard evidence. So now I have very little anxiety when I get the standard denials back, knowing the student is almost surely trying to gaslight me, and that's just one step in the usual process.

Obviously, you still want to cover your bases, be responsible, and if in doubt (if the case isn't ironclad), default to just letting it pass.

You inquired if your choice was even correct? I say, it was. You discovered an anomaly, you reported it. As you were expected to when you accepted the responsibility of teaching a small class.
That you have empathy for your student is commendable and shows that you care deeply about what happens to them, That you took time to learn about the plight of your student reinforces, bodes well to your teaching future.
Consider the situation when you did not follow the procedure that was set up for situations like this. Would you have felt anything different when you later discover the student benefited from your 'inaction?'
Correct also signifies there was no error, no mistake. So your reporting of student misconduct was correct action on your part. What may be bugging you that you have doubts that your action was not proper, as in, morally acceptable.

It's okay to have conflicted feelings... even if the student DID cheat
Life can be pretty brutal so it's normal to feel guilt when you are bringing immediate harm to another person's existence, even if they set the events in motion themselves. This is especially the case when it is the result of a machinery of rules or a larger institution which you are beholden to and have no control over.
There is a strong element of moral luck in those situations. Ideally, you'd want to be able to apply rules that make for a better world, but in practice some people get caught and other do not, and the consequences are often disproportionate compared to the harm done to society. That student might have their life upended by their cheating, but the overall harm and justification for that punishment might not actually make sense even if on paper it follows the social and legal rules as they are laid out (cheaters not prospering). You know deep down that although the student brought it upon themselves, it is also the result of your decision to flag them that they will pay the price. There is no escaping your personal responsibility.
However, the system has evolved to take on these situations
Academic dishonesty is a well-oiled process in most institutions, and they are generally risk averse, requiring a high degree of evidence. The student might also continue cheating in various ways later on, so a wakeup call in a 'safe' context can actually be a blessing in disguise.
At the end of the day, systems such as these cannot be solely based on sparing people's feelings, otherwise they become meaningless and ineffective. It also introduces an element of unfairness, as then sensitivity becomes the barometer of the application of consequences: both that of the person who will suffer the punishment and that of the person who is worried about punishing others. Essentially a return of moral luck but where the luck has to do with the personality of the people involved.
Academic integrity is still a big deal since it underpins much of the price the institution can demand for their services, and much of the value of the diploma that results. The best path, moving forward, is to clearly analyze and come to understand the responsibilities you have been given, and to confront the harder decisions before you have to make them in the future. If you had done this moral and emotional prep work, this would perhaps have resulted in less intense feelings because you would not simply have come to rely on the argument of 'just following the rules' to assuage your guilt post-facto.


text:
Inquiry regarding my MSc degree in Mathematical Physics
I did my post graduation (MSc) in the branch Mathematical Physics in India. I have qualified national level Mathematics examination for this. Now I want to pursue my PhD in Mathematics but I am feeling like a dilemma. Although I understand that this is an interdisciplinary branch of Math and Physics but am I eligible to pursue my career in Math or should I have to switch over to Physics. Is there any Mathematical body or Association who can clarify my dilemma regarding my eligibility. Is Mathematical Physics more towards Mathematics or physics?

Note: this question has been asked first on math.stackexchange here

does this question & answer helps you? (it's about physics and maths https://academia.stackexchange.com/questions/110352/what-is-the-eligibility-criteria-for-doing-research-in-physics)

@JackRed Actually I want to ask how can I show that mathematical Physics is indeed a branch of Applied Mathematics. Is there any research article or book to act as  supporting evidence for me?

I would advice to edit your question then, to clarify it and express exactly what you want. You should check out how to ask a good question and what types of questions you shouldn't ask

how can I show that mathematical Physics is indeed a branch of Applied Mathematics --- I would think anyone in applied mathematics (and many in pure mathematics) evaluating your application would have enough background knowledge to judge your background. And, assuming (which seems reasonable to me) that nearly everyone applying to a competitive program is "qualified", for competitive programs the actual issue would be whether you are better (in whatever way is being used to make such a judgement) than x% of the applicants, where x% is the percentage of applicants that can be chosen.

mathematical physics is mathematics.

source: Stack Exchange

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

sort: votes


text:
Referring a paper which is still under publication
My domain is Image Processing and Computer Vision.
I've written a follow-up paper for my previous paper which is still not available in IEEE Xplore. I am submitting the new paper in a conference. I want to ask what is the best approach for making the previous paper available to reviewers?

Upload the previous paper in arXiv
Submit the previous paper as a supplementary material

Please guide me.

Are you sure that you can upload something at arxiv that is pending for publication in IEEE Xplore? You should look into the IEEE terms.

@Alexandros: Yes that is possible. Please see: IEEE's self-archiving policy

I would make a distinction between whether your paper has been presented at a conference and whether it has appeared in IEEE Xplore.
If it has already been presented, then it's out there in the community and, in my opinion, it is entirely reasonable to take advantage of IEEE's self-archiving options and post it on a personal or institutional website where it can be readily found by search engines.  There is no reason to wait for the (sometimes painfully slow) updating of the IEEE Xplore database.
If it has yet to appear, however, then I would recommend instead attaching it as supplementary material, if possible.

As I've mentioned in question, my paper is still not available in Xplore (it was presented in a conference in November 2015). So better to attach as supplementary material (possible)?

@stalin Actually, since you already presented it, I recommend that you simply post your pre-print publicly online following IEEE's self-archiving policy

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
Does it look bad to have a PhD thesis unrelated to the rest of future research?
The short version of my question is: will it be perceived negatively to have a PhD thesis unrelated to the rest of my future research or work?

For more context, I currently hold a bachelor's degree in computer science, and am working in my first full-time job as a software developer. I have a unique opportunity to pursue a PhD as part of my day job, with little change to my economic/living situation. I already planned to do a PhD in computer science in the near future, so this works well for me. The downside is that while the project I would be working on for my thesis is exciting and interesting, it is not what I would have picked for myself or an area I foresee wanting to work in long term.
I am not worried about lacking the motivation to finish the thesis, or the opportunity cost of not starting directly researching the area I am interested in. What I am trying to get a feel for are any unexpected roadblocks I might hit in the future for picking a PhD topic more for convenience than passion.

Will it be perceived negatively to have a PhD thesis unrelated to the rest of my future research or work?

Relative to what?  Having a PhD is generally perceived positively relative to lower levels of education, but it is perceived less positively than a PhD that is more directly in the research field in which you intend to practice.
In your case it sounds like you will be within the general field (computer science) that you want to practice in, but you are considering doing a research project that is not of great interest to you.  The PhD program is generally considered to be a training program for researchers, and the goal is to get you up to a level where you can do independent peer-reviewed research that is up to the standard acceptable for academic publication.  You will probably find that a PhD program in computer science gives you a wide range of high-level skills and abilities in that field, and you will benefit from it even if you end up doing research in other topics in computer science.  Having said that, if your PhD is in your future field of research then you get a little head-start, since you are already more familiar with research in that particular topic area.  This will not be much of a head-start, since you should graduate from a PhD program with the ability to learn a new area quicker than you learned it during your candidature.
In regard to this issue, it is worth noting that it is extremely common for PhD researchers to move around into different research areas as their career progresses, and correspondingly, it is uncommon for experienced researchers to still be doing research on the same project that they did in their PhD candidature.  As you get more experience you will get better and faster at absorbing and understanding material in a new research project, and so the disadvantage of not having researched in a topic before diminishes.  Once you are adept at research, you will find that there is not a huge difference in difficulty in researching in the topic of your PhD candidature, versus researching a new project.

