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Why do some professors with PhDs leave their professorships to teach high school?
I can surmise that some of them mightn't have gotten tenure and needed to find another job, but wouldn't these former professors be bored teaching the same (relatively basal) material yearly?
Let me know of other examples, but I was riffling some fee-paying schools and lighted upon:

Audrey Budding, of the Harvard Academy for International and Area Studies

B.A., Swarthmore College 1982
  B.A., University of Cambridge (UK) 1984
  M.A., Harvard University 1991
  Ph.D., Harvard University 1998

Eric Casey, former Associate Professor of Classics, Sweet Briar College. Now at Trinity School NYC.
David Gomprecht at Dalton School.

Gomprecht, PhD, graduated from Wesleyan University, where he majored in mathematics and physics, and then went on to receive a Ph.D. in mathematics from the University of California at Berkeley. After working as a research mathematician for a few years, David returned to his hometown of New York City, where he has now been a math specialist and private tutor for over twenty years.

Mara Naaman at Dalton School.

Interesting, never heard about something like this in Germany.

Sweet Briar College almost closed a few years ago and is still in dire financial circumstances. https://www.chronicle.com/article/After-All-but-Closing-Sweet/241100

be bored teaching the same (relatively basal) material yearly --- My experience was entirely the opposite of this. After many years (during graduate school, then a few years after my Ph.D.) of teaching college algebra, precalculus, trigonometry, and mathematics appreciation courses (only a couple of first semester calculus courses, and nothing more advanced), I taught several years at a state-wide "magnet" boarding high school in which I got to teach several levels of calculus each semester, differential equations each year, (continued)

and topics in precalculus courses that I wouldn't have touched when teaching college students (because the HS students were so much more talented and capable). Three or four of the students I taught at that HS were more mathematically talented than anyone I would likely have seen in a lifetime of teaching at most any (U.S.) state regional public college or mid-ranked private college. Back in 2009, out of curiosity I googled a bit to see how many Ph.D. mathematicians I could find currently teaching high school in the U.S. I found 15 of them (not including me, as I taught HS in the 1990s).

@stats0007 probably because our private school system isn't as established or in the limelight, so if there are instances, its just that nobody heard about it

Your examples are kind of a mess, and don't seem to demonstrate what you are talking about. Budding: your info doesn't show that she ever was a professor at Harvard or anywhere else. Gomprecht: your info could just mean that he got a postdoc, but never got a professorship. Naaman: it 's not clear whether she was tenure-track.

Working at Dalton (or another fancy NYC prep school) is probably a pretty sweet gig compared with a lot of university jobs.

What possibly made you think it was OK to randomly select these individuals and post their details along with their names, just to bolster your question? I think we could all assume that you aren't making things up. Can't the examples be anonymised, at no cost to your question?

@stats0007 I have heard that the German mathematician Kurt Heegner was a gymnasium teacher, but Wikipedia has almost no information other than his being an amateur mathematician. So he may have had no Ph.D. (despite solving a very advanced question in number theory).

To speak to the main part of the question, once I had my Ph.D. and understood math at a different level, a great deal of pre-calculus and elementary linear algebra looked beautiful. Go review the proof of the Law of Cosines.

@DaveLRenfro "Three or four of the students I taught at that HS were more mathematically talented than anyone I would likely have seen in a lifetime of teaching at most any (U.S.) state regional public college or mid-ranked private college." I believe this. Sad but true..

@MichaelMacAskill These details are all publicly accessible.

I have done this so perhaps can answer your question. I was a tenured full professor of physics at a state university but currently teach high school.
There are several reasons I chose to do this.

Most importantly, I love teaching and am great at it, while I dislike the constant drudgery of research and will not be winning any Nobel Prizes. I never have to hit my head against the wall of grant competitions or peer review.
There came a time when I needed to solve the Two-Body Problem and the high school option made me far more mobile.
I get more time for myself. Classes generally require only about 5 minutes of prep time each, if that. The time between periods is sufficient. Grading takes less than 10% of the time it took at college because of the level of study and can often all be done in class while students are taking a quiz or test. When school is out, I go home and forget about work. There is no constant e-mailing from students wanting help and extensions.
My interactions with high school students are closer and more positive than those with most of my college students. I never learned most of my college students' names. In high school, I have a relationship with every student.

