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How do professors and lecturers learn to teach?
I am a PhD student in the field of education and I enjoy reading SE questions to stimulate my mind when I need a break. I find academia to be one of my most frequently visited sites.
When reading questions, answers, and comments to questions of teaching practices I often see content I consider problematic given what is “known” (a word I will use loosely here) from research in educational psychology.
How do professors and lecturers learn to teach?
I do not mean this flippantly as I often see high-quality contributions on SE as well.
I suspect teaching courses as doctoral students is a consistent practice across fields, but I am curious to know what accompanies this in fields outside of education.  What other resources are provided besides having professors and lecturers learn on the fly and make their own conceptions of what good teaching practices are?
I understand this may be largely field and institution dependent. I also am asking from a U.S. context, but I would be interested to know if the structure is noticeably different between countries.

They just jump.

My university provides optional seminars for learning how to teach and for improving your teaching in a variety of ways, as well as a peer mentoring program. I strongly suspect this varies from school to school.

I improved a whole lot at teaching by TAing and tutoring during grad school. (Still have a lot of room for improvement, of course.)

Either you swim, or the students drown.

I suspect there is nothing approaching a general answer that can be given to this question. In my PhD program, there was a three-hour TA training but no other required teaching training unless the PhD student took initiative to seek it out.  Most people I witnessed "learned" to teach by TAing, and when it came time to teach their own courses by copying whatever their professors did and developing from there through trial and error.

That doesn't go to say there weren't some resources. Some faculty offered, of their own volition, to witness a teaching session and provide feedback. And there were pedagogical support departments that would film your class so that you can see your performance and provide feedback. But, again, this was at the initiative of the student, and often the resources available were not made as visible as they might have been. Moreover, most of the faculty at the research institution I went to had no interest or knowledge of recent advancements in this area.

I suspect teaching courses as doctoral students is a consistent practice across fields - Not at all, not even within a field.

Trial and error.  At least in my experience, more of the latter, as most professors aren't really all that good at teaching.

"I often see content I consider problematic given what is “known” (a word I will use loosely here) from research in educational psychology." You are welcome to answer questions here. I saw recently a video explaining that there is very little communication between research in education and actual teachers.

The same way students learn to learn: with great difficulty.

Unfortunately, they don't. The saddest part of my student life was that there were so many professors who clearly had amazing knowledge, and absolutelly no ability to pass it on.

I could not be happier with the responses as I was seeking a multitude of experiences! I greatly appreciate the time and insight great people had to share. Some of the out of country information is pretty neat to consider. Despite getting responses that answered exactly the way I desired, I now notice how difficult picking a single answer would be. What did I get myself into on that front?

@Taladris I have reservations about responding to answers and comments when my response does not necessarily help answer the question, but rather seems confrontational to someone else’s contribution. Perhaps I need to practice being tactful, or go straight to providing an answer myself as you suggest.

They are by definition - professors and lecturers. Professors have reached far into the subject they study, but have little skill usually as teachers. Lecturers do just that - they present the subject matter, hoping it will be digested by the listening students. They don't teach per se. Teaching is more a term for those who teach in schools - primary and secondary. Their job (and skills) very different, usually with a very different audience that is not necessarily there because they want to be, unlike university students, who should be more than capable of delving deeper into their subjects.

Do we 'know' anything from educational psychology? Psychology as a field of study currently has a severe replication crisis, and many many problems with the entire field. I'm not sure we can say with certainty that we know anything from educational psychology.

I'd be very interesting in learning more about this: -- content I consider problematic given what is “known”

@crobar I used the word “know” loosely. However, there are many developments from educational psychology that have a great deal of consensus. Operant conditioning is pretty well agreed upon as being “known”. Cognitive stages of development are well agreed upon in general (but maybe not exact stages and when). There are certainly many statistically significant teaching strategies that have been shown to be replicable across contexts and subjects.  I think you’re right to question flawed studies (I have read many as well), but those do not discount the well-established ideas.

@Cardinal, not suitable for discussion in a comment, but no, I disagree, psychology is something of a citation ring, where everyone agrees with each other, but objective reality may disagree. Replication rates are poor for even 100 top studies (36% replicated), and those that replicate have lower effect sizes than originally claimed (see here). At this point we should view with skepticism anything from the field of psychology unless it is just confirming something already known since ancient times.

@crobar It's still better information on average than what some professor thinks is true "from experience."

Frankly, they don`t.

"Please Fry! I don't know how to teach I'm a professor!"

@ElizabethHenning, that might be true, but only randomly. No information can be better than bad information.

@crobar Your citation pulls from psychology journals not education journals. Without taking the time to look at each study they attempted to replicate its not possible to rationally discard educational research as easily as you have. I have no problem being skeptical of psychology; I question many aspects of psychology. Claiming that research supported best practices for teaching are only randomly better than having no information at all is ignorant of the research.

@crobar Perhaps I should have emphasized the education over the psychology. What this all boils down to is that there are certain pedagogical actions that are more likely to lead to desirable outcomes in learning. Even if you believe best practice to be trivial or obvious knowledge (many times it is), this doesn’t change the necessity of using best practice over whatever one personally thinks works best.

[US/R1-specific] Although faculty usually have recourse to some sort of university teaching resource center that can provide videotaping, training, professional evaluation, etc., it is rarely the case that either research or instructional faculty are required to engage in teaching development activities. My impression is that those who become genuinely good teachers are (1) talented and (2) take the initiative to educate themselves about the research. But this seems to be a rather small minority--most faculty apparently come up with their own pedagogical beliefs and practices based on their personal experience.

This answer is based on my experience in Germany, and in an engineering field.

For interested teachers, universities usually have a central department that offers training, workshops, brochures, and plenty of information about how to teach. For example, here, here, and here.
Many lecturers do not take advantage of these possibilities and still learn on the fly. Doctoral students often have recently attended master courses and observed how teaching was done there. In many cases, the professor gives the lectures and the doctoral student teaches the corresponding tutorial, which consists of doing practice exercises on the board. This is easier to do than teaching concepts, and provides an opportunity for the doctoral student to become confident in teaching.
Evaluation by the students also plays a role. The students are asked to give anonymous feedback on the lectures and tutorials approximately at the middle of the semester. The teacher can then learn what they can improve in their method of teaching.

My experience in Germany and Austria supports this answer. The traditional postgraduate education in both countries does not include learning how to teach. Graduate schools, however, make teaching (small) part of their curriculum. Some universities require that new lecturers complete a mandatory teaching workshop, before teaching their first course. All universities also offer institutional resources (workshops, handbooks, "learning centers"); but their use is voluntary. Most lecturers, however, have acquired most of their teachings skills (or not) on the fly, especially the older generation.

@henning--reinstateMonica: “The traditional postgraduate education in both countries does not include learning how to teach.”  It doesn’t include classes on how to teach, but (in both what I’ve seen myself and been told by my elders) it has always included learning how to teach, roughly like you learns in an apprenticeship: you watch experienced people do it, and then you try doing it yourself, with feedback and self-reflection.  Pedagogical courses/seminars can also be useful, but it bothers me when people seem to give these primacy over  learning the practice of teaching.

@PLL sure, you can - and should - also learn by observation, but this shouldn't be the only source of training. Pupils don't become teachers by going to school, and although I listen to a lot of music, I don't know how to play an instrument.

A German “tutorial” is analogous to a discussion or recitation in the United States, by the way.

That "evaluation", the way it is done in German academia, is a total idiotic nonsense, to say the least. If they would start asking students three semesters later, "how good did that course prepare you for the exams you had to take this year", then it would start making sense.

And those teaching courses and workshops are a very new addition to the spectrum. No prof older than sixty has ever taken one, and their lectures are on average far better. Meaning half of those old guys (forget the other half) give good and sophisticated lectures, but unfortunately all the younger ones only seem to show brainless powerpoint slides.

Some copy what they saw from their lecturers - hopefully only the best bits of course.
Styles of delivery - spacing of materials, topics etc
Types of assessments and combinations of continuous assessments with exam(s)...
Some do a teacher training course - some places offer a level for schools, others a level for higher and further education. And I can still lay my hands on my reference number for my teaching qualification.
Met some who make excellent teachers without training and others that should not be allowed near a classroom even after training...

In the UK, there is UKPSF (Professional Standards Framework) and HEA (Higher Education Authority, of which you can become a fellow if you complete the right modules). They encourage a "reflective" style of teaching (I.e. do more of what works).