...it is not what I would have picked for myself or an area I foresee wanting to work in long term.
  ...
  I am not worried about lacking the motivation to finish the thesis, or the opportunity cost of not starting directly researching the area I am interested in.

Now for some unsolicited advice - You say that you are not worried about lacking the motivation to finish the thesis.  You should be worried.  It is a bad idea to take on a PhD candidature unless you are confident that the topic will be able to command your interest and passions for a period of several years in your candidature (usually 3-4 years full-time).  If you are already viewing the topic in this way before you even start, it is highly likely that you will lose motivation and struggle with maintaining interest in the topic well before the end of the candidature.  This will make your candidature a major burden on you, and it is likely to lead to failure.

I'll note that many academics change fields after earning the doctorate. Switching between Math and Computer Science (either way) is quite common. Likewise, Philosophy gives you an opening to several somewhat related fields. Once you establish a publication record you are known for that, not for your dissertation.

@Ben - Relative to sticking near the area I start in, becoming some well-regarded expert, and retiring after a long career of fascinating contributions to the field I suppose. What I'm hoping to achieve is similar to what you outlined in your second paragraph - do my "apprenticeship in academia", learn the ropes of research, and have the title for some credibility about what the quality of my research work should be. This opportunity (I hope) will let me do that on an interesting project with less of the "starving artist"-esque hussle I've seen others have to go through. (1/2)

However, from the little experience I've had researching/publishing I've been occasionally surprised by connotations attached to decisions people make in their career or practices individuals/labs can have that are faux pas, that I wouldn't have picked up on without being told.
So this question is me dipping my toe into the waters to see if making this decision could mark me in some way in the future that would be hard to work around. From your third/fourth paragraphs it sounds like that wouldn't be the case, which is a relief. (2/2)

To your advice - perhaps a more honest wording would have been "for this question I'm not worried about...". It's definitely a concern of mine, and something I'm taking into serious consideration as we work out what this opportunity would like in practice. I had just read a lot of answers regarding motivation in other questions and was looking for something different here.

@Guest: Ah, I see.  So you were merely limiting the scope of the question!  In any case, good luck with whatever you choose to do!

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


text:
What do I do about a professor that demands I publish a nonsense proof?
tl;dr: Skip the first two paragraphs.
I'm a student working in theoretical computer science. I recently did some research where I came up with most of the ideas, but would regularly receive feedback from a professor. (I am not receiving money from said professor.) After I was finished, the professor suddenly decided to get heavily involved in the project, rewriting the entire paper (aside from pseudocode). This was offensive, but no deal breaker as he was not trying to claim first-authorship and some of his contributions (e.g. background research) were a huge improvement. Then I read his proof. It was incredibly non-rigorous and, after spending 10-20 hours parsing it, I realized that it was totally invalid and that he definitely does not know if the algorithm is correct or not.
Also, there was a glaring error in the first draft of my proof that was repeated in his rewritten version. This is the second time that I have caught an error in a proof that I have written and both he and the 3rd author has checked and told me is correct. This is totally my fault but, at this point, I have lost faith in my ability to rigorously prove something of this complexity with total certainty, and lost confidence in the two professors involved to check it. I would not be confident our work is correct without writing up a rigorous proof and getting the opinion of a mathematician.
When I told the professor that his proof was way off, he was furious and refused to be a second author on the paper unless he is the sole writer. Is this reasonable? He wants to publish work that I'm not sure is correct, and has a proof that I consider embarrassing because 1) if someone skims it, it's obvious that it's not rigorous, and 2) if somebody does take the time to fully understand it, he is exposing that he does not know if the algorithm is correct or not.
One comment I have received is that I should do whatever he says and that, as a student, I don't bear responsibility for the paper's correctness. Another is that if it is wrong, the responsibility is on the review process to catch it. However, I suspect that the conference we're submitting to will not rigorously check the proof and the argument in the proof does sound intelligent and plausible at first glance.
Is it true that I do not bear significant responsibility for the correctness of my work?
What should I do?
Also, the other professor involved (third author) suggested I just ask him if I can publish as a single author. He made it sound like no big deal, but I got the sense that this is a very bad way to go; after all, the second author spent many hours advising me on this project, did most of the background research and wrote the introduction and much of the less technical parts of the paper.
Some context (put in spoilers in case you want to think about this post with less bias first):

 I am an undergraduate senior working with a professor at a lesser-known US research university. I have secured my own funding for a PhD and I have objective evidence that I am one of the top students at my present university. I have reviewed one paper for a conference; however, I have no prior research experience and this professor has many years of experience as a researcher and a reviewer.

 I am applying to top Master's programs (and have been accepted to some), with a view to probably going on to PhD. This professor wrote me letters of recommendation. He also controls the grade for this research. So I did not take defying him lightly.

All comments, no matter how frank, are appreciated.

When I told the professor that his proof was way off, he was furious and refused to be a second author on the paper unless he is the sole editor. How does this work? Are you submitting to a conference/journal in which he is the editor? Why would he be negotiating with you then instead of other members of the editorial board?

If you are unsure about the correctness of the proof or how to fix it, maybe you could ask about it in the appropriate math/cs stackexchange.

"I would not be confident our work is correct without writing up a rigorous proof and getting the opinion of a mathematician." This is what you should do. It might not even be necessary to get a mathematician's opinion. When you write up the rigorous proof, or when you share it with the professor, everything might become clear and you might both agree about what is correct.

Just a side comment on "if it is wrong, the responsibility is on the review process to catch it". Don't ever rely on peer review to fix your own sloppiness. Peer review is rather the final line of defence, not the main guarantee of a paper's correctness. You as the author should be convinced the paper is good before submitting it to peer review; reviewers have orders of magnitude less time than authors to look for flaws so they're pretty much guaranteed to miss most errors.

"Is it true that I do not bear significant responsibility for the correctness of my work?" No.
"What should I do?" Start to act like you bear significant responsibility for the correctness of your work, the rest will follow.

The professor is wrong on both counts. You are right to be skeptical whether the review process will catch any mistakes. If he missed actual mistakes (not just typos or slightly misstated equations and such) in your proof which he claimed to check for correctness, then you are right to be skeptical of his claim that the proof is correct. If this is a possible scenario for you, I'd consider stalling until you no longer need his letter of recommendation / grade. At the end of the day it seems like you are entitled to submit the paper as a solo author, though perhaps omitting his contributions.

@Allure No. He wants to have total editorial control prior to submission to the journal. The journal will then accept/reject with comments on any requested changes.

@EarlGrey So if the professor agrees to correct the one remaining error, but demands we proceed with his non-rigorous proof that I am not sure is correct, what do you advise I do? Tell this professor with decades of experience that I do not trust his opinion that our paper is correct and refuse to publish?

@Fricis I honestly don't have an opinion. Please remember libraries are full of weak papers with questionable proofs.
How much time do you need to significantly improve the proof? do you have so much time?
In general, I suggest you to focus on your own, you can always prepare a correct proof in the future and then publish alone a correction to this paper.,
Maybe go ahead with publication, and pray for a peer review rejection? nonetheless, professor experience is not relev, if the resulting paper is bad it will be simply forgotten, if it is interesting it will be cited despite its flaws.

We don't have enough information (nor can you provide it) to know whether the algorithm is correct or not or, if correct, whether the proof of correctness is correct.
Wrong proofs and faulty algorithms occur naturally when exploring new areas. Some have been published - but not by honest people who knew at the time that was the case.
You should not be an author of a paper that you know is wrong.
You should not be an author of a paper containing a result that you suspect is wrong unless   the result is potentially interesting even if it is wrong. Then it might be OK to publish it with sufficient expressions of doubt.
This rather blunt answer does not address the personal issues between you and the other contributors, nor the possible effects on your future academic career.