The down sides are minor. The pay kind of stinks compared to what I used to make, but the free time makes up for that. I sometimes have to loop in the Headmistress when making grade decisions that involve teacher's discretion, which grates on my sense of academic freedom. But I think I can deal.

What kind of genius are you that requires only about 5 minutes of prep time for each class?

Another factor might be quality of life.  Most universities are located in cities, and some people eventually get to the point where the positives of an academic (or research, in my case) career no longer outweigh the negatives of having to live in a city

@jamesqf Of course this is a personal thing and for some people, the decision might be the opposite because some find higher quality of life in a city.

@user4052054 If you are capable of teaching physics at college, highschool physics is peanuts...

Ya sure? I mean, of course the material is easier, but you also have to direct that super-easy material to kids' minds, and make the class last the correct time. I don't think that teaching high school is much easier than, say, calculus.

@user4052054 Right, in my experience giving “great” lessons and 5 minutes prep is fundamentally mutually exclusive. Otherwise a great answer though.

@KonradRudolph When I think back to my high school (well, local more or less equivalent) time I can think of several great teachers who probably prepared very little. I think there are some people who, given enough freedom, can pull of great lessons with 5 minutes of preparation. I can also think of great lessons which took as much time to prepare as to give them (which I know because the teacher told me), it just depends on the kind of lesson and many other factors.

@Nobody Respectfully, you’re probably wrong. A teacher’s preparation isn’t usually visible but “effortless” lessons usually take a ton of preparation. In fact, both students and parents substantially underestimate how much work lesson preparation is. I’ve done enough teaching (and gotten good feedback), that I’m quite confident in this assessment. Conversely, I know of teachers who think they can give great lessons without preparation. They … don’t.

@User405 Making the class last for the correct time is something that comes easily with practice, especially if there are preset topics you have to cover. I taught college for four years and for the vast majority of that time I never kept students late or let them go early.

To be fair, I can imagine that the prep for a class might be very short when you've given it every year for the last ten years. It's not the same as the first time.

@Flyto and on top of that, it is at a lower educational level.  I can't imagine anything on subject at the high school level will stump anyone that was a tenured university professor.  Even going from Grade 12 to Grade 9 is a significant jump, as I was a grade 10 math teacher's assistant after taking all the Grade 12, and I can complete the 1 hr student tests in 10-15 minutes.

@Nelson If you think that a high level understanding of the subject itself means teaching at high school is a breeze, then I don't think you have understood teaching. For instance, I think that teaching fractions to middle schoolers (a subject I have some expertise in with a masters degree in algebra) sounds more difficult than teaching basically anything at a high school level. Teaching something like introductory general topology or commutative algebra to graduate students would be a breeze; I think I could do a decent job at that with 5 mins prep time.

Especially for maths and physics there is not much to prepare, once you've understood the topic. Especially for high-school level. If you have some experience in teaching e.g. from the years before, then there is not really anything that changes. Just a quick refreshener on today's topic does it. I've been giving a-level crash courses for students in the past years and it doesn't take much to refresh the mind and explain it to the students. So far my reviews did not suggest I explained it badly or appeared unprepared.

@Michael Mior: Sure, but that's a dog in the nighttime sort of thing.  The people who are content with their urban life won't be seeking jobs in rural areas.

@Nelson teaching at a lower level absolutely does not mean that less prep is required. Maybe even the opposite. It's not about whether high school content might "stump" a university professor (though you might be surprised!), it's about the time spent getting ready to teach it effectively. But my point is that much of the prep only applies the first time you teach it.

@infinitezero sure, explaining can be done easily a.o.t. aking it interesting (e.g. physics experiments) and math tools. E.g., one of my teachers used to show math apps for a honours-like course (with only 8 pupils or so) which were pretty new at the time. Of course he'd just show what he was working on because that interested him personally but it made the lessons much more interesting (even if not always related to the content of the actual lessons). If you want to learn about X, easier to read about it. Much more fun to have interesting discussions (for both teachers and students, IMHO)

I suspect the answer is they don't, at least not with the frequency your examples would suggest. Let's look at your examples.

....Ph.D., Harvard University 1998....

This does not mean that this person was a professor. This means they earned a PhD. A PhD qualifies one to do research; it does not give them a permanent position. If they cannot find a permanent position, or are not interested in continuing in research, they will have to make other plans.

... After working as a research mathematician for a few years ...

This person was probably not a tenured professor either. A "research mathematician" is a bit vague, but I suspect it is a post-doc position, or perhaps a non-tenured faculty-level position. Either way, when the temporary position expires, they will need to find a job.