"Met some who make excellent teachers without training and others that should not be allowed near a classroom even after training..." Me too.

In the UK, there are pedagogical courses which all permanent staff with teaching duties are encouraged to complete (often as a formal requirement of their appointment).

Those are the courses (Cert Ed and PGCE) which I referred to...

Teaching in Germany -- as well as in other countries -- is seeing an increasing degree of professionalization since the last 10 to 15 years. Usually grad schools, career services for phd students and post doc offer a wide range of courses for rhetoric, pedagogical and didactical methods and the planning of courses as well as e-learning, etc. Above that, a growing body of literature is available that especially focuses on teaching at universities.

Sadly, the US doesn't require such things, which horrifies my European colleagues.

But essentially all US school will offer these opportunities even if they don't require them.

Even those of us who do a little lecturing on a research-only contract are often encouraged to do short courses (up to a few days). Even a one-day course can make a big difference when you've never been taught to teach. (I'm also in the  UK)

@SolarMike PGCE is a full-time school-teacher-training course for graduates.  It's not what professors and lecturers do

@ChrisH it is, or was, for further education... especially since the people teaching on it were from further education and biasing their examples towards further education. The qualification for teaching in secondary schools was different.

@SolarMike FE maybe, but not HE.  It's never been an HE qualification, which is what the question is asking about

There are occasional courses about how to teach - they teach things like inclusiveness, whether certain groups need more attention, and so on.
That said, I imagine most people "learn" by watching their teachers teach. For example if I'm struggling to understand some concept, and then eventually understand it, I could very well look back at my learning experience and think "My professor wasn't able to explain the concept very well, but I know how to explain this so that I'd have been able to understand it!" This kind of thought eventually becomes the foundation of what I do when I teach it myself.

When I was in grad school in a U.S. university, a while ago, the section of the university I was in had a series of workshops taught by professors in various departments.  These were optional, and met only for a short time in each case (one class session or a few class sessions).  I found all of the workshops that I attended to be useful to one degree or another, but they varied a lot in content.  In one instance the university brought in someone from outside to teach a special workshop on her methods.  I think the university had a commitment to keep offering these workshops, but the content probably depended on the professors tapped to teach them or on the people coordinating the program that year.  My department never offered any training of its own.  There are few things that stuck with me, one of which I make use of constantly, remark on to students occasionally (I did today), and that has even played a role in one of my publications.

Speaking as an adjunct professor in the US: We don't really get any additional training. In graduate school, I recall being required to attend a "TA Orientation", in which we were taught a little about how to teach. After that, the only training came from observing the instructors I worked with, talking with my fellow TAs, and the occasional one-day optional seminar. At institutions I've worked at since then, I've been required to complete pedagogical trainings - but on the scale of a few hours over the course of an entire academic year.
The most helpful has been direct feedback. Every institution I've worked at has had a student evaluation system, in which students provide feedback about the instructor's teaching; unfortunately, this has been demonstrated to be unreliable, as students tend to evaluate based on how easy they found the course. Unrelatedly, but more concerningly, it has been shown that students tend to give lower scores to instructors who are female and/or people of color than to their white male counterparts who perform similarly. On the other hand, I've on some occasions had more experienced instructors sit in on my classes and offer feedback; that's been almost uniformly helpful (though compromised by the fact that they often haven't had any more formal training than I have).
Apart from that, it's entirely experience; over time, if you're paying attention, you learn what works and what doesn't. I like to think I've picked up a bit more than average by teaching in a wide variety of contexts, and by having a close working relationship with several colleagues who actually do have degrees in education, but there's still a long way to go.

Regarding the people of color having statistically lower evaluations than white males: did they control for nationality? Many professors from international backgrounds can have quite thick accents that might result in lower scores by students due to a difficulty in understanding their speech, and I wouldn't be surprised if they made up a larger proportion of the "people of color" demographic than the "white" demographic.

@nick012000 The study I linked doesn't seem to be controlling for nationality; accent certainly is a contributing factor, because separate studies have shown a bias based on accent. Though difficulty understanding isn't the end of the story; in https://www.fasebj.org/doi/abs/10.1096/fasebj.2018.32.1_supplement.21.3, students were demonstrated to have complicated biases related to accent (like a Chinese speaker being rated as less organized than an American one, despite identical content and learning success).

@nick012000 There is quite a bit of research showing that students have higher opinions of white men. It's a very robust finding.

I agree with Solar Mike.
I taught some courses while being a phd student. Those courses were related to some other courses which were taught by a professor. Whenever I asked him something related to teaching, he said "That's your decision." I then went afterwards to a university teaching job -- I never formally learned teaching, it was all on the fly and copying what worked for me. (I agree that I have the same weakness many non-educated teachers have -- we do not know how to teach non-interested/not-good students.)
(Western Europe)

I'd like to expand a bit on @wimi's answer about the situation in Germany (chemistry in my case).
In general I agree that university teaching could be improved if the university would educate their lecturers in how to lecture. Just as academic research could be improved if the universities taught their PIs/group leaders/professors how to manage a group.
Nevertheless, the learning-by-doing approach is IMHO not as bad as it is sometimes made to sound.

The typical teaching career as I've seen it doesn't mean "swim or drown" with someone suddenly being thrown into doing a full semester long series of lectures. Before that, there are tons of opportunities to learn step by step various skills that are needed for lecturing:

The usual start is with 1 : 1 or 1 : few  teaching situations: a PhD student teaching in a labwork practicum (in my case: the same few experiments over and over again) or research students. This provides lots of situations where one can hone ones explanation skills and where one gets immediate feedback on whether the explanation is understandable or not.
(In parallel, one also learns how to examine/grade.)
One will give seminar and conference presentations. The seminar presentations may include the express task for the audience to also comment on how presentation skills may be improved. I've met this explicitly in seminars that were trial-runs of important presentations (thesis defense, first international conference talk, ...), but more experienced group members may also approach a speaker with particular suggestions after the normal state of project report seminar (in private, afterwards).
One may teach "excercise class", i.e. a class where solutions to questions that accompany the proper lecture are calculated and students ask questions about the lecture. Again, this often starts by being responsible not for a whole semester-long series but only for a few instances - leaving time to properly prepare these classes.
At some point one is asked to provide workshops that teach ones group particular techniques. Here we're very close to lecture settings, but the audience is still small & friendly.
At some point, one starts to occasionally act as substitute for a lecturer who cannot deliver one of their lectures. Again, this usually doesn't happen to random persons, but someone is asked whom the lecturer trusts can deliver the lecture in appropriate quality.

This also means that inexperienced and thus bad teaching is restricted in its impact, and higher impact "formats" are entered step by step as experience improves.
One point (bad exception) that I have to mention is: if someone decides they want to become professor and do their habilitation (or take a junior professorship), they have to teach lectures. But there are two "motivations" for becoming a professor: research and teaching. So there's a certain population that never wanted to teach but is forced to do so because they want to have a research career. This of course is not promising for lecture quality.
It is no secret who is a good lecturer and who isn't. So looking how others teach is not picking up random techniques from random lecturers, but there's the possibility to look what the good lecturers do (and ask them for advise).
It is true that not all good lecturers can explain what they do why - and that teaching knowledge may be transfered faster in other ways.
Still this way of learning is closely related to how I acquire knowledge as experimental researcher, I'm quite proficient in this way of learning.
We're talking about fully qualified professionals.
If I as a chemist start working in a research project that involves, say, biology I'm expected to get myself to a sufficient level of biological knowledge that allows me to efficiently work on that project - and without anyone telling me what lectures I should attend. I'm expected to be able to find out myself what resources I need.
IMHO the same applies to teaching: as fully qualified professional it is my responsibility to acquire those skills.

There's nothing that hinders someone to prepare for their teaching by reading up theory on teaching.
Nor is it forbidden to ask the audience for explicit feedback on the teaching.
I give university lectures only very occasionally, but more often I teach in industry settings, and I also teach with the carpentries. When I run my courses, I often have a student helper who keeps the logistics going smoothly and has the additional task to make notes on suggested improvements, ambiguities, problems. If I'd become a university teacher now, I'd ask e.g. a PhD student from "my" (or a related) group who'd profit from the lecture to attend and give such feedback.
I may say, though, that I found it rather difficult to find good resources on the didactics I need(ed) - much easier to find a biology textbook on genetics. Things seem to have improved in the last years, though (see links in wimi's answer).
Actually, the greater difficulty in teaching for me was(is) not teaching my actual profession, but to teach programming basics because in contrast to my profession I don't remember how my "mind set" was before I knew about programming (I started programming at age 12 autodidactically)
This difficulty/deep disconnect with my audience got me involved with the carpentries, and that that's where I attended some lecture about how to teach.