The statement could be formulated a conjecture, with the proof idea suggested, rather than asserting a formal proof. This is a bit wobbly, but at least it is not claiming rigorous correctness, and might still be a valuable publication if the method is promising.

"You should not be an author of a paper containing a result that you suspect is wrong unless the result is potentially interesting even if it is wrong." That's a bit of strange advice. One does not just write down a proof and add a caveat that the proof might be wrong.

@CaptainEmacs Thank you. In this case, the result would not be interesting enough for publication unless it is proven.

+1 thank you. I see one definite error, but after that is corrected, I only have generalized uncertainty, and I do not believe the professor's proof is rigorous. If there is another error in our work, the current proof would not be rigorous enough to reveal that.

Academic papers have a long life. If you go on to get a PhD and want to have an academic career, the last thing you want is a paper on your publication list that you are not only embarrassed about, but actually know is flat-out wrong. This will literally haunt you forever. Even if the error is not detected for a while, you will see this paper every time you look at your publication list (and you will be looking at it a lot, every time you update it, or convert it from LaTeX/PDF to HTML, or reformat it for a grant application, etc). You will think about it every time you mention how many publications you have when preparing a cover letter or updating your CV. And you will live with the knowledge that you knowingly published something incorrect. It will be a most unpleasant feeling, which will be made worse if you actually achieve a good level of success publishing correct and even good research. You will probably feel like a fraud, and come back to this site in a few years' time with a post saying you cannot live with this error from your past and asking what you can do to fix it. (I have seen such posts here, maybe you can find them if you spend some time playing with the site's search feature.)
Of course, there is always the possibility that the error is detected. So you'll need to worry about the paper some day being retracted, possibly after other authors have published papers that make use of your incorrect result. It will be a mess to deal with, and will hurt your reputation. Even if the risk of that actually happening is low and in the most likely scenario the fallout may end up being minimal, just having to worry about it happening over an indefinite amount of time sounds extremely unpleasant.
I am very sorry about the unfortunate set of circumstances that make you feel it's difficult or impossible to resist this lunacy. It's a tough situation for sure, since all the practical, short-term incentives are pushing you to do something that in the long term will be very damaging to you mentally and possibly to your reputation. But the bottom line is, publishing a nonsense proof is a Really Bad Idea.

What should I do?

No one can tell you that, you must decide for yourself. But do think about the bigger picture and the things I mentioned above. Good luck!

I think there are many good points in the other answers and comments that I will not repeat here; instead, I want to highlight one aspect of something you can do that I think has not been fully explored in the other answers, which is to improve how you identify and communicate your concerns about the proof.
In particular, if the proof is truly objectively and overtly wrong, then you should be able to provide a concrete counterexample to aspects of the argument in the proof that are invalid. Such counterexamples should make it unassailably obvious to your professor and coauthors that the proof is invalid. Note that I am not suggesting you should find a counterexample to your overall conjecture; rather, just to the individual logical inferences in the proof's internals that are suspect. Moreover, the simpler and more direct of such a counterexample you can Construct targeting more specific internal steps of the proof's arguments, the better, in terms of it's ability to communicate the errors you observe with the proof.
What if you can't find such counterexamples, or otherwise can't construct a "formal proof" for the proof's incorrectness? Then, frankly, you don't actually know that the proof is wrong. It is possible that you are just unsure of the proof's correctness (which is very different from being sure that the proof is wrong). While you absolutely are responsible for the validity of work that you are an author on, as others have said, it is acceptable to rely on other, more knowledgeable authors for aspects of the work that you are less certain of. E.g., if you don't fully understand aspects of the proof, but the professor asserts that it is correct, it is still reasonable to remain an author od that paper and submit it.
The underlying message of my answer here is that I suspect some of the difficulties you're experiencing here (especially those difficulties that you can control) boil down to how you have communicated your concerns to your professor. When pointing out things that others have done wrong, you want to appear as humble as possible and make it as clear and concise as possible what said others have done wrong, that way the easiest and (in some ways) only option for the person you're talking to do is to acknowledge and respond to the objective errors (and to feel safe from judgment in doing so). It doesn't sound to me like you you did this from your description. E.g., "when I told the professor that their proof was way off" seems like a very different way of communicating your concerns.
Another strategy you can take is one of asking questions -- e.g., rather than saying "your proof is wrong because step 3 is invalid with this counterexample" which carries with it undertones of judgment and can lead to conflict, you can say "This proof is really interesting! Can you help me understand step 3? I'm not following the logic here--how does this work given that in counterexample it seems like it would behave differently?" which is much more conciliatory and invites your professor to identify their own error and use it as a teaching moment which can enhance their own status and standing.

"Then, frankly, you don't actually know that the proof is wrong. It is possible that you are just unsure of the proof's correctness (which is very different from being sure that the proof is wrong)." But the OP never said they were sure the proof is wrong. What they said is that the proof is not written at a sufficient level of clarity/rigor to be able to tell whether it works. This is a major problem regardless of whether or not there exist counter-examples to any of the steps in the proof.

What will most likely to happen? You will lose your faith in the academia. Your paper will be published, a chance that reviewers catching the error is low. In a typical TCS venue, reviewers need to review a dozen of papers within a month. If your professors couldn't catch the nonsense, it is quite likely that these reviewers couldn't catch that too. After publication, almost no one will notice that error unless your paper got famous or written by famous people.
I've seen quite a number of nonsenses in TCS, theoretical ML papers but never raised a question, simply because there are so many and no one cares about them.
This field (math-heavy-CS) is broken by design. Conferences are not the right way to publish technically delicate works. Heavily mathematical works typically require at least an year to review rigorously. Frankly, everyone in this field knows that but they choose not to fix it because you can publish more papers per year in this conference system.
If you want a rigorous review process, I guess math journals are better place to put your work in. Or become a real mathematician not a theoretical -ist.

tl;dr

Is it true that I do not bear significant responsibility for the
correctness of my work?

No, it is not true.

What should I do?

Start to act like you bear significant responsibility for the correctness of your work, the rest will follow.
(it may even be that you give up on doing stuff because you realize you cannot take responsiblity of the possible outcome...)

We see only your side of the story. And there are some unclear things in the description and temporal order of the "facts" you present.
As a frame change, I suggest you to read the situation this way:
First, the "good" aspect: you working for them without them paying you ... they sensed you could do good stuff, otherwise it's just a burden! A professor may or may not have money to support research, but they have a fixed amount of time. A professor get money to do research but the funds they get goes to both them and their hired researchers. Professors always get a slice of their students money, directly or indirectly (at the very minimum they can put in their CV they supervised a grant winner). In your case, they used their time with you without paying you, it means they did not get any slice of the money cake, and they solely invested their time on you, expecting to have some return on their investment.
Unfortunately for them, you provided research that looked good but it had flawed proofs. It happens, you are only a student, their bad, they could not figure out your proof was wrong (and consequently they cannot produce a correct proof).
Now let's start with the "bad" aspects:

This is the second time that I have caught an error in a proof that I
have written and both he and the 3rd author has checked and told me is
correct.