Former Associate Professor of Classics, Sweet Briar College

So this one definitely has "professor" in the title, and this person probably has tenure too. However, "professor" is an overloaded term -- I suspect your question refers to professors at major research institutions who do research and publish and teach college classes and advise graduate students. In contrast, this person was a professor at Sweet Briar College, which has about 300 undergraduates, no grad students, and no mention of mathematical research on their website (that I could find) at all. So being a professor here is not all that dissimilar from being a high school teacher, and is quite different from being a professor at a major research institution.
As others have noted, Sweet Briar College has had severe financial and other problems recently; this could explain this particular decision.

...Asst. Professor of Arabic, Williams College (7 yrs 1 mon)

Assistant professors are generally not tenured, and 7 years is usually the longest one can postpone a tenure decision. I'm not sure what happened here, but I'm guessing that tenure was denied.
So, I would challenge your premise: you have not provided any examples of tenured professors at major research institutions who left their position to teach high school. I suspect this happens very rarely, and when it does happen, it's for highly personalized reasons.
You also ask:

wouldn't these [PhD mathematicians] be bored teaching the same (relatively basal) material yearly

Well, maybe, but if you don't become a professor you have to do something. Personally, I find "the assumption that you would not want to be a high-school teacher if you could be a professor [to be] a bit belittling" (to quote @Jeffrey). Some people probably enjoy teaching and working with younger students; others just need a job and prefer the familiarity of the classroom to the unknown of industry.

The assumption that you would not want to be a high-school teacher if you could be a professor is a bit belittling.

"Research mathematician" doesn't necessarily imply an academic position.

Concerning Dr. Gomprecht:  Sweet Briar College nearly closed in 2015, with most faculty receiving termination notices at that time.  Due to legal action, the college didn't close after all, and most faculty were offered their positions back;  but there was also a radical academic restructuring at the time, and I can completely understand a professor jumping ship for a more stable job around that time.

@Jeffrey It's also something I've heard for 20 years now.  I wonder if it's true.

@Jeffrey Accurate though. Not because being a professor is superior to being a teacher (although this is definitely the public perception) but because the academic career path is a substantial time and money investment, which is unnecessary to become a teacher. So if you want to become a teacher you don't do this investment. If you invest in the academic career path, chances are the aim wasn't becoming a high school teacher (exceptions exist but are just that).

I know (fleetingly) at least one person who was an Assistant Professor in maths at Sweet Briar until 2015. Did the department fall victim to the restructuring? Its website, at least, is still around.

To echo @Jeffrey there are high school math teachers with incredible amounts of mathematical understanding and communication skills that are just truly gifted at high school teaching. I'm 100% sure Eddie woo would have been able to get a PhD and become a successful mathematical researcher but he chose to be a high school teacher because it's truly his passion https://www.youtube.com/watch?v=tt2DGYOi3hc

Implicit in your question is the idea that it is "better" to be a professor than to teach at high school. If this weren't the case, then it's not surprising that some people would choose to teach at high school instead of be a professor. This assumption isn't necessarily true. It might be for you, and it might be "obviously" true for some people, but it's not true in general.
There've been a variety of essays by people who've left academia on the reasons they did it. Here are some examples: 1, 2, 3, 4, 5. You can Google for a lot more (search for "why I left academia" or "why I quit my professorship"). Common reasons cited for doing so include:

Dismal academic job market
Constant competition for (too little and decreasing) funding
Low pay
Lack of permanent contracts
Constant demand to be "available"

For example here's a paragraph from (5) above:

In fact, scientific life was proving tough. [Young researcher] found himself working 60–80 hours per week doing teaching and research. His start-up funding had run out, he had yet to secure a major grant and, according to a practice common in US academia, he would not be paid by his university for three summer months. His wife had not been able to move with him, so he was making tiring weekend commutes. It seemed that the pressures had reached unsustainable levels. Something had to give.

Many of these problems are not present when you teach at high school. You might earn less, but you also work less, so it's not fatal. You have job security. You have well-defined office hours. You won't be receiving emails from students begging for help in the middle of the night. You don't have to worry about what happens if your next grant fails to come through.
At this point you might as well flip the question around: why aren't more professors with PhDs leaving their professorships to teach high school? I'm not making a statement here that it's better to teach high school compared to being a professor; I'm just saying that it's conceivable that reasonable people will choose the latter over the former. Society might consider the former as more prestigious, but that doesn't mean it's "better".