I am assuming professors and lecturers have PhD.
A part of the experience comes from their teaching assistantship during PhD.
Further, when they join a university as an academician, the department conducts teaching-learning workshops where experienced professors discuss new pedagogical skills and feedbacks.
Teaching is a process that needs to keep improving everytime we take a lecture. And, this is a beautiful thing.

"I am assuming professors and lecturers have PhD": They may not: not all countries require a PhD to become a professor (e.g. in my country the PhD was established just some 30-odd years ago and virtually all older professors don't have a PhD). In addition, not all departments conduct teaching-learning workshops.

@MassimoOrtolano I completely agree. I just was focused on the majority case. There can be exceptions.

"Experienced professors" have no clue about pedagogics.


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How do you become a referee for a math journal?
I am in the early stages of my career (post PhD) and I would like to referee papers to (1) get the experience and (2) be exposed to unpublished writing to learn to improve upon my own writing.
How do you become a referee? Can you register?
Edit: I'm not asking about reviewing.

‘careful what you wish for: like Hotel California you can check out but you can never leave.

@AnonymousPhysicist I think typically reviewers post public reviews of published articles, whereas referees proofread papers submitted to a journal. Perhaps this is different in other fields, but I'm specifically asking about refereeing.

Indy500, what you call referee is called reviewer in all other fields, so the linked questions are really duplicates.

My first referee assignment was from a senior professor at the department where I was a postdoc.  She was an editor of a journal.  Then, in my efforts to write a report, I would see her around the department, and I could ask her what sort of thing was expected.

If you want to increase your chances of getting selected as a referee, I suggest improving your visibility in a few ways.  Editors use many sources to get referee names, some of which you can control.
Make sure you are visible on the internet, and that it is clear what are your areas of expertise.  An editor may well look to names listed in a paper's references or try names suggested by an author or some other mathematician declining to referee, but before sending you email they likely will verify who you are and what sort of mathematician you are.  If you are hard to find you may get passed over.
Many (most?) mathematics journal editors are ordinary professors, and you will meet them in conferences.  If you ask questions at talks, and more generally show interest in mathematics not directly related to your latest research, then your name might stick in their mind.  Make sure to attend conferences, even virtually, assuming that you are able to do so.  The list of attendees at a conference where an author presents is an obvious list of candidates.
I agree with @Scott Seidman that it might be worth mentioning to someone like your PhD advisor and let them know you would be interested in refereeing.  Editors tend to overwork the names they know, partly in hope that the person they know will suggest a younger name the editor did not know.
In summary, it is about networking, which can help your career in many ways.  Just be careful, or you will be asked to organize conferences, referee papers, serve on editorial boards, serve on funding panels, and too much of that is a problem early in your career.

Thank you, this is a very helpful answer.

Generally, you would publish in Journals, and the Section Editors will descend on you like vampires in search of fresh blood asking you to do reviews.
If you have trouble breaking in, talk to a mentor, and ask them if they can recommend you to the section editors (in place of themselves) for any refereeing jobs that are really up your alley.

I am not in math, but as far as I know the ways to become a referee are pretty consistent across fields. In my own field, referees are chosen by editors through some combination of the following categories (in no particular order and of course these can overlap):

Authors who have published in that journal in the area of the submitted paper

Authors cited by the submitted paper who do related work (also more generally people who publish in that field; this depends on how familiar the editor is with the specific field and whether they feel qualified to identify the right people)

Referees suggested by the authors of the submitted paper upon submission (some journals request such a list explicitly)

Past referees the editor has worked with and had a positive experience

An invited reviewer doesn't want to review the paper and suggests someone else. This is perfectly fine if it goes through the editor, however sometimes a busy professor might present it as their own review but it's actually written by a graduate student or post doc, but I find this unethical.

(4) doesn't really apply to you if you haven't reviewed in the past; (1-3) aren't really things you can influence besides publishing in the area in which you are qualified to review, which you're doing anyways (right?). (5) is a possibility.

If the editor knows you and sees a paper that you might be a good fit for reviewing, he or she might e-mail you and ask if you want to review it.

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Will a mismatch between my name the papers I authored and the name in my official documents cause trouble in getting hired?
When I submitted my first article to arXiv, in the article I mentioned my full name, which is just 'Afham' (I do not know whether it is not allowed to mention such personal information in a question, sorry if it is not). Because of this, my name is not listed as a co-author in the google scholar entry of the paper and neither is the paper listed under my google scholar page.
Do people use unofficial names while submitting papers and can this lead to career related consequences in the future?

Are there any other names used in your culture, like a patronymic?

@AzorAhai-him- Yes, for the most part. It does not answer the last question - will it have career-related consequences. Like would potential employers/universities make an issue when all the papers are with one name and official records show another name?
Yes, I unofficially use my father's name as my last name, but it is not present in the official certificates, hence I am hesitant to use it in papers.

Papers don't ask for your birth certificate.

Yes, but employers will, and then there would be a disparity between the names on the documents and on papers. This was my main concern.

For legal purposes, universities do not care what name you publish on. The people who check your documents are not scientists and do not look up your papers.

If you edit to something like 'Will a mismatch between my papers and my documents give me trouble getting hired?" I'll retract my CV and edit; but you should also add a country tag

Thanks, that is a good edit suggestion. I will edit the question. And thanks for the help.

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My PI publicly humiliated my colleague. I want to report the incident but don't have a recording. What should I do?
Update: I did contact the department's teaching committee about this situation and they seemed to keep an eye on my PI. Six months later (I have graduated at that time), the girl who was humiliated and another young PhD student in my group asked for a long medical leave at the same time because of mental health.
My previous colleagues recently told me that this PI has been removed from the department's faculty group, but he still stays in the department as a technician.
Background: I am a PhD student in my final year, and I'm writing my thesis now. My PI (not a professor) is in his late 40's and is generally kind in public. However, he is often moody, and I feel he stresses his students out by repeatedly making judgemental statements about them in the lab. We usually try to keep our cool and let him take his bad mood out on us. One colleague is a major target of his bad mood. This is probably because she is not always in a good health and asks for sick leave occasionally. My PI only allows us to take in total 4 weeks of leave every year (despite our university grants 8 weeks of leave in total). However, in my opinion see she works hard on her experiments day and night.
Situation: Last year, at a lab meeting, this colleague said that two of her cousins had COVID. My PI smiled and said 'Oh now I see the problem in your family gene.' There were 4 PhD students (including me) and a technician present. I was shocked and the others also seemed to be at least surprised. After the lab meeting, I asked the colleague if she was OK, and she smiled embarrassedly.
I would like to report this to the department. However, I wonder if this may be more of my colleague's choice. In my opinion, my PI has created a toxic environment for all of us, and I don't want to let this go. He makes micro-bullying or threatening statements occasionally, but this public humiliation seemed very serious and crossed a red line. We've been treated similarly but not as bad as this, so people seemed to accept my PI for who he is. However, recently my colleague is treated especially badly by my PI and she looks very frustrated. I feel bad for her and feel I need to do something.
Question: As this public humiliation happened about one year ago, how can I report this if I don't have recorded proof? Are there other choices to make our research environment healthier? What can I do?
Thanks ahead for any help and suggestions.

You have five witnesses (six, if you count the PI).

@JoelReyesNoche I'm not sure whether they'll support me except the colleague who was humiliated :(

@Wetenschaap Usually only 2 weeks of 'leave' was granted by my PI. '4 weeks' usually include the Christmas and New Year holidays. Sorry for being unclear.

@Wetenschaap Thanks for making this clear! Before I felt that I was keeping my mind clear about his bad behaviour, but now I realize that I still 'accepted' some of his ill-treatment :(

Have you spoken to any of your colleagues about your PI's behavior, in this situation and in general? Is there a general sense of solidarity in your team or has the toxicity spilled over to the relation between lab members at the same level?

Given that, as you shared here earlier, your adviser also called another lab member into his office to yell at them for 5 hours running, over a period of 2 months, every day, it should be easy to find others to support your claims.