So you prepared two times a written manuscript and you submitted it to your co-authors, only to tell them afterwards "sorry, the proof is wrong".
I will be frank, sorry being abrasive: you are a PhD student, you think you are one of the best in your cohort, but you are still learning and you still do sh%t as every other human. One thing you have to learn during your PhD is that you carry responsibility for your errors. Your co-authors are not simply (and not only) reviewing your work. And the co-authors are peers. If you prepared the proof and the proof is wrong, the fault lies on your shoulders because you published some wrong stuff, your peers may or may not find it out, if the proof is wrong you carry down them with you.
If the only reason for them to be in the paper is because they are only reviewing your work ... well, then they are reviewers, not co-authors.
Should they have spot your error? yes, but not at the paper writing stage: did you not present them the proof in advance? did you thoroughly check your proof before writing it?
Be glad for their contributions, not for missing your errors.
Should you tell your co-authors their proof is wrong? absolutely. How should you tell them this? this is a matter of interpersonal relations. If a peer of mine does something wrong, does tell me about it at a late stage and then I have to rush to put a patch on it, and afterwards said peer tells me "you are way off" I would be at the minimum disappointed, thinking "well, then you provide me a decent and correct proof firsthand, if you are so smart".
To say in the most neutral terms possible, at this point you put yourself in a narrow corner: there is an issue with the paper, you pointed out strongly there is an issue but you did not provide a solution. Note for the future: if you have a strong opinion about an issue, you should have also a quick solution to the issue.
It's very easy to say "this is crap", it is very hard to replace crap with "something meaningful". As you showed with your first iterations of the proofs, it is even easier to produce crap, just with different flavours.
Your professor is probably not strong on the theoretical proof side, they may even have started working with you because that was your potential strong point in your CV/profile (we do not know), so they are let down a bit by your inability to come up with a correct proof (I mean, if you were writing a paper with them it means they had full trust in you).
Afterwards, with the pressure of publish-or-perish or whatever time constrain/availability they had, your professor put together some kind of proof to make up for your wrong proof.
To conclude:

I have lost faith in my ability to rigorously prove something of this
complexity with total certainty, and lost confidence in the two
professors involved to check it.

Science is not about providing answers, science is about building the path to provide the answers. Build the correct path and you may (may) get the correct answers.
Having doubts about oneself ability to tackle complex issue is the best spark you can have to actually find a way to tackle the complex issues.

I think you missed reading the spoiler. The OP is an undergraduate, not a PhD student. And if they asked their co-authors to read and correct the proof and neither of them found the error, this doesn't speak very highly for their capabilities. Of course we, at all career stages, are responsible for our own errors, but if an undergrad asks two profs to check their proof, and the profs fail to find an error the undergrad later finds themselves, that is to the undergrad's credit and reflects very badly on the professors.

@terdon undergrad got PhD fundings, so I consider them a PhD student. And OP should think of himself the same way, without indulging in additional "ladders"
It's "easy" to wok with world champion, let them do all the job. To work with normal people is less easy. To pick your collaborator it is even harder but one has to take the blame for one's own choices. If OP undertook a too ambitious goal for their capabilities (publishing papers with normal/incompetent supervisors) ... it is to OP to critically reflect on themselves, it is unhelpful to think what reflects good/bad to them/others.

"I am an undergraduate senior working with a professor at a lesser-known US research university. I have secured my own funding for a PhD [...] I have no prior research experience [...] I am applying to top Master's programs (and have been accepted to some), with a view to probably going on to PhD." (emphasis mine).

@terdon "I have secured my own funding for a PhD"  is enough to me to consider OP a PhD, i.e. a person that want to learn how to do research and to perform it. The other things are just bureaucratic wordings and byzantine overstrucutres that preclude access to pursuing a PhD via nonsense examination and selection procedures to "filter" the "best" candidates...

OK. This makes no sense to me, you are categorizing an undergraduate who hasn't even graduated from their first degree yet, one who has simply "secured" funding (apparently; this seems odd and is contradicted by the other statements, so I think it might just be a "sure kid, I can fund you, talk to me when you graduate"), who then says they are probably going to continue on to PhD, presumably after the Masters to which they are currently applying, as a "PhD student".

@terdon you are just stuck with bureaucracy and all that crap. Regarding " this seems odd and is contradicted by the other statements,": I wrote in the opening of my answer "there are some unclear things in the description and temporal order of the "facts" you present".
If you need to interpret OP's question, do it in the comments to the question. I take the "secured funding" at its face value, i.e. "I have funds to pursue a PhD". Whatever the origin of these funds, either a highly competitive grant or the profit from selling lemonades, I do not care.

I agree with @terdon in that it does not make sense to me to describe this person as a PhD student. However, I also agree with some of what EarlGrey is saying in  that even an undergraduate researcher has responsibility for their own work if they'd like to be considered seriously, and clearly that is OP's intent: they want to publish this work, they see themselves as a top student, they feel in some cases that they know better than people senior to them. So, if OP wants that, they need to be prepared for the responsibility that comes with it and understand what the expectations are.

@terdon Apologies for being vague, but I am deliberately avoiding any chance of doxxing myself or the professors involved. The comment about funding was to emphasize that, if I chose to accept my offer to a PhD program, I am not reliant on a professor or university to provide me funding, so perhaps that gives me a degree more independence.

+1, I asked for it frank. As for my responsibility for the errors, I do take responsibility for my mistakes. My point was that if my second author is demanding complete control over what we submit and asking that we submit a proof that I believe is not rigorous, he needs to take responsibility for future mistakes, but I don't trust him to ensure the proof is correct.

@BryanKrause Is this to say that I should push back against the professor and demand we do a more rigorous proof?

@Fricis I live in a world of empirical study rather than proofs, so I can't really advise on the exact details. I do know that I wouldn't want my name on something that I don't feel comfortable with; I can't tell you whether your discomfort in this case is warranted or not.

@BryanKrause Thank you for the quick response! The alternative viewpoint I've heard is that when you are starting out and have no reputation, your discomfort level is significantly less important than later in your career, and that people will tend to be very understanding that if a professor is on the paper, that they bear much more responsibility for the correctness. This viewpoint seems to correlate with my professor's anger if it is really his reputation on the line, not mine. Does that change your view? Would you be inclined to give the professor the extreme benefit of the doubt?

@Fricis It's clear that many people get ahead in academia by various levels of fraud and misrepresentation. In general, I think they pay too little a cost for those misdeeds. So, strategically, should you join them? I can only tell you what I would do, not what you should. At the same time, I don't really know the full situation here; I've heard your telling of it. Maybe it's not actually as bad as it seems, maybe you're misunderstanding something. I don't and can't know.

@Fricis There are (at least) 2 responsibilities: he takes responsiblity of publishing a paper with a weak proof ... and you take your responsibility of asking them to take you out from the paper and authors list. They will stll use psrt of your work, at this point is probably impossible to remove all you did and all your contributions, but at least formally you will be in peace  with yourself and you will not be associated with this paper


text:
What's the best way of starting a private lab wiki site?
My labmates and I were thinking of creating a wiki site for sharing protocols, links to github repos, some metadata and other useful lab related material. Contentwise mostly text, maybe some images, but nothing too heavy in terms of storage. We want to keep it private though since there'd be a lot of confidential information. Can you recommend sites that are most ideal for this purpose?
Edit: free services would be preferred.

As you are already on github, did you look at their option to create a linked wiki page? See https://help.github.com/en/github/building-a-strong-community/about-wikis.

Appreciate the suggestion! I'm not familiar with any of the advanced features of github but I'm looking at it now. Will have to do some reading to see what it's capable of.

Have you checked whether your university offers such a service? There must be dozens of groups there who would benefit from the exact same thing.

Find appropriate university/department/group server. Pick any one of the free wiki platforms. Install and enjoy.

We decided on github's wiki feature. It requires a pro membership but that's for free thanks to our student status. It seems to accomodate all our needs for now. Thank you all for your suggestions.