Actually, maybe you don't work "less". But you work different.

@Buffy The young researcher in the quote worked 60-80 hours a week. I might be wrong, but I'd be surprised if high school teachers don't work less.

Actually, I have counterexamples. And note that some high schools have higher academic standards than some colleges. Generally, though, we need to better reward pre college teachers at all levels.

@Allure I have worked as a secondary (high) school teacher in the UK and I can tell you it is not at all unusual to work those sorts of hours during term time, but there is some degree of compensation when the holidays come around.

At least in the US teachers don't get paid for the summer either.  Just like professors they are able to make additional money.  I think people are very unrealistic about how much time teaching takes, just to start they are in school usually from 8:30 to 3:30 and teaching a lot more things and expected to grade homework and do class preparation after hours.

Because not everybody wants to do research their whole life, and because being a high school teacher is a fairly fulfilling job for many people.

Edited to remove ad-hominem attack. Please keep things civil.

+1 because it’s the only answer which focuses on something besides pay and prestige.

Some reasons might be:

Didn't get tenure
Better pay
Prefer to be a big fish in a small pond
Don't enjoy research
Never got a tenure track position (e.g. research mathematician)
Wanted to be in a certain city
College potentially shutting down (e.g. Sweet Briar)

In some disciplines, such as physics or classics, the number of tenure track positions is very low and many people never go into either tenure track or "teaching professor" roles.

RE the last point, my roommate at university wound up as a (tenured) professor at a school that folded. It took him 2 years (!!!) to find another professorship. Sometimes the dice just don't roll your way.

I have a feeling that Trinity (elite and very wealthy school in Manhattan) probably is a lot more enjoyable to teach at and better paying than Sweet Briar even with the pressure of the world of private schools in Manhattan.   According to Wikipedia "Trinity is also notable for having a full Classics department, which is widely recognized as one of the strongest in the nation. Nearly 40% of the student body takes either Latin or Greek." With its $40 million endowment no worries about closing anytime soon.

"Wanted to be in a certain city" is a good one. Most people in the academic job market take what they can get, which usually means having no choice in where they live and living far from family.

Probably additional point for your list: "Don't want their job to define their life."

I really don't understand why you find this all that mysterious. Some people with PhDs end out focusing on teaching, for whatever reason, and sometimes for them the best teaching option is at the high school level.
Some people from your list teach at the Dalton School. According to Wikipedia, "The Dalton School, originally the Children's University School, is a private, coeducational college preparatory school on New York City's Upper East Side and a member of both the Ivy Preparatory School League and the New York Interschool." Suppose you had to choose between teaching there and teaching lower level college math to classes of 100+ engineering students primarily concerned with their grades, and who mainly have little to no interest in the course material. (Yes, a lot of college math teaching is like that unfortunately.) Why is it so shocking that someone who is dedicated to teaching might prefer to teach at the Dalton School?
You ask "wouldn't these former professors be bored teaching the same (relatively basal) material yearly?" Guess what, most college teaching is the same way. The exception would be graduate-level teaching, but jobs with a lot of such teaching are hard to get, and usually go to people who have a substantial research focus. The ones who don't do a lot of research are mainly going to be teaching the lower level courses regardless.

I'd like to add a footnote to your last paragraph: Sometimes it's not about the material you teach, sometimes it's about the lives you impact.

@J.R. I've never taught professionally (well, at a school), but there's definitely loads of material that's taught on high schools that plenty of adults don't get and their lives would be far improved by a better understanding. Things like how fractions and percentages work. The impact of understanding e.g. that 2% growth is still exponential and unsustainable is quite eye opening, but something most people still don't get, and it doesn't require anything beyond high school level knowledge. Or that a 20% flat tax does mean high-income people pay more taxes, all else equal.

The three schools in the four examples you've given are widely considered to be in the top ten private schools in the United States. The academic standards at many top private high schools are much higher than you find at small colleges around here. My wife taught at a small directional state university and then followed that with one of the top private schools in NYC and has been much happier with the quality of the students she has here. She teaches college material (biology & chemistry) to students four or five years younger and not only do they grasp it better, but they try harder.
Plus, well, top private schools pay more than small universities.