@henning--reinstateMonica Yes I have some good friends in the department and I've spoken to two of them about my PI. They're surprised because my PI 'seems kind in public'. I think the toxicity spilt over the relation between lab members as they kept quiet on my PI's bad behaviours. Our lab is known for being a 'quiet lab'. Sadly, my colleagues focus on their own stuff and try to avoid being ill-treated by my PI.

@gnometorule Thank you for reading my previous posts! I really struggled for some time on my PI's problem. When I talked to the colleague who my PI yelled to, she was angry but said she understood my PI still had a good purpose. I wonder whether she realizes the problem in my PI. Similarly, I wonder in this quiet environment, whether everyone thinks the same way.

It takes all sorts to make a world.

We do not know your local laws and culture, so beware that advice here may be inaccurate.

He makes micro-bullying or threatening statements occasionally, but this public humiliation seemed very serious and crossed a red line.

It is the pattern of behavior, not the specific example you gave, that is what you need to report.
A recording is not necessary to make a complaint.
Reports are usually made to a union, ombudsperson, office of civil rights, or diversity office.  It depends on local customs.  Check your university's policies, or possibly local laws.
Usually being rude, offensive, inappropriate, wrong, or stupid is not against the rules, but threats, bullying, and harassment are.  Do not expect all bad behavior to result in punishment.
Do expect to get the same amount of leave that the university policy
says you should get.

making judgemental statements

Keep in mind that judging people is part of the PIs job.  But it should be done in an appropriate manner.

Thank you for your answer and I will check the university's policies before reporting my PI. In terms of 'judging people', my PI seems to do this in a way of bullying. For example, when he is unsatisfied with our work, he says 'you don't read' 'you don't do experiments' 'you're wasting money and time'. I believe he and us all know how much we read and did, but he still finds words (no matter fair or not) to hurt us. I talked with another PI in our department who I have a good relationship with, he said it's very unprofessional to say these words and release his mood on us.

I need to check the definition of being rude, offensive, inappropriate and how threats, bullying, and harassment differ from them (if this is pointed out in my university/department's policy). If his behaviour doesn't result in punishment, at least he should be exposed and warned.

This should definitely be reported and, as it seems nobody has done it yet, the ethical choice for you would be to do so.
Of course, it would have been much easier to gather evidence if the incident was reported at the time when it happens instead of a year later. However, as Joel pointed out in a comment, there are several witnesses and (by a simple binomial distribution), it is quite probable that at least some of them recall it, albeit in a patchy manner.
Your university should have a platform which enables you to submit such things anonymously so that you aren't scared of any backfire from your PI. It is only if the case is judged by the university's disciplinary panel that you (and your colleagues/technician) may be asked to testify publically. Since you seem to be in your fifth (final?) year, by the time  this were to happen you should be (essentially) done with your thesis, which practically eliminates any chance of retaliation from your PI which you may be concerned about, at least directly relating to your graduation as a PhD.
If, however, you are applying for postdocs or other roles which require recommendation letters in their application, you should consider avoiding testifying in public against your PI until you have secured this next role, as the lack of a good LoR from your PI could be a hurdle into securing such a role.
Overall, I do think this should be reported (better late than never). Just think that if you just let it through, your PI would continue to abuse (verbally and otherwise, as already done to you) to future students. You don't want this to happen, do you?
Edit: Even if the PI is not sanctioned due to lack of evidence, knowing they have been reported will be a warning that he cannot go on with this kind of behaviour without any repercussions.

I don't know. I think the PI acts badly and something needs to be done about it. You are absolutely right in that respect. But I'm not sure if, at this point, the anonymous report is a good strategy, at least without any prior coordination. Given the small number of witnesses, there is no real anonymity, which means the PI might retaliate against whomever they suspect to have reported the incident or even just against the whole team. This depends of course on how difficult  the PI really is and on their anticipation of the team standing firmly together or not.

That's why I said it may be wise to wait until having secured a role elsewhere

Thank you for your answer. Today I talked to the colleague who was humiliated and she seems still remember the words my PI said. She told me 'this was fine and PI had said many things worse than this in person.' I think when I decide to report, she may agree to recall those bad words. I totally agree with 'be wise to wait until having secured a role elsewhere'. Your answer is helpful and I appreciate your support :)


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Career options after Masters in mathematics outside academia
Basically, my background is the following: I was a very good student in a not so bad university in my bachelor, and now I'm doing alright (~ good student but not one of the best) in a very good university at Master's program in Europe. Obviously, mathematics gets harder and to be realistic it will not hurt to keep in mind career options outside academia after I finish my Master's, especially if one takes into account the current competition level in academia.
What scares me is the fact that I feel totally useless outside research. By that I mean I have no teaching experience at all, no classes in statistics, probability, applied mathematics, no programming skills(though I had one class in C programming 3 years ago which sucked and in addition I totally forgot it). Instead I have always been doing courses which are highly abstract like category theory, homotopy theory, algebraic geometry(most of the Hartshorne), topology and this list goes on. There is no way I can use outside academia/research anything I learned before, so I don't see any difference between me and a high school graduate.
Are there any options besides academia with my current background or realistically I'd better stick on academia to survive?
P.S. Even though I enjoy research, but recently it had started becoming tiring so I'm looking for a plan B. Next year which is final will be spent on writing thesis and there is no time to take any additional classes outside of my current research.

"realistically I'd better stick on academia to survive?"  I doubt academia is ever the easiest way to survive.

In industry, you constantly need to adapt and learn new things. The same is true in academia unless you get a job at the institute of advanced study or something. The question for you is,of those high-demand areas/skills you don't know, which are you willing to learn?

@ASimpleAlgorithm actually coding sounds interesting. On the other hand, priority is given to the job which can accept just right after graduation and which allows me to learn on my way. That was actually my question and I have an impression that one needs to spend a relatively long time developing programming skills and only after getting a background there is an actual job. Am I right?

@researcher nope! perhaps if you want to be a pure developer at a software company. But a company/lab/agency doing heavily mathematical work will preferentially seek math skills, though you'd need some kind of computer skills to actually do useful work there (i.e. using R, SQL, python, ...). I would guess it would generally entail developing/implementing advanced algorithms on data. Some places have people specialized on both sides too (math and software) so your programming would be minimal and high-level, handing over a working script for the software team to implement.

I am in the same spot as you. For survival, this depends on the country. In the US, people are open-minded, but you said Europe, and this is scary. I wish you are not French. Because if you are, it's pretty much over. Pure math is useless and not valued here. Your "smarts" also won't be valued (at least not officially) and you'll spend your life being paid like a fresh high schooler ("SMIC") if you don't do engineering. Also, companies are all conniving with each other so you'll be forced to accept their offer, there's nowhere else to go unless you plan to leave. Stick to academia if you can

@ASimpleAlgorithm could you please write couple more words elaborating where you said "some kind of computer skills to actually do useful work"? How can I develop this skills on my own so that I prepare myself for the future? Any books, websites that can be useful..?

If you think coding might be fun, you should start learning some of the basics to get a better feel for whether you would enjoy doing it for a living. While some companies do look for people with a lot of experience, there are also companies that recognize that the most important skill for a programmer is the ability to learn, and a master's degree in mathematics is a great way to demonstrate that. Usually, these will be the larger companies who have the capacity to train you and don't need the new employee to deliver production ready code from day one.

@researcher there is a wide spectrum of directions you can go. From security to finance to "data science" to many other hot areas. In those fields they may use different tools, so you need to focus a bit first if your goal is to check every "desired skills" box the job has before you show up at the interview.  I'd say start by looking at job postings which accept a MS (including in math), and considering which direction you like. Note that textbooks may be out of date regarding the currently-used tools.

This question will probably be closed as it is shopping. You might want to try and learn what people do after having bachelor's in mathematics. There are statistics online and, to my suprise as well, mathematics seem to bring in a quite respectable salary (on avarage, in US). My understanding is that there is some demand for mathematicians in certain jobs. They may train you so you don't really need to know much beforehand.
Given your specific interests a more ideal, non-academic, job placement would ideally use your qualifications. Private companies do have their researchers (for example IBM has researchers for quantum computing) doing serious research. There might be oppurtunities for you, that I am aware of, in communications (coding theory) or data analysis.

It looks like data analysis requires knowledge of statistics and some specific computer software at least.