It's not clear what level of "confidential" you're talking. You're unlikely to find a free site that is sufficiently private for storing, e.g., personal information about people.

No such level of confidentiality. Just a bunch of protocols and scripts we don't want other people have access to before we publish them.


text:
Publishing with APS open access with a CC-BY license on a preprint server
This is a follow-up on these two questions:
When can I safely use CC-BY license on arXiv? and
What arXiv CC licenses are compatible with American Physical Society publishing?
From the answers to these questions, it seems that it is not possible to publis an article that is already on a preprint server (in particular arXiv.org) with a CC license in the American Physical Society (APS).
However, in Physical Review Letters (PRL), it is possible to publish open access (by paying a higher fee), and in that case APS use the CC-BY license. This license is also available for posting on arXiv.org.
My question therefore is: If an article has been posted on a preprint server using the CC-BY license, will APS accept it for publication in PRL, either using their normal "Transfer of Copyright" (I guess not), or open-access? It looks to me as if it should work for open access, because the license under which APS would publish the article is exactly the same under which the article was posted on the arxiv.

I got a reply from APS on this issue. My question was:

We accidentally chose the CC-BY 4.0 license https://creativecommons.org/licenses/by/4.0/ for our arXiv preprint of a manuscript submitted for publication in Physical Review Letters instead of the standard arXiv license.
Does this license conflict with the standard Transfer of Copyright
  agreement? If so, is it possible to instead choose the option "Retain
  copyright and complete the Creative Commons publication agreement"?
As far as I understand, the second option should work, since APS would
  publish under the same CC-BY 4.0 license as we used for the arXiv
  submission. Is this correct?

APS answered:

Choosing a CC-BY-4.0 license for your arXiv submission does
  not conflict with choosing the standard Transfer of Copyright
  Agreement for submission to an APS Journal.

So in short, you can use a CC-BY-4.0 license for your arXiv preprint and still publish the manuscript in PRL under the usual conditions (i.e., not open-access).

I haven't seen a definitive answer from APS, so it'd be useful to confirm with the editors directly. However, based on the agreement below there's no reason to think they would reject open access papers for that reason. They could, in principle, have some internal policy to that effect, but APS is generally quite permissive when it comes to preprints so I wouldn't expect them to. (Given that CC-BY even allows commercial redistribution after publication, it also doesn't make much sense to ban preprints just because they were posted before publication.)
When publishing under open access there's no need to transfer any copyrights. Instead, APS uses a shorter publication agreement that, in its entirety, reads

Subject to the acceptance of the [above-listed] Article for publication in a journal of the American Physical Society (APS), the Rights Holder(s), where applicable, or the Author(s) hereby agrees:

To grant APS permission to publish the unpublished and original Article, the abstract forming part thereof, all associated supplemental material, and subsequent, if necessary, errata in a journal of APS under the Creative Commons Attribution 4.0 International license (CC BY 4.0), http://creativecommons.org/licenses/by/4.0/.
That further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
That any subsequent Reply to a Comment accepted for publication in a journal of APS, for which this work is the target of the Comment, should also be published under the same Creative Commons license as this work.

By signing this Agreement, the Rights Holder(s), where applicable, or the Author(s) jointly and severally represent and warrant that the Article is original with the author(s) and does not infringe any copyright or violate any other right of any third parties. The signing person(s) also represents and warrants that they have the full power to enter into this Agreement and to make the grants contained herein.

Note that, unlike their usual copyright transfer agreement, there's no mention of preprints or copies on your website. However, since all you give them is the permission to publish the article (not the copyright to it), as far as I can tell posting the preprint under CC-BY should be fine.
For future papers it could also be worth using the standard arXiv license until you know where the paper will be published, and under what terms. The license can always be changed when the arXiv posting is updated.


text:
Feasibility of a Makeup Exam
I'm currently a TA for a first-year math course (at a US university), and one of my students wasn't feeling well on the day of the midterm exam for this course. They emailed the instructor their concerns but did not hear back until about 3:30 p.m., while the exam was scheduled for 3:00 p.m. As a result, they took the original midterm exam (just in case they were not approved for a makeup exam later, as they did not have documentation to prove that they were not feeling well - unfortunately, the health services center ran out of appointments that day.)
To the best of my understanding, they would have been approved for a makeup exam if they did not take the original exam at all - but now the course instructor refuses to let them sign up for a makeup. I have not had direct communication with the instructor about this issue, but I'd like to advocate for my student for the following reasons:

They are a hardworking and consistent student, and I believe their problem is genuine - i.e., they could not give their best performance on the midterm due to underlying health problems. I imagine a makeup exam will help them improve their score.

Had the instructor gotten back to them before the exam, we would not be in this ugly situation. Maybe the instructor is partly at fault here? However, as a TA, I can only do so much, as the final decision-making power obviously rests with the instructor.

Today, the student approached me, explained their concerns, and expressed interest in taking the makeup exam. I have to communicate the situation to the course instructor effectively, and I'd like some help doing so. Likely, I am unaware of any potential reasons behind their decision that the student cannot sit for the makeup exam if they have taken the original.
Thanks for your advice and suggestions on how to approach this situation!

First, this is not your fight. You are just a conduit of a student complaint. Feel free to share your assessment of the student with the instructor, but do not act as an advocate, as it might make working with the primary instructor more difficult. Unless asked, do not even express an opinion.
Second, US instructors in Mathematics in the US certainly see their part of student manipulations. They are also under pressure to decide cases based on data only, not gut feelings. They are also not obliged to check their emails very frequently. A student who takes the midterm while advising that they are feeling unwell in effect asks for an automatic second chance. If the grade is fine, they stick with it, if not, they get another try at the make-up. This seems an unfair advantage, even though it is negligible if the student was truly sick. But the student was not sick enough to not take the exam. As I hinted before, if you are teaching math in the US, you quickly stop trusting student explanations because of just a bit of too many manipulative students.
Third, the student can also be directed to talk to the chair. This allows the instructor to follow a simple, strict policy while making exceptions on the suggestion of the chair person (or dean of studies, ...)


text:
My post-doc is ending and I am applying to faculty positions. In the mean time, does being unemployed look better than taking an industry job?
I am doing my first postdoc in pure mathematics, which will come to an end in four months.  I have been applying for numerous positions, of course, but to no avail.  It is about time (has been some time?) that I considered a contingency plan.
Now a rule of thumb is, I hear, that once you get an industry job, you do not simply get back into academia. Even outside of the US (which I am).
I am interested in applying for jobs in the next application cycle in case I am not offered any job this time.  Given the rule of thumb, would I be more likely to be offered an academic position if I stayed unemployed (except for odd jobs, if need be) after the termination of the current contract than I would if I got a full-time job in industry?

Taking a "gap year" is only useful if you had a reasonable expectation that the outcome of your job applications would be different next year than this year. How are you going to make sure that that is the case?

This discussion about Einstein and other topics has been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on [meta], or in [chat]. Comments continuing discussion may be removed.

What about a part-time job in industry leaving time to writing papers or doing research?

once you get an industry job, you do not simply get back into academia

I think you're missing the causal structure of this concept. The issue is not that having an industry job is somehow disqualifying for academic ones, but rather that it's extremely difficult to produce the work that is valued in academia (in particular, publishing research) while not employed in academia.
Can you improve the pace at which you publish in academia while being unemployed relative to when you were a post doc, enough to get another job in academia? Maybe you think you can, but I think it's very low probability. There's also the practical issue that being unemployed means you don't have a paycheck to pay for the things you need.