I went to high school in Canada. It was a regular high school, not particularly prestigious but not known to be a terrible school either. Couldn't get any more "average" than that in my neighborhood.
I mention this because some answers have said that teaching in some private schools can be as prestigious as in a University. I was not at one of those schools, and one of the religion teachers had a PhD in theology.
Theology might not be the "typical" PhD, maybe there's not as many avenues for careers in research, but his rationale behind teaching in high school rather than doing something else was to pass on his passion to people who may not have been exposed to the subject yet (or at least not properly or in deep detail).
This rationale applies for other fields too, few PhDs get to introduce their fields to people who are truly new to it. For example, a physics undergrad student (and even more so for grad students) should already be at least somewhat knowledgeable of what physics is and be generally interested in the field as a whole.
Someone who has a passion for teaching might find it more enjoyable to introduce new people to their fields than to help advance the people who are already in it, regardless of their own degree of education.

And as a sidenote, he was the best religion teacher I ever had, he analysed the Bible instead of blindly preaching its contents.

Merci! Ne pas hésiter à incorporer votre commentaire dans votre réponse.

I agree with all the answers, including the skepticism that it is as common as OP thinks.  But one more reason I didn’t see mentioned is the offensive actions of some administrations done for the sake of publicity and/or athletics.

Can you elaborate? E.g. with an example (that is public)?

I’m sure most of us are aware of many scandals regarding athletes.  And it’s not just a new thing.  Long ago, a college basketball player was discovered in bed with a female he shouldn’t have been with (back in the days when that was taboo).  The president of the college gave a long speech about mercy and forgiveness, and he continued to play.  Later that year, the art student that had built a hollow sculpture near the running track was expelled because some other people were caught smoking weed inside it.

@WGroleau neither of those are examples of professors leaving their positions because of offensive actions of administrations. You made a good point that some may leave because of such actions, but it would be worth elaborating upon it.

He asked for a reason. That would certainly make me leave—or rather choose not to enter.

There is huge workload being a professor. Lots of duties and stress. You are responsible for courses, research in your department, maybe applying for grants, writing papers, teaching, supervising PhD students and people writing their MSc thesis.
At some point in life it can simply become boring and too draining on health to keep working as professor.
Other things simply start becoming more important in life. Maybe wants to spend more time with family. Pass on knowledge to future generations. Write memoirs. Maybe start doing other things altogether. Compose music, travel, any hobby you could think of et.c.

I don't think they leave professorships unless it is for a job of 'higher academic standing'.
As an example, my son goes to a private secondary school in the UK, St Paul's School (SPS), which is known to be very academic and very well-endowed (they have a Scanning Electron Microscope, so it's much nicer than any 'high school' I've gone to).  Several of his lecturers have PhDs, and some have lectured (i.e., assistant prof-ship, perhaps temporary, or postdoc-ed) at good Universities, such as Harvard and Cambridge. AFAIK, none of his lecturers have been tenured at universities. Note that at SPS, they should have relatively high pay compared to their secondary-school-teaching peers, and effective tenure. They can and do publish some academic research.
The High Master (equivalent of head-master) is a full professor of History at University of East Anglia. In becoming the high master, he had an effective promotion, housing provided, and I'm almost certain higher pay. He did take a leave from his professorship rather than to give it up altogether. He did continue to do research and for instance, has written a recent book together with some of the other History lecturers at SPS. This year, however, he is leaving his position at SPS having served something like 6 or 8 years. And, he will return to being a full-time professor, focusing on his research and teaching.
In other words, money and stability can be an incentive, but tenure at an established university is likely to trump all others. Temporary positions, career difficulties, all can drive people from pure academia to high schools.
Perhaps the most notable example of career difficulties (forced to resign from U of Minn because of post-war harassment by the House Un-American Activities Committee) is Frank Oppenheimer, former Professor, later High School Teacher, and founder of the Exploratorium (see Frank Oppenheimer (1912-1985). In that instance, Wyoming High School students were probably amongst the luckiest in the US.

"I don't think they leave professorships unless it is for a job of 'higher academic standing'." ... "Temporary positions, career difficulties, all can drive people from pure academia to high schools." Your answer seems built on a very narrow assumption that everyone is driven only by prestige and no one would move "downwards" unless they were forced to by some unfortunate circumstance. Have you considered that there may be reasons other than "academic standing" that may cause someone to change jobs?