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Attributing Teaching Material Under GPL
I teach a course where my teaching materials are a combination of 1: original material, 2: material from colleagues, and 3: material provided by the textbook. My colleagues have given me permission to use their material with no requirement for attribution, so I tell my students this in class, but do not have any written statements attributing this material. I do this primarily to avoid adding more information to an already long syllabus.
The material provided by the textbook includes lecture slides (licensed under GPLv3) and problem sets/exercises (licensed under GPLv2). This material is provided in the form of .Rnw files and data that allow R to produce PDF lecture slides and problem sets. My understanding of GPL is that if I were to distribute my .Rnw files, I would need to license them under GPLv3 and credit the original author of the teaching materials.
However, I'm sure not what I should be doing in a teaching context. GPL was designed for software, and while this material is code, the students never see any of the code. They only receive the PDF files produced by it. Should I add a footnote on the syllabus about the origin of some of the material in the course? It feels weird to upload a license file to the course site, and I'm worried doing so may confuse students. I'm assuming GPL requires some form of attribution in this context, but I really have no idea what the correct choice is here.

Yes, the GPL requires that you mark the material using the license. But for teaching materials, one of the Creative Commons licenses is probably better suited.

I agree that CC makes more sense, but I'm stuck as the materials I adapted came under GPL. A good lesson for when I share wholly original teaching materials, though.


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Listing (peer reviewed) software article on CV
I am a contributor to an R package, and we are preparing a submission to the Journal of Open Source Software (JOSS). Submissions are peer reviewed (guidelines available here), and articles are typically ~5 pages in length.
However, I am a social scientist, and the JOSS peer review process is vastly different from that of journals in my field. Peer review is conducted publicly on GitHub via an issue thread, and the journal does not outright reject submissions as stated in their review criteria:

We ask that reviewers grade submissions in one of three categories: 1) Accept 2) Minor Revisions 3) Major Revisions. Unlike some journals we do not reject outright submissions requiring major revisions - we’re more than happy to give the author as long as they need to make these modifications/improvements.

Given these differences, I am hesitant to include a JOSS article in the peer reviewed publications section of my CV if this article eventually ends up being published by JOSS. These are the options I've considered so far:

Include a link as part of the entry for the package in the software section of my CV
As an entry in the non-peer reviewed publications section of my CV
Don't include it in my CV at all

What is the best practice here?

I don't think this should be treated any differently from any other peer-reviewed publication on your CV. There is still some standard of quality that's applied before a manuscript will be published in JOSS. In practice, there isn't a huge gulf between "major revisions" and "rejection" - both indicate that the manuscript needs to be changed significantly before it can be published. The category of "rejection" just indicates that the journal editor does not want to be involved in that process. Even though you can't be "rejected" from JOSS, that doesn't alone indicate that the papers which are accepted are of lower quality. A low quality paper could receive a label of "major revisions" every time it's revised and submitted if it's still low quality - it never gets outright rejected, but it never gets published either. The fact that it's not rejected speaks more to the patience of the editors than to the quality of papers they choose to publish.

Did not realize the role of "major revisions" in practice, and I feel better about (potentially) including a JOSS article in the peer-reviewed section of a CV now. Thanks.


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Is the '°' wrong in a degree centigrade mark?
My PI helps to modify my thesis. He keeps changing the degree mark '°' to '0' as the superscript in a degree centigrade mark. He also changes every 'in the phase' to 'at the phase'.
As I searched, superscript 0 was used when initially creating the degree mark. But now ° is used in all the degree mark. 'Phase' means a period of time and in most paper and textbooks, people use 'in the phase'.
I'm confused about these changes. Is the '°' wrong, or 'in the phase' wrong? What do you use in the paper/thesis writing?

An example of using '°' and 'phase' in my thesis:
'The cells cultured at 30 °C for 3 days were in the stationary phase.' 'Stationary phase' is one of the cell-growth phases that range from several hours to several days.
Thanks to @Houska for your vision and practical suggestions <3
Thanks to @AndreasRejbrand for correcting the degree sign to be 'U+00B0: DEGREE SIGN'. I have changed the sign in the title and body. In my PI's comments, he highlighted my degree sign (that I added through 'Symbols' in MS Word) and commented 'Should be a zero in superscript! Change all the rest.' So I believe he means using a zero.

PS. My PI is a Chinese who has been working in the UK for 20 years. His spoken English is fine, but sometimes he mixes up "she" and "he", or forgets to add 's' in a verb with the third person.

Don’t use the symbol, simply write 23 C.

Or, use Kelvin. :p

@Aruralreader - 23 Coulombs is very different from 23 degrees Celsius - you must use the degree symbol. My AIP style manual (American Institute of Physics) clearly indicates that the degree symbol is not a superscripted zero but instead its own thing.

I’m sure the context is clear, but you’re right about them being different.

@Aruralreader and AppliedAcademic: given that the question refers to "phase", it has probably nothing to do with degree Celsius ;-)

@MassimoOrtolano - fair enought, but that style manual is also quite clear that the degree symbol (whether degrees Celsius or not) is the degree symbol, not a superscripted zero.

@MassimoOrtolano I think you're probably correct given that the question clarifies the meaning of "phase" as a period of time and not e.g. a thermodynamic phase. But the question specifically mentions "degree centigrade mark" rather than "degree symbol"...

I had an graduate course in elasticity where the (old) professor insisted that we all use the notation that he developed in the 1950's for easy use on typewriters. Which, of course, had no relation to accepted notation in any textbook or journal from the 1970's onward. Sigh...

Can you give an example sentence where you use "at the phase" or "in the phase"? Possibly either could be grammatical depending on the context.

I wonder if you are sending an electronic document back and forth and the professor's machine is either doing "autocorrecting" or is missing the fonts you are using and does a substitution.

This is more about English language and I am not native. Concerning "phase", it should likely be "in" for both angle phase and phase matter. But as astronat said, it might be context dependent.

While contrary to modern notation, apparently Wikipedia claims that it did used to be a raised-zero!  Wikipedia explains that this is like the notation 40.1875° = 40° 11′ 15″, where additional prime-marks noted higher-order divisions, with the first being a raised-zero as it was a zeroth-order division.

Just to note it: in modern usage, a degree-symbol is just a raised-circle, probably generally understood as a reference to the unit-circle depicted when students learn about angles.  The mark denotes that the unit isn't a scalar unit, so scalar math shouldn't be applied to it.  For example, (0 K)^2 = 0 K^2, but (0 °C)^2 isn't 0 °C^2.  Likewise, angle-degrees aren't scalar (since they wrap periodically or else are in a bound range).

@theonlygusti A shortcut key of 'option+k' in Mac. However, this is not the degree symbol. I've corrected it in the title and body :)

FYI - I use ALT 248 every single work day to put in degree marks in Windows 10. At this point it's automatic.

@Nat: No, that's wrong. (0 °C)^2 would indeed be 0 °C^2 since temperature is a dimensionful quantity: degrees Celsius and kelvin are no different in this regard. Strictly this is also true for angular displacements (degrees, radians etc.) but they are conventionally dropped. See https://math.stackexchange.com/questions/1097581/why-are-angles-in-degrees-dimensionless

@Zorawar: The simplest way to understand it might be: an ideal-gas (one that obeys PV=nRT, and so V=nRT/P) has a volume proportional to temperature, T.  So if you double temperature, then you double volume.  That said, do you believe that (2°C)/(1°C) = 2?  (Note: It's actually ~1.003647638.)

@Zorawar: BTW, I looked at that question -- the existing answers are wrong.  We say that something is "dimension-less" when using dimensional logic and all dimensions are to the zero-power.  A value with a degreed-unit-qualifier isn't a dimension-having value, like a dimension-less value, but it's also not "dimensionless" because that'd imply that it's a value within the scope of dimensional logic that has all dimensions to the zero-power.

@Nat: I'm sorry, I can't follow that argument. Every quantity is either dimensionless or dimensionful. Like you said, if all powers of length, mass, time, charge etc. are zero, then it is dimensionless; otherwise it is dimensionful. They are complementary, much like if a number is zero, then it is not greater than zero. I think a more pertinent example would be 2.54cm = 1in, so what do you think (2.54cm)/(1in) makes? Dimensionless 1?

@Zorawar: Depends on how technical we want to get.  Usually, yes, I'd say that (2.54cm)/(1in)=1.  But if we want to get pedantic about it, it's 1*Prod([dimension]^0, for all dimensions).  The reason we need to include the product of all dimensions to the zero-power is that they're part of the context when we're using dimensions.