It's also worth considering the other possible causal structure.  No post-doc role in academia will pay more than a small fraction of what you can earn by taking those skills into industry and being able to apply them.  The biggest disqualifying factor is developing a lifestyle which academia could never support.  (And that "lifestyle" merely needs to include one of a car, house, partner or child to potentially be beyond an academic salary.)

@Graham: "No post-doc role in academia will pay more than a small fraction of [...]": I hear similar claims quite often, but would seriously advise some caution here. After a first postdoc I worked in automotive industry for one and a half years and then came back to academia for another postdoc. The postdoc salary was indeed lower than what I was paid in the industry, but it was much more than "a small fraction". The postdoc position also happened to be in a much cheaper city, so the difference in lifestyle was essentially zero.

Depending on the local there might be unemployment benefits available which will enable the OP to keep working without a significant hit to his lifestyle. (He says he is outside the US so that makes it more likely). I know people who have worked on research on unemployment benefits for a year. (This might come with some annoying obligations of applying for jobs you are never going to get anyway. Or even worse being required to apply for jobs you might actually get and don't want.)

It is not a matter of you not being offered jobs after going to industry. It is more that people who went to industry don't want to go back to academia. So, don't worry. Take a job if you get an offer and see what the appeal is. That is better than being unemployed.

+1 for “It is more that people who went to industry don't want to go back to academia.”

People who go into industry generally find they like earning money more than the pittance you get in acadaemia

@ScottishTapWater: There is also the fact that, at least in some industries, you can "publish" things without going through the rigmarole of external, third-party peer review, and other people in industry will take your "publications" seriously even if academics don't. Google in particular has been doing this for years.

Yes, isn't it sad that the typically better good-work life balance in industry in combination with better pay (in some fields) and not having to do so much committee work can be so addictive that many PhD holders can't find the willpower to go back to academia?

@DCTLib There are problems in academia and (different) problems in industry. Why should all PhD holders value these the same way? Let each do what is best for them, without attaching a value judgement like lack of willpower to such choices. Academia is not the only or best way to do some good.

@DCTLib - I'm in industry now whilst doing my PhD part-time... I love acadaemia and I love research but I have no plans on even applying for a postdoc position

@MaartenBuis Hmm, I thought that the "lack of willpower" being meant ironically was obvious when starting the comment with "isn't it sad" and only listing drawbacks of academic jobs before. Looks like I was mistaken here.

I don't think this is accurate. In many fields (and I think pure maths is one of them) you have to keep publishing to keep having a shot at a position in academia. If you work for a year in industry without any scientific publications you will have a very hard time finding any position. It is not the most healthy thing to do but I know someone who kept doing research and publishing while on unemployment benefits who found a job in the next cycle (post-doc in this case). Going to industry might very well be the better option but the answer should at least include its downsides.

I wonder whether you have really considered all of your options. If your job search has been focused too narrowly it is harder to get any position. If you are willing to teach, primarily, rather than do research there are many more options (in the US, at least). Nearly every US college needs math faculty since even non-math majors take some math courses. And many, while small, still have active faculty.
So, broaden your job search if you think it is a bit narrow.
But if you do leave the academic market for a while it is harder to get back for (at least) two reasons. In industry you make much more money than academics and it can be hard to give that up once you get used to it and raise your cost of living. The other reason is that it is difficult, in most industry positions, even research, to do things that are relevant to academia. Much industry research is product focused, not knowledge based.
One option, if you can afford to do it is to take on some academically relevant project to fill a gap year. Writing a book is a possibility for many. It could be a textbook or something more focused on your research area. Among other things, it gives a reason for a gap.
And, keeping contact with potential collaborators is also possible.

What is the benefit of having a teaching job instead of an industry job?  Both leave little time for research.  (Unfortunately, for the reasons I sketched in my comments above, and lack of recent teaching experience, I don't know if the former is feasible.)

Few recent doctorates have much teaching experience, actually.

@Buffy I'm not sure if "few recent doctorates have much teaching experience" can really be applied across the board. I know many, from those at Stanford to those at state schools in the U.S., who are required to devise syllabi and teaching prior to graduating with the PhD.

I didn't do a Math PhD, so I don't know if they were taking Math Teaching modules or not. I can speak from my experience as someone who taught undergraduate (and some graduate students) all but three semesters during my PhD, along with everyone else in my cohort at an R1. : )

I was in exactly your position nine months ago (applied math rather than pure math). I was geographically limited by where I looked for faculty positions, and while I got interviews, they never led to offers.
As mathematicians we have an advantage compared to other sciences: our research is often not limited by a lack of funding. Not sure what side of pure math you do, but my guess is that to get work done all you need is pencil, paper and laptop. Get yourself a day job, and treat math as a hobby. Work on hard problems that you were too afraid to work on before, perhaps for lack of progress or a perception that "this problem is for people with job security". Publish as unaffiliated or, if you don't want to list your home address as your institution, incorporate and register a non-profit research centre that only exists on paper (I'm looking to do this right now, if only because it's an adventure in its own right). Or, as others have suggested here, try to get a job where publication is expected.
If a professor position is your dream, that's fine. But don't let the dream tie you down. You might find, like I did, that there are plenty of interesting careers outside of academia, many of which pay more (either initially, or have a longer runway of earnings potential), allow great work-life balance and provide superior benefits. And besides, there's no rule saying that you can't go back later. Industry experience is valuable, and depending on the industry you enter and the role you get, you might find that what you do is transferable if you decide to throw your hat in the ring for a tenure track job along the line.

In addition to the answers already given, I would like to point out that there is at least one other option.
If you can afford to be unemployed for a year, you might be able to obtain some sort of "affiliate" status with your current university that can allow you to effectively have an additional year of unpaid postdoc in your current position.
This isn't a very good solution (and a terrible precedent), so you definitely shouldn't do it for more than one year. It's worth considering, however, within the space of possibilities.

@Trunk Agreed. And yet, for some people, that may still be better than the other alternatives.

@Trunk—I believe the issue, as other commenters have described, is that a full-time government or college teaching job will typically leave no time for research that academic hiring committees will value, making it impossible to improve one's application prospects for the next cycle.

@Trunk—My impression is that many teaching-track positions come with few or no research expectations, and accordingly demand full- or nearly full-time teaching. I've never had a teaching-track position at a university, though, so I can't speak from experience.

@Trunk In the US, those positions are things like "adjunct professor", which are non-tenure-track and often very poorly paid relative to the amount of work required of them.

Working in a company provides you with useful experience, not just in terms of CV, but of personal growth too. You get to see problems and situations from a different perspective. If you want to learn about leadership and effective management, a company job may help you a lot and turn out to be useful even if you decide to go back to academia. Moreover ...
@Buffy "The other reason is that it is difficult, in most industry positions, even research, to do things that are relevant to academia. Much industry research is product focused, not knowledge based." Yes, but that depends on the irrelevance of a lot of academmic research. Experiencing how mathematics or physics or whatever are actually used in practice gives sense for which problems and techniques are actually relevant, as well as providing insight into their deep motivation, beyond the formalism. Often deep, new results emerge from concrete problems , rather than from academic ruminations.


text:
How to approach research advisor after failing first semester of master's program?
So, I started grad school during the Sep 2020 session in lockdown. Within a month or two, I was struggling to reach deadlines for assignments of all the courses. I found the online mode of classes very tedious and just could not perform to my best. The monotonous lifestyle and the pressure of graduate work became too much for me. In the end, I was feeling so demoralized and anxious that basically, I didn't attend the last month of classes. So I got an 'F' in 3 of the 5 courses as I missed the assignments, presentations, exams, etc.
Now I have to face my research advisor about everything that happened. I don't know how to approach him regarding this. I know it reflects poorly on my performance and I feel awful. But I can't change what has happened.
I really do want to turn my situation around and successfully complete my grad school. Please let me know any suggestions for how to proceed.