This is absolutely a fair comment and my comment was unnecessarily strong. Some professors will opt for high schools. It is also true that some professors opt for colleges with little to no postgraduates and lots of teaching rather than the “prestigious” schools, at times because they actually enjoy teaching. I believe Oppenheimer, perhaps because of his high school teaching experience, learned to be an educator, wanting to drive change in education, something truly noble.

"and spent the next ten years as a cattle rancher in Pagosa Springs, Colorado". Whoa, way to prove that you're an American!

Or to prove you are “Not an Un-American.”

Congrats to your son! Sounds like a smart kid, at least smarter than I. You may be interested by https://academia.stackexchange.com/q/104193/13306?

Well, first of all some universities pay poorly. In my neck of the woods it is generally accepted that if you want to work at a UNI you are going to take a pay cut of at least 20 percent compared to what you would earn in the private sector. For some people this is worth it because the work they want to do they can only really do at the universities. For some people the pay cut is not worth it.
Also it is worth noting that some AP classes are in essence first year college modules, so if you find yourself in a High School with such a program you are not doing a curriculum all that different from a 1st year college tutor.
What is also a real bummer is the cutthroat way in which jobs are allocated. The politics and backstabbing nature of UNI's seems to be a real reason why some grow tired of it.
And lastly, some people are just natural-born teachers. Some don't get the amount of teaching kicks at UNI and yearn for more personal teaching environments. You should really not underestimate how hard it is to teach a 4th grader long division or how rewarding it is when you get a class of 4th graders to do it correctly.
It also seems to be a thing that in private high-schools because the parents have to sacrifice so much to get them in to the school they do tend to have better work ethics, not always but some of the time.
Teaching in such an environment where there is a thirst for knowledge, where you can often be better paid and have regular time of to spend with family and don't have much in the of Machiavellian antics, could seem to many a step up.

Labor exploitation at universities in some countries.
At the University the average salary per hour in the classroom for people under 40 years old can be about one half of what is paid to high school teachers (which in practice requieres highschool education instead of doc/postdoc as in the university)
Although the time for class preparation (unpaid in that countries) can be significant in both places, it is easier to safe the situation explaining highschool content, at worst you can be poorly clear. At college the chance that you get stucked in the blackboard are far much greater. For example, many times you have to be hours 3-5 solving problems smoothly in front of 50 students, and the next day (or lately the same day) doing the same in other completely different subject. Many times the positions are not in the ones specific areas of research. So you have to be about 40 hours a week explaining in front of students and almost the same amount of time studying in your free time. Notice that most of the time the positions are not for an specific subjet but for sets of subjects. When the year starts you have 4 or 5 subjects and the second half you may change some (or all) of them, and continues changing by 6; months periods. So the situation does not get solved with time.
The balance is that you can earn the same for real 20 hours a week in high school than for real 70 hours a week at university.
The election of reducing the number of hours at University is not an option because that high load is required for a salary close to the line of poverty.
I bet this is not the situation of the people that you put as example, but are reasons in other countries.


text:
First-year PhD giving a talk among well-established researchers in the field
I am currently a first-year Ph.D. student, before that (as I have posted about before) I was forced to leave my Ph.D. program after one year because of a bullying supervisor. Previously, I made a good relationship with other researchers in my field and other scientific volunteering activities.
Now, there is a workshop at a highly ranked conference, and I asked about the possibility of sending a paper for the workshop. They don't solicit papers, however, I have a good relationship with the professor who is the main organizer of the workshop, and they voluntarily  asked me to be a speaker in the workshop for 30 minutes.
The other speakers are the most well-established researchers in my field, I felt excited but afraid in the same time. I don't have yet any publications concerning the current research. I don't know if I should apologize, maybe the professor does not know that I have been kicked out from the earlier program. I don't know what I should do, all the speakers are the elite and I think I am not deserving to be among them as I don't have the same experience.
Should I try or would this be counterproductive to my future career?
EDIT 1
Thanks for answers encouraging me to try, while there are pragmatic answers that I don't have to waste the audience time, honestly, I have self low esteem since all peers have papers published in top journals and conferences, I don't know why the organizers listed me as a speaker, I am not doing great as other students or there is no indication in the right moment that I am doing fantastic research.

In addition to Allure answer, avoid apologise. Apologise for what?  Of course I do assume you will do your best and have enough to speak for a half an hour. Do not say things like "I am sorry.... " out of a normal use, audiences do not like that.

You should discuss with your current advisor, especially consider your current workload ie what you should be concentrating on and discussing any possible consequences.