@Zorawar: But if it helps understand the argument: is the color-red "dimensionless"?  Or is it "positive" just because it's not equal-to-or-less-than-0?  Or is it a "real number" because it doesn't have an imaginary-component?  Likewise, a degree-unit-having value isn't "dimensionless" -- not because it has a dimension, but because the dichotomy doesn't apply in the first place.  (The easiest way to reform a degree-unit-having value is to convert it into a scalar; for example, adding 273.15 to get from degC to K.)

@Nat: well, that's much the same thing, the former is the defined by the latter. The point is that, technically, (2.54cm)/(1in) = 2.54 cm/inch (sorry, I clearly should have said 2.54 instead of 1 in my previous comment). By convention, however, we drop conversion factors like this -- it's not that neither metres nor inches are dimensionful. Using degrees to switch from linear to angular dynamics is also such a conversion factor, so it is conventionally dropped.

For the International System of Units, the units of measurements are defined by the SI brochure. For the degree, unit of plane angle, and the degree Celsius, unit of Celsius temperature, the SI brochure at p. 133 and at p. 149 uses a circle and not a zero.
However, at table 8, the circle is rendered with an "o" (probably they didn't have the circle in that font). In any case, no zero.
You can refer your professor to that document. Further, if you're using LaTeX, you can use the siunitx package and write the angles with the command \ang and Celsius temperatures with the command \SI{23}{\celsius} (example with 23 °C). From the package documentation, you can see that also in this case the degree symbol is a circle.
If they still insist, let it go.

Also, if you are using LaTeX you might want to set up a macro so that by editing one line at the start of your document you can change every instance to a superscript 0 (to please your PI) or the proper degrees sign (to conform to the SI standard).

@dbmag9 If you use siunitx there’s no need to set up a macro because the symbol is customisable through an option ;-)

I'm considering switching to LaTeX. My PI only uses MS Word so I still need to change the file type before sending it to him :(

@Metis533 If you don't know it yet, a free tool that could help with the conversion is pandoc. For complex documents the conversion is not perfect, but it's a starting point.

@MassimoOrtolano That's helpful. Thank you!

@Metis533: Given that your PI is using MS word, I am suspicious that the real reason your PI is correcting you is that his machine is failing to render the degree symbol properly.  Then, he thinks he is sending an e-mail like: "Stop using ◘ as your degree symbol!" but your machine renders his e-mail as, "Stop using ° as your degree symbol!" This would make for a confusing e-mail exchange.  If this is the issue, you may need to embed your fonts into the MS word document.  Possibly Andreas's recommendation to use ° would fix this.

Clarification: My first degree in the comment above is °, since I didn't realize the subject of the question was edited after Andreas posted his answer and just took for granted that the symbol didn't match.

As you (presumably) continue down the academic career path, you will be buffeted by all sorts of "helpful suggestions" that span the range from ignorable noise to microbullying by those in positions of authority over you. Editors wanting picky little formatting edits, some good some bad. Reviewers with weird comments. Granting agencies and university bureaucrats wanting you to fit something to their format or structure even though it makes no sense in the context.
Choose your battles. Let people "win" on the small stuff if it greases the wheels to get the real help and support you need.
Fighting over degree symbols is pretty certain to not be a battle worth fighting. If your P.I., your University thesis office, or a journal publisher wants it some specific way, just do it. And be prepared to revert back if someone else with higher positional authority wants it differently (e.g. the publisher of your accepted paper trumps your PI).
As to your "phase" question, I'm a bit confused about it. But apply the same logic. Maybe it's sufficiently wrong or jarring to insist on doing it right, maybe it's not worth the bother. And maybe you can just smilingly say, "no, I'm sure this is right. If you want, I'll double check."
Finally, recognize that someone's pencilled edits on a manuscript may not mean "I insist on this other way" but "I'd do it this way, use your judgment". So maybe you can just say, "thank you for the comments" and not do it.

Picky edit to end of 1st paragraph: you probably mean "even though it makes no sense".

@DanielR.Collins or it could mean "even though it already makes sense" (without making the requested change).

Upvoted, even though I'd be incapable of taking your advice in this case!

Yes, it is completely wrong to use ˚ as a degree sign.
The reason is that ˚ is U+02DA: RING ABOVE. It is not at all a degree sign; instead, it is (semantically) the ring above the A in Å.
The correct character is °, U+00B0: DEGREE SIGN.
This is almost the first time I have seen someone misuse U+02DA: RING ABOVE as the degree sign.
However, it is very common that people misuse the masculine ordinal indicator, º, U+00BA: MASCULINE ORDINAL INDICATOR as a degree sign, especially in fonts in which it is not underlined. The ordinal indicator is used in some languages to indicate ordinal numbers, e.g. 1º for primo in Italian.

Note: Just ° in HTML (including StackExchange questions and answers, but not comments).

Good catch, it would not occur to me that the symbol might be some other ˚ when ° is what I can find on my keyboard. I guess Scandiavian keyboard users might have it the other way.

There's also U+2070: ⁰, which is explicitly the "Superscript Zero".  Not sure if this is what the OP is referring to?

For those confused: the original question was using the RING ABOVE character in the title and has since been edited to the degree sign. Even with the current edit it's useful to see additional incorrect ways this sign might show up.

authors: Vladimir F Героям слава


text:
Dropping out of PhD in my home country to start a new one in the UK
I saw question similar to this but wanted to specify my problem. I did my Master in the UK and graduated in 2018 and decided to start PhD in my own country last year. As it took a little bit time to verify my degree in home country and application process had been closed, I had to apply in 2019 for 2020 academic year, hence the one year gap.
Now, however, I want to drop out of my PhD and apply for one in the UK. Significant difference in quality of education, lack of engagement with theoretical issues (and quite obsolete methods of doing things) and lack of usage of sources in English and my struggle to adapt again to academia of my own country are main reasons of my decision.
My question is:
How to explain it in my CV and justify it in order not to give a wrong impression? I mean, I could avoid writing that I had already started my PhD (which I did with my Master, applied already studying one in my own country and got offers from 5-6 UK universities) but filling the gap of 2-3 years constitutes another problem. Another thing might possibly be references because most people here do not have knowledge of English and it might sound odd asking them to write references for me.
What would be the best thing for me to do in this situation?

I think the explanation you give here is fine. Combine it with Covid disruptions... But it is what it is.

Should I say that I am currently doing my PhD on CV and then specify things I mentioned above on personal statement? Would it also be fine to get references from my previous university in the UK as I would not have completed this one by the time of application?

All of that sounds reasonable. I think reference from your MS experience are probably best, unless you have a good relationship with someone local.

Oh, thanks for support. Will try to write as articulately as possible to avoid any misunderstanding.


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Administration threatening expulsion over absences in audited class
I just received an email from my school's administration (Pima medical if that means anything) that due to having an average of over 15% absence from class, I have to meet with someone from student services and administration where I may be expelled from the school.
For context, I'm retaking two of this semester's classes, and auditing a third as a reference before the end of program certification exam. The audited class is where most of the absences are, largely due to unexpected sickness or severely spraining my ankle. At the beginning of the semester, I was under the impression that the audited class would not be counted for grading or attendance, as that's how most other schools seem to handle it, but only recently realized that they don't see it that way.
I have the meeting with admin Monday after my classes, what would the best course of action be in the meeting, and is there anything I could/do beforehand or after for damage control and to make it go as smoothly as possible.

Go to the meeting, explain what happened. Try to get the lecturer from the class you audited to support you. I honestly don’t think there’s much you can do if you’re expelled, but I don’t think it’s the likely outcome. You’ll get a warning or something.

In addition to @Spark's advice, if you can get doctor's notes or records of medical treatment for your ankle and/or illnesses you should take that to the meeting.

Sometimes university student associations offer advocacy services, where a more experienced senior student may accompany you.

Okay, thanks. I'll go in to the meeting and do my best to explain the situation. Unfortunately, the professor has already been very unsupportive, and I don't think I'll get any help there.