3 of 5? That's really bad, normally if you cut you losses and salvage the majority of classes you might have some leeway.

Just shoot the advisor an email in which you briefly say what you've told us here and you want to meet about next steps. Don't over-explain, and make it factual. Don't make it look like you're trying to get sympathy or make excuses. Something like, "Due to difficulties with the pandemic, I did not perform as well as I would have liked. Would you be available to meet to discuss next steps?" Hopefully your advisor is a decent human being and has some compassion, though they may have little or no control over what the next steps actually are. Still worth at least touching base with them.

@transitionsynthesis Looks like something to put in the answer box rather than a comment.

Does this answer your question? How should I phrase an important question that I need to ask a professor?

Aside from the actual question, think about whether you need a break until things settle down. Also think about talking to a professional counsellor both about your study and your mental health.

You need to get help locally.  The pandemic is a new thing for everyone, so we cannot advice you on what to do.


text:
If someone turns down a university fellowship does it open up a spot for the waitlisted candidates in the same department?
Recently I learned someone who received a university fellowship (with no TA duties) turned down the fellowship and position at a department I applied to for a doctorate. I was placed on a waitlist for admission to the program.
I'm wondering whether this creates a vacant spot (in the same department) or the funding goes somewhere entirely different, given it's funding provided by the university and not the department.

It depends on how the university has structured the fellowship.

In my experience, usually the answer is no. Usually getting a fellowship needs to meet some sort of eligibility criteria and it would be awarded to individuals based on their resume and their past achievements. But, if somebody is not selected for that particular fellowship, it means no matter what for this round your application is rejected. If someone else withdraw his/her application (no matter what if it is still pending or already approved or even the fund is transferred to the individual's account), it would possibly would add up to the funding that would be available next year.

If this question is really about whether someone else declining an offer improves your own chances of admission, it might be more constructive to just ask the department where you are on the waitlist instead of trying to angle the system.

Dawn, AloneProgrammer - please consider putting your answers in the answer box; answers-in-comments may be moved to chat or deleted.

@ElizabethHenning I am not quite sure how asking an honest question in a forum is trying to angle the system. Also, usually, the departments prefer that the applicants refrain from sending them emails concerning admission status, etc. during the application season. So asking the department is at least in my scenario, not a wise choice. Also, it begs the question of how I learned about these facts in the first place which I am not at liberty to say.

@AnonymousDuck I think your question is fine and on-topic. Wondering how departments work is important if you plan on spending the next five years to the rest of your life navigating them.

It's impossible to answer in the general sense. The two main constraints on PhD admissions are funding and mentorship capacity.
Someone who received a fellowship turning down the department might not free up any money, so it is possible the department does not have enough money to accept more people.
But that does free up a supervisory spot. So if the PI they intended to work with has the money, perhaps they would move to the waitlist.
Other factors can include the size of the previous cohorts. If they were large, then the department might take this opportunity to reduce the size of the department by not going to the waitlist.

Recruitment fellowships often don't last through an entire degree, and some of them require the department to kick in funding, so a declined offer might free up department funding too.

@ElizabethHenning Good point, edited

Not necessarily in the same department, but in a case in which the university bothers to have a waitlist and notify people that they are on it, then I would think that is is more likely than not that it will be offered to someone on that list.
But, it may be that people from different departments are on the waitlist, so it might not be offered to someone from that same department. This would depend on the nature of the fellowship and it might be possible to deduce from the original announcement how widely it might be available.
It is possible, however, that, even in this case, things have changed and the fellowship won't be offered or that applications for it would be reopened.

Thanks a lot for the reply. I suppose it could have been easier to answer if I mentioned the university. But I am not sure whether one should do that in a public forum.

There is no need to do that, and it is unlikely that the answer would be any more accurate, since no one here is likely to be in the chain of responsibility.


text:
Some students giggle at me while I teach!
I am an associate lecturer and it's my second term with the undergraduate students.
I noticed some of my students laugh when I teach. It's the most annoying thing I have ever felt in my academic life so far. I always think, why some laugh while others appreciate my way of teaching? It's very puzzling.
At the end of my first trimester I received a very positive feedback from the majority of students. But just those couple of giggling students ruin my whole confidence.
I don't speak funny and I look average too but why why that happens to me?
Is it normal in academia? Did this happen to anyone else? And how I can deal with them?

One thing that's often effective is to simply stop talking and look at them until they stop.

Frankly - if they indeed laugh at you, these students are still in their teenage years. In that case, they are immature and you, the lecturer, should not be perturbed by them. There is a saying, not sure where it comes from: "The dogs bark, the caravan passes." If they do not laugh at you, then it's not your problem. They are adults, and it's their time and concentration they are wasting. In short - no reason to worry, as long as it does not force you to speak louder.

I took a defense course for about a year and it made me much more confident in class, less likely to get upset at small things, less likely to escalate stuff (ironically: less emotionally defensive), and as a result experience significantly fewer ongoing disruptions from students. Just a thought.

What @NateEldredge said works like a charm. And in the cases where they continue to giggle (or talk, or whatever), simply ask them to leave the lecture on grounds of their disruptive behaviour.

Check your trousers zipper. :)

Related: http://academia.stackexchange.com/q/56749/20058

It may be a cultural thing. E.g many Asians giggle in stress situations.

I don't speak funny - Judging from your post, your use of English is not what I would call normal for a native speaker.  I'm not saying this is the most likely scenario--I'm just trying to alert you to possibilities you're dismissing--but it's possible your way of speaking could be unintentionally amusing to some at times.  (This is possible for both native and non-native speakers, and isn't something to necessarily take offense at.)

Sometimes a teacher will pause and ask, in a pleasant way, if they want to share the joke, for example, "Something funny?  Care to share the joke?"  It might have suddenly hit one of the students that the problem, as stated in the book, somehow reminds them of Donald Trump.

@Kimball  this might be one of the reasons. I am a non-native speaker so it's possible that a couple of them find it bit amusing. But rest of the class find me alright so I will not worry about it a lot.

@Greg It can be as two girls who were laughing belongs to a Asian background. But I still wouldn't entirely agree with this notion. They two just seems careless students.

Sometimes, I would find an insight in something the instructor wrote on the blackboard, and I would smile delightedly while sharing it (unobtrusively, of course) with a nearby student, and I would receive a nod and smile back. I remember learning not to do this in a class taken by a specific professor, because they interpreted our smiles as us laughing at them, and it would upset them incredibly. This may or may not be similar to your experience, but I think it is worth trying to elaborate on how and when this laughter occurs, for more clarity.

It's true, though maybe not typical, that some students may in fact by amazed by your lectures' contents! In my own experience, I remember vividly hearing an amazing thing for the first time in a lecture, and I (as a 19-year-old) laughed out loud and exclaimed something like "wow! far out!" (the idiom of those years). This was not taken as a positive by the instructor... though I did try to explain that I'd meant it as a positive. :)

In my experience, there are some students who just cannot take class seriously. They may not even be laughing at you. Rather, they may be talking with a classmate and find what they are discussing amusing. They may not be paying attention to you at all. When they take a test and do not do well, they may react by thinking that is funny. If it bothers you enough, you should talk with the students after class and explain that their behavior is distracting to you, and probably to their classmates. This might appeal to whatever sense of fairness they may have. If they continue to be a distraction for you, a pointed remark about immature behavior may be appropriate, again after class. You may, if you wish, indicate that their behavior shows a lack of respect for you, the course, and their classmates.
I would not call the students out in class. I would also consult the department chair for suggestions on how to handle the situation.