Congratulations! Clearly you must be well thought of in your field, and your work must be valued! Well done :)

Do you actually have results?

Let's flip this question around and imagine that you, as a first year anthropology PhD student, are now visiting your high school. One of the students asked your former teachers if you would be interested in a local, anthropology-related research project they were doing (e.g., they could be investigating the attitudes of people towards those who are HIV positive, and contrasting how that varies between countries). The teacher promptly arranged for them to give a talk on their results while you were there.
The student feels excited but afraid at having to give this talk. She knows she doesn't have the pedigree you have, she doesn't know if she should apologize, maybe you don't know she flunked her latest exam, and she thinks she is not deserving to be giving the talk because she doesn't have as much experience as you. Should she go ahead and give the talk or would it be counterproductive to her future career?
I'm pretty confident you will say she should go ahead, and the same applies to you. These well-established researchers probably know (or can tell) you're a PhD student, and will not demand that you have done groundbreaking work on par with theirs. Instead of focusing on all the things that could go wrong, think of all the things that could go right: you get to present your work to a well-established audience. They're the people you most want to know your results. You get to network with them. You get to practice skills that you'll undoubtedly need later in your career. What's the worst that can happen anyway? Even if you give a truly atrocious talk they'll probably all have forgotten about it by next year.
tl; dr: stop worrying and do it.

The conference organizer thought you had enough snap to run a presentation to this august body.  Given that you have a previous and good relationship with the organizer I discount that you are being set up for failure.
You had planned to submit a paper.  Your paper was going to be among papers of the elite.  This is nerves.  At the worst while speaking folks will just check their email and converse in low whispers EXACTLY like they will do to some of the most well-established researchers in your field.
(Actual advice) Go back to the organizer and express both your desire at the opportunity and your concerns.  They are the organizer and it's their job to balance these things.  The feedback will be valuable and should help in whatever decision you make.

Go ahead and present (the whole point of conferences and workshops is to give and receive criticism on your and others' research)
Academia should be about ideas and research, not "status". If you have good ideas and are producing good research (NB: I say "producing", which is not necessarily the same thing as "publishing"), you should not feel embarrassed. Of course, it is often difficult to ascertain how good your own work is, which is precisely why we convene things called "workshops", "colloquia", "round tables", and, for that matter, conferences. Go ahead and present on your work, and go with an open mind that is receptive to what others have to say about it (although that does not mean you have to agree). You should trust the convenor's judgement in having invited you to present (and besides, if the convenor made a mistake, this is your opportunity to make a big break, just like Monet did when he was mistaken for Manet!).
Part of the remit of these fora is to encourage intergenerational dialogue on work-in-progress. And, by the way, the quantity of publications do not necessarily correlate to the researcher's ability. You should spend less time thinking about "keeping up with Jones's publication record" and more time thinking about your research.

Other answers make excellent points, but one more that hasn’t been mentioned yet as far as I can see:
Talks from junior and inexperienced researchers are very common.  However eminent some of the audience members are, they’ve all seen plenty of other talks from inexperienced researchers, and they probably remember giving their own first few talks when they were getting going.  They will be sympathetic to the fact that junior speakers may be nervous, inexperienced, and have less of a body of work to present.  None of those things are unusual or surprising; they’re just what it’s like for almost everyone first starting to give talks.

If you think you can give a good talk, do it. If not, don't.
I would lean towards don't based on the no papers and you not brimming with comments about your results within this question.
The issue is not your rank or your social confidence. Just that you don't have significant things to say in real content.

I'd change the "If not, don't" to "If not, practice and prepare."

It’s fairly common for researchers to present material/results not yet published. The only difference here is that the OP hasn’t published prior, but that shouldn’t speak to the quality of their currently unpublished work. The fact that the OP has been invited to speak tells me that they do have significant things to say in real content.

I'm well aware of that.  It's why I also mentioned she is not burbling with touted prepub remarks in question either.  Other data points are her being first year and a transfer with some hiccups.  Likelihood is high, bayesian assessment, that she has low results.  In any case I STILL left it open that what matters is what she has to say, what results.  So in the possibility she does, that is covered.

WBT, you missed my point. If she has results your advice is great.  Otherwise it's like putting yourself in the advanced ski class as a beginner.  You waste other peoples time as well as your own.  Part of growing up and being a non emo whiner is to consider others.  Not just tender bullied you.