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Graduate student with abysmal English writing skills, how to help
I am a math professor at an R1 university. I have taken up a new graduate student (my n'th for n<=10), who is mathematically quite strong, but whose writing skills are a couple notches below what I have had to deal with so far.
We have a new result, which he currently is writing up. He is relatively new to English, and his native language is much unlike English. Though one can understand what he says in a conversation, writing a paper is a real struggle.
Most research students that I have worked with start with poor mathematical English skills. Their first drafts have several major problems, and require many rounds of thorough revision. However, there is always at least something which is right from the start. In contrast, this student's drafts appear nearly unsalvageable: they have hardly a sentence in common with any proper exposition. I have lost the track of revision number, but it is likely to be in double digits now.
The student is working hard, and the draft is showing some signs of improvement. However, I cannot shake the feeling that there should be more that I can do than provide extensive feedback. I am also worried that if this continues for another few months, the student can get much discouraged.
I believe that a part of the problem is the sudden jump in writing difficulty. The mathematical content of the paper-in-writing is more complex than it is typical for a first paper of students that I have supervised so far. This makes the writing task harder. I wish only that the student could practice on a simpler, shorter paper first, to provide a smoother transition from writing homework exercises.
I am looking for suggestions. Note that I would like to avoid writing the paper myself (which would be far less work for me than this), for I want the student to learn how to write himself.
What I have done so far:

extensive comments on drafts, with some verbal explanations
suggested some mathematical readings which I know are well-written (to learn by example)
provided general encouragement

Is the problem the structure of the paper or the sentences in the structure or both?

A key point I can’t see addressed in your question is what your student thinks of all this. Is he aware that his English and writing skills are holding him back, or is he saying to himself “My professor is prejudiced against me, Google Translate says it’s English!”?

@JenB Both. That is in addition to the usual things that students have trouble with: choice of notation, mathematical typography, finding the right amount of detail, and the math itself.

@MartinKochanski He is working hard on the writing, so my impression is that it is the former. However, "working hard" is not the same as "making much progress", hence the question.

Are you located in a country where English is the primary language of conversation?  This matters for how easy or not it will be for the student to improve their English skills.

Is this an 80/20 situation that needs to be switched to 20/80? Let the student focus the rest of summer on English.

One piece of advice I received when learning to write was to "write how I spoke". If he is understandable in conversation, advise the student to write his first draft as if he were explaining it to someone, and then try to work that into something better. Alongside this, he should "be a careless artist and a ruthless editor".

You may have answered your own question. Perhaps this student isn't ready for such an ambitious task, and should take the opportunity to write a less ambitious paper as practice first. It doesn't even have to be original, he can just get practice re-writing a well written paper from scratch, only working from the math.

Reading is often an important stepping stone to writing; does the student read enough English-language papers in mathematics?

Related question that might be of interest: https://academia.stackexchange.com/questions/94054/how-to-train-students-to-write-high-quality-research-papers

Did the student ever take English classes? Or is he  trying to learn by himself? Perhaps an "English as a second language" class would be a very useful investment.

I suggest giving the student some encouragement - he might be freaking out and having major imposter syndrome episode - then discussing with him ways to address the problem. Maybe a class on writing papers would be appropriate?

Sincere question – why are students with very limited English-speaking abilities allowed to enroll into English-speaking programs when problems like those are bound to arise and will hinder the student's ability to produce quality work, restrict collaboration between the student and his fellow students, and place a heavy burden on the teaching staff?

Elsevier English Language Editing: "Ensure that your work is written in correct scientific English. Elsevier’s English Language Editing Service will handle the language editing and make sure that your paper is free of grammatical, spelling, and other common errors before submission!"

I guess you need this version as it includes "Special focus on the logic and flow of the manuscript's content".

@Alexandred'Entraigues For the same reason that students with limited mathematical skills sometimes end up in PhD programs: inability to perfectly assess the "skill", strength in other area that compensates the weakness, competition for stronger/more perfect students.

I am thankful to all respondents. Some of the suggestions here have already proved helpful, while some others are either unappealing or impractical. I will not comment in more detail as that might compromise student's anonymity. Thanks everyone.

My wife, who was a writing coach for scientists, once had great success with a native speaker of Japanese whose written English was poor. She suggested he write the first few drafts in his native language, so that he could be sure he had the main ideas right. Then he translated his own work into English as best as he could, ready for revision.
Another possible strategy with a similar goal (getting the structure and basic ideas right first) might be for you to sketch a first rough draft, with the theorems in place and some of the expository scaffolding. Then the student could work on fleshing out the proofs and adding details - to be revised, of course.
(I wish I could check that second strategy out with my wife.)

This is the first idea that springs to mind. The student is apparently capable of the subject, and assumedly of writing conpetently in their first language, so why not start there and gradually transform it into an English-language text? The last stage would be supported by the suggestions of other answers, like a writing centre or ESL tutoring.

From a language learning point of view, translating a text from ones native language may not be the best way to learn a language.  Ultimately one needs to learn to think in the other language directly, or one will never reach fluency.

However, it is much easier to structure an essay in one's native language, @gerrit. And there's no harm in trying both approaches at different times.

@GeorgeM I wouldn't suggest a translator. After the native language draft is done the student should do the translation, en route to learning to write in English from the start.

This is the strategy that I use with non-native speakers who get stuck, either in speech or in writing. Say it in [Italian] first and then self translate. It's a slow process, and it's not infallible by a long shot because word-for-word translation has huge pitfalls, but at least they are able to communicate basic ideas.

@GeorgeM I think the primary goal of graduate education is to help the student become an independent productive mathematician. Some of that is finding theorems. Some is building communication skills. I think it's a false dichotomy to say "painstakingly teach English" vs "publish quickly".

@gerrit: that's a good remark but the goal here is not language fluency but to obtain a workflow that helps the student create documents of improving quality. English and Japanese (not sure what the OP's student language is, I am just taking the example of this answer) have quite different sentence structures, so the student would probably need a professional ESL teacher if he wants fluency.

As a partial answer, perhaps your university has a writing Center you could refer the student to for help. For example the University of Wisconsin-Madison has a writing center and Texas Tech even has a graduate writing center.

This class will help students whose English is already at intermediate level or higher. Pretty hopeless in cases where a student cannot write a single coherent English sentence. In speech, there is often context and a non-native speaker's gestures and facial expression will provide essential clues that enable us to guess with a certain degree of accuracy, meaning and intention. But this interpretative skill becomes almost useless when the speaker's communication/message is transcribed, then we only have context to go on.

Another way to put it:  This is not your job; send your student to somebody who does have this as their job.

This was my first thought. I've worked in several writing centers, and I've had many graduate students over the years who came in for recurring visits. A good tutor or consultant will give scaffolded feedback that, over the course of a few months, will most likely make him into a stronger writer. Ideally this student would have multiple points of contact: an advisor can focus on discipline-specific writing skills, a writing center can focus on building general writing skills (from planning to sentence mechanics), and perhaps a graduate writing group can help him with motivation.

I'm not offering a full answer, but your question really moved me. I am a non-native English speaker, who studied at LSE (a while ago now), and did well. However, a few of my classmates, also not first-language speakers, did find it heavy going - all were bright enough to take content IN, but getting it OUT was an issue. I saw their frustration and often embarrassment, which is exacerbated by the fact that they were top performers at their home universities. I offer this - which is fairly non-academic advice, I'm sorry - if you want to really help, encourage your student to use English more in their day-to-day life, and to get themselves into all-English settings. One of the challenges with big, high-profile universities (esp. in the States) is that there are such large foreign communities that, as a student from, say, China (I'm not) - I would be able to basically remain in a Chinese-speaking bubble. This is, of course, wonderful in many ways, but it also means that I never cross the bridge (only done by being immersed in a linguistic environment, which is rather uncomfortable for a while) to the land where I now feel the new language is also a part of me. Once once this transition is made, I can deal much more comfortably with such abstract topics as you suggest.
Your student needs the playful interaction of everyday messiness, not because they need to use nuance and idiom in the paper, but because their English-worldscape sounds, to me, still quite small. It's an issue of confidence, not perfection.
Now, it does not sound like you have the time and resources to do this, and besides, ordering their nonacademic life is quite outside your ambit. So I don't think this can be of much help; but I do think that, in an ideal world, this is where the answer lies.
Finally, this is not meant to be pro-English. In fact, native English speakers have it worse, because you get by in so many places in the world using only English, it's rare to find an academic also able to ply their trade in another language. Moreover, and as academic you be most likely only ever targeting English journals.

Yes, immersion works.

a +1 to this answer, with the added caveat that conversational English is very much unlike academic writing English. One would need exposure to both (both formal and informal).

Have them write up mathematically simpler things first, to reduce the English complications.
Giving fairly-formal oral presentations, on relatively simpler things, can also "expose" in real time issues with formation of sentences.
I do also encourage my students, native English speakers or not, to write as-simple-as-possible sentences, thinking in terms of subject-verb-object, rather than lengthy compound-complex sentences. (Many textbooks and papers are bad models in this regard.)