Thanks. Its helpful. I emailed one of the students so they know this now that its not acceptable.

@Ahmad - Better to avoid one-way communication about this.  We don't know yet why they're laughing, but if it's because they find you pompous and/or out of touch with regular people, such an email could accentuate that reaction.

90% of the time the "someone else" isn't even thinking about you.  For future approaches, I would not start with declaring what is acceptable or not, but invite the student into office hours, leading with "I've noticed you're doing a lot of giggling in class" and then waiting for their response.  Response or no, let them off the hook softly, like "well, these things are occasionally unavoidable; but, please keep it below disruptive levels"  This shows compassion and professionalism.  That's often gets better behavior than authority.

Maybe ask one of your colleagues to attend a lecture and observe.  They may be able to tell you what the students are laughing about.  (Who knows... maybe you look like a TV star they all watch.  Maybe you sound like a certain politician.)  And your colleague may be able to tell you whether the same thing happens in other classes.

It seems a good idea and I possibly wouldn't ask my colleagues but I have joined a public speaking club in my area which might able to give me a constructive feedback.

Young people are always laughing. They could have an inside joke.  They might have said they even love the way you say a certain word or it's from a song they like.  It's usually not them focusing on you.
Young people will laugh in a beautiful way at things we've learned to find mundane, just an accent or if a word sounds like a dirty word.  When I taught French my whole class laughed when I said dix-neuf (19) which only slightly  sounded like "dees nuts" or "these nuts" from rappers as in when they might grab their crotch and say "suck these nuts."
I was relatively new but I was able to laugh it off and ask what the joke was.  I pretended to laugh even though I just thought it was kinda dumb because I couldn't "hear" it like they could.  They asked me to repeat it a few times.  I humored them and they kind of forgot it about it but it was a chance to bond.
You never really know. It's OK to let loose a little and laugh to bond with students.  I taught high school, so less formal, but I had no regrets.  Or if  they are laughing at you ... it could be a chance to laugh at yourself a little and show you're human if it's them just finding your accent cute or something.

I am a sub and my 5th grade students started laughing, then looking at me and laughing again.  I never figured out what they were laughing at.  While they worked I decided to make myself a desk in the back and sit behind them.  They immediately stopped laughing and started working.  I can see their computers and now they are the ones looking over their shoulder, not me.  Change your perspective or position that may help.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
Which one matters more - grades or qualifications - for admission to post-graduate study in Germany?
I'm looking into applying to study abroad in Germany after my Bachelors (majoring in Statistics). My question is:
which of these hypothetical candidates would have a higher chance at receiving a scholarship and being accepted in a Masters program?
1- Someone studying in a top university with good qualifications required for the course, including German skills, English skills, knowledge about their field of study etc. but with a less than appealing GPA
or
2- Someone studying in a mediocre university with mediocre qualifications but a high GPA

There is too little known about the "candidates" to make any reasonable judgement. If you are one or the other you need to explain and account for any deficiencies. And everyone's definition of a "mediocre university" will be different.

I usually base my opinions about a university's "mediocrity" on the global or national rankings which, I know, aren't very credible but can be a way to help differentiate between the quality of education. But I think it makes sense that these factors aren't enough to judge the candidates - thank you for your answer.

@Buffy: "If you are one or the other you need to explain and account for any deficiencies." In some situations, yes, but not necessarily. There are many Master's programmes at German universities where you are automatically admitted if you earned a Bachelor's degree in the same field with a certain grade (and for some of these programmes this minimum grade need not be particularly good). In this case, nobody will ask the applicant to explain or account for any deficiencies at all.

@JochenGlueck ... though the universities have "translation tables" for grades, which depend on where you got your grade.

Since you're specifically asking about the situation in Germany, here are a few remarks that might be interesting for you (although the main point of these remarks is that it is essentially impossible to answer the question at the given level of generality).

Admission rules at German universities depend on various things: for instance, the specific university/universities you're applying to, your intended field of study, and the specific programme(s) your applying to. Also, admissions for scholarships will strongly depend on the particular scholarship(s) you're applying for.

Things might also depend a lot on whether you are a citizen of a country within the European Union. Some (but certainly not all) Master programmes in Germany have quite loose and simple rules of admission for German citizens and thus, by EU regulations, also for EU citizens. For instance, for many Master programmes in mathematics, a Bachelor's degree in mathematics with a certain grade will suffice for admission.
(But one important issue here is, of course, how grades will be converted between different academic systems.)
On the other hand, things can be more complicated (and more expensive, by the way) for international students from outside the EU.

Concerning the "top university vs. mediocre university" stuff: Generally speaking, prestige of universities plays a much smaller role in the German academic system than, for instance, in the US (even if an applicant has done their undergraduate studies in a country where such prestige questions play a huge role, chances are that this won't be weighted as much in the decision process at a German university as the applicant might expect).
But then again, as pointed out above, things depend a lot on the particular circumstances, and there is at least a non-zero chance that such prestige questions might play a certain role in the admission process. For some programmes that are specifically designed for international students, it can even happen that private agencies are involved in the admission process and, for instance, make a recommendation on whether an applicant should be admitted or not. Whether such agencies take the purported prestige (or ranking) of universities into account will, again, depend on various circumstances.
As a corollary of the cultural aspect described above, I should probably add the following point: In case that the application process includes the submission of a cover letter or a statement of purpose or a personal interview (which might be more likely for applications to scholarships than for applications to study programmes - but again, it probably depends), my advice would be to be a bit careful in case that you're in situation 1) described in the question. If your application leaves the impression "My grades haven't been good so far, but my degree is from a top university, which certainly makes up for the bad grades", there's a considerable probability that this attitude will backfire.

It might be noteworthy that there very few scholarships exist compared to other countries.

I'm unfortunately not an EU resident so it will be much more difficult for me.

I specifically asked about the university's "quality" because I had my pick between a low tier university where they just hand you grades and a top university where you would be challenged. I picked the top university and now I'm worried about what it means for my future. I certainly don't rely on the fact that my university would be considered "good" because what matters is how educated I ultimately become. I don't have enough reputation to cast a vote but this was very helpful, thank you so much!

There is a good chance you will get accepted in a German masters program, as there are plenty of good universities in Germany. Whether it will be the one you were initially hoping for is another question, but that is true everywhere. So, don't worry about things you can no longer change, and start applying. That is the only way to get an answer that truly matters.

@Feiznia: Even the "top" universities often only have some (very attainable) fixed cutoff GPA requirement for their masters degrees. Or not even that. Some will invite you to an interview if there's doubt but in general getting into most programs is fairly trivial if you meet the formal requirements (i.e. took the right courses and have "good enough" grades).

@Peter: Yes, this is certainly true for many of the "standard" Master's degrees. On the other hand, many German universities now also have some programmes which are specifically designed to attract international students, and for some of these courses, admission requirements are sometimes a bit different (though this is probably not always the case).

@MaartenBuis This gives me so much hope! I have a few universities in mind but I'm not too picky given the circumstances. It might be worth mentioning that I'm still a freshman so I'm planning way ahead, however I can't help but to worry. Regardless, I genuinely appreciate your response.

@Peter I've heard about the interview but I was worried if they would see someones application and immediately ignore it after seeing they don't have a very high GPA.

@JochenGlueck You're right, I've seen programs and scholarships meant for international students and students from developing countries. I guess those would be my best bet!