Something absurdly simple perhaps, such a proof that the square root of 2 is irrational, and go through it with him carefully. But make sure he knows why he’s doing it, and what the aim is.

As a non-native speaker myself, I have to disagree. Grammar, sentence structure, and vocabulary are all things that aren't that different between a new result or an easy old result. The student doesn't seem to have a problem with the mathematical concepts themselves but lacks the feel for the language; reading a lot of well-written texts (even/especially fiction), possibly along with (non-mathematical) ESL classes, will probably help them much more.

@GuntramBlohm I have to disagree with your disagreement. Difficult proofs are difficult to write even for native speakers, and new grad students are often very poor at writing proofs -- this may be surprising if you've never worked with grad students in a mathematical subject. The student here is trying to run before they can walk by trying to write a difficult proof in a language they're not very good at yet. This answer tries to address one of the two problems the student is facing at the same time.

Ideally, the student needs a tutor, preferably someone trained in ESL (English as a Second Language) and also familiar with the student's native language.
Ideally, but probably impossible to find, is someone conversant in mathematics.
The student probably needs a crutch, but also a plan to be able to throw away the crutch before he graduates.
This isn't, of course, a zero cost solution, but it might be worth it if the student truly has promise to contribute.
Of course, writing in the student's native language is another possibility, but it would, then, be hard for you to evaluate it. A colleague with the required language and math skills might be able to do that. This might be preferred if the student intends to return to his native land eventually.

Recommend the student to take an advanced English grammar and vocabulary course, at CEFR C1 or C2 level.  My English is fine but if I were tasked with writing a scientific paper in German, I would probably make grammar and prose errors averaging more than one per sentence, unless I spent a huge amount of time double checking everything.  A CEFR C2 course is aimed at reaching a level of fluency in writing comparable to a native speaker.  They might need to take a C1 course and pass the C1 exam before entering C2, but C2 would be really good to have.  The university probably offers such courses.
This will be much easier if you are located in an area where English is the primary language of communication, but even elsewhere many big cities will have CEFR C2 English language courses, and otherwise student can take such a course online.

@GeorgeM This is true, and possibly in non-English speaking countries too (but maybe not all universities worldwide offer quality C2 education).

You could rewrite the paper with the student. This will expose the student to their mistakes (which they'll hopefully identify themselves in the future) and to good writing (which they'll hopefully strive towards in the future). Unfortunately, it is a highly labour intensive approach. As an alternative, one of your better students could rewrite the paper with the student (possibly in exchange for co-authorship, which seems reasonable, given they'll be rewriting the paper).

Rewriting the paper with the student is what Frank Harary used to do, and not just with foreign students. The results were good, but, as you said, it's a very labor-intensive approach.

What do you mean by "rewriting" the paper? You mean physically sitting at a computer together and writing? Because currently, in addition to feedback about overall structure and grammar, etc, my feedback also includes replacement sentences and sometimes paragraphs. If I simply rewrite it offline, then I am afraid that it will not teach the student to write their next paper.

It is exceptionally difficult for anyone, even a native speaker, to learn from extensive comments on drafts. (I have experience of receiving and later on in my career of giving them). I learned that better progress is made if you start by focussing on the logical structure of the argument - maybe by drawing linked boxes on a blackboard - and only then moving on to sentences and grammar.

@TeacherOfMathEnglish By "rewrite the paper with the student," I meant physically sitting at a computer together and writing.

@JeremyC I didn't suggest learning from extensive comments on drafts. (That said, I learnt that way.) Whether logical structure is the problem isn't clear from the OP's question.

That is a good method of learning a language (not sure if it's the fastest one, though). That's how I was learning Japanese: I would write a short essay first, at home, then print it on paper, bring it to the class, fix it together with the teacher (crossing out, circling and drawing arrows to indicate which moves where, changing or adding some stuff), I take it back home, stare at it for a while, incorporate the corrections into my original text, print it on paper, repeat. Would take several weeks for a single paragraph at first (with a class twice a week and my level close to zero).

@user2768 I was forced to learn that way too. It wasted my time and the time of the people making the extensive comments. In my experience the problems described by the OP are almost invariably to do with unclear logical structure. Get logical structure right and you can tell the story in simple words (especially in mathematics). Get it wrong and no amount of fine writing will solve the problem.

Have them take a look at this online course by Berkeley: Academic and Business Writing
edX may very well have exactly what they need if this isn't quite it. It's remarkable how much information and graded instruction is absolutely free or low cost on this platform by Harvard and MIT.

Here practice makes mastery. Let your student be exposed to a lot of articles similar to those he has to write, and ask him to try to copy their style.
Also, review his writing with him and point out different ways to express his ideas that fit better in your context

TL;DR
Suggest him to write a blog or more simple content, like technical reports.

As you said:

I believe that a part of the problem is the sudden jump in writing difficulty.

This is a big challenge. Writing regularly on a blog will help him to gain experience and writing skills. He might start trying to explain his work for a non-math audience, and then try to go deeper and details and complexity, as the paper requires.
You can also ask him to summarize his weekly work/research in a report (article-like or free form), just for getting used to different writing styles and contexts.
For now, if there is no hurry with that paper he can keep iterating or if the paper is unsalvageable, you can kindly suggest him a different paper structure to start from or divide it into more manageable parts for him.

I disagree with you. As the OP consider there is a sudden jump in writing difficulty, the student needs to practice in a more simple context. He will receive feedback not just from the OP, but from other people who read what he writes. Obviously, you can learn how to drive doing it in a motorway and receiving feedback, but it is not the best way to learn it.


text:
What does 'soon' mean in PhD applications?
I had a PhD interview on 8th March. One of the interviewers told me they will let me know the decision 'soon'. I had the impression that the interview did not go bad. It is been more than a week that I haven't heard anything from them. I wanted to ask you is it still soon to get in touch with them? I am asking since there is an exam in the next week and if I'm accepted, I will withdraw from that exam. The university is in central Europe. Thanks.

There is nothing wrong in writing a polite email similar to your question here, explaining that you have this exam coming up and the outcome of the interview will dictate whether you take it. The best case scenario is they let you know you have been successful; probably they will just give you a date by which they will tell you the outcome. I think you have nothing to lose by asking.

That's a good advice, I'll add that the typical "soon" in central Europe means "in less than two weeks".


text:
PhD interview: Why in particular us?
I have applied to a very well-known institution for PhD in Europe. They evaluate students first and then match them with advisors, so this is not a position with a specific supervisor; an admission committee will decide, not a single supervisor.
I am thinking about an interview that one will have with them. This university has almost the best group in my field and is extremely famous for it. It’s obvious that many students, who are interested in this field, want to study there. I was thinking about the following question in their interview, and how I should answer?
“Why did you decide to apply to this institution/Why in particular this university?”
I am having a hard time in preparing an honest while strong answer to this question. The problem is that, as I said, it’s obvious they’re good and I think they aren’t interested in hearing this from an applicant. At the same time, that’s basically my reason for applying there: since there are great professors there, very talented students, etc. On the other hand, their research is very specific and I believe they do not expect from a candidate to show off with “knowing” their research in “detail”. I know what they are doing, I believe it is important and valuable, and it matches with my interest as my background shows. However, I cannot prove to them by examples or other ways I know in details what they are doing since that’s not right. My question is this:
What is your suggestion to me? Should I start reading their research in detail to be able to make specific examples to support my reasons for applying to their group? I am a bit puzzle about this.
Please if you think more information is needed leave a comment before writing an answer. Thanks a lot!

Does this answer your question? PhD application question: "Why do you want to join my research group?"

@GoodDeeds Thanks. I think not specifically because as I said, they have an admission committee there, and they’re almost the best group in that field in Europe. So my question is kind of more specifc, I think.

Don't overthink this. Tell the truth! "Your group is the best!" (... and I want to be with the best)...
Yes, if you can make some incidental remarks about how/why you know that their group is "the best"... and in what field, precisely... that would be good. Not just "gee whiz! Gosh!", but something a bit substantive.
I'd think departments/groups would want to hear from prospects that those prospects appreciate the expertise of the group/department/whatever. Otherwise it's really silly cold-calling. (When I (in the U.S., in math) get cold-call emails from people who're manifestly using a uniform template about "Dear Sir, I've studied and admire your research", with no details pertaining to me (either in the form-of-address or anything else) it's easy to hit "delete".

I'd add that the other piece of the puzzle is that group X is the best group in their very specific field. You might want to add why you are particularly interested in that very specific  field.