I would remove the words "you think".  If you can give a good talk, do it.  Meanwhile, practice and improve, even if you already give good talks.

The issue I am raising is not presentation skills but accomplishment.

Any practice you can get at doing presentations is good practice.
No one expects a first year PhD student to know particularly much nor to make good presentations.

Some of the most interesting and up-to-date talks at conferences are from postgrads, and for good reasons.  A bit of enthusiasm always helps, but mainly it's because it's actually a talk about your research.  Many of the senior people end up, despite their paper title, summarising their group's work (only slightly updated from the same conference last year and several in between) before finally getting to the interesting bit near the end.
Nerves are normal.  Some people (not me) even think they help when giving a talk.  They generally don't show from the audience, and if they did most people would be sympathetic.
Concentrate on giving a coherent presentation of your work. Giving sufficient context and background takes a fair bit of time anyway, so you often need less material than you think.  And practice in front of an audience or two.  Your research group should give you at least one chance to practice properly in front of them, with questions and comments. Your peers from other groups in the department can be the best audience of all, as they're not experts in your exact work but in related fields (you would, of course, return the favour).  Once you've given your talk a couple of times (and dealt with any issues your audiences find), you'll feel much more ready to present.

What is the very worst that can happen? 30 minutes feels like a long talk, but it is pretty short in the grand scheme of things. Even if it's a real yawner, at worst people will use the opportunity to take a bit of a break. More likely, some people will find that it relates to what they're working on and some people won't, but that's what you always get.
Skip anything about your past or any apologies, just stick with a basic introduction and then get on to your work. The most respectful thing you can do is spend plenty of time preparing so that you give a clear, well-organized talk.

I recently had the same experience. DO IT! I was invited to speak at a very prestigious international conference - by layman standard these scientists were brilliant (Spectrums of Harvard, Hopkins, Columbia, Duke faculty...) As a senior undergraduate still, they were, to say the least, intimidating to me. But what helped me the most was this:

Believe that indeed, if you were selected, you deserve to be there.
I spent a FAIR amount of time adding "novelty," updating my talk with research that *just came out in 2019, hoping to establish solid ground.
Most of all, I straight up said, "I'm new to the field, but I am extremely happy and honored to be here. I believe I can offer some fresh perspectives and insight!"

I echo what has already been said! Hope that helps quell the nerves!

In the future, merely having a record of the paper you can list on your resume' / CV will be very useful.
Also, the talk is likely to go very well for you.  In the unlikely event it doesn't, almost no one will remember.  But the citation on your resume' will still help!
I had a talk that was considered a failure, but it didn't impact my career.

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Prepared for 40 Hour Research Internship - Changed to 20
A bit of backstory- I'm a rising sophomore undergraduate student studying computer science who is strongly interested in urban planning as well. This spring, I put about 12 hours a week of work into conducting undergraduate research with a lab at my uni and was offered a funded research assistant internship with the same lab this summer.
As this is my first time getting a real job (outside of high school), I had assumed that I would be working full-time this summer without communicating with my professor that much. Obviously, this was wrong to assume, but I have since learned from that mistake and take full responsibility.
However, my professor recently wrote me an email saying that he expects me to be working 20 hours a week, even though I have worked 40 hours a week for the first week of my job. I contacted HR and they said I was down as a full-time employee, but that if my professor expects me to work 20 hours, then I should only work 20 hours. This is the first time we have ever really communicated about work hours at all.
To make matters worse, I had planned to write a paper this summer, but the timeline I composed had assumed I'd be working 40 hours a week. The paper's deadline is on August 1st, and I'm concerned I won't be able to complete research working just 20 hours a week.
I am really interested in working on this paper, so much that I am even willing to put in time outside of my job to work on it, if necessary. My prof is unwilling to negotiate hours with me until mid/late July, and I plan on getting another part-time job now. I'm also taking 2 summer courses (online and CLEP though, so not too bad).
Should I propose to drastically narrow the scope of my paper so that I can finish it with a 20 hour work-week, or should I bite the bullet and try to keep working on the paper as it stands outside of work (time permitting)?

Have you talked to your professor about how to go about the paper specifically?

The communication problem is a bigger problem than anything else. You should be communicating on a regular basis about what your goal is for the summer, what timeline you need to follow to get there, and how that plan needs to be revised as the summer proceeds.

As in 50% of the questions on this forum, the answer to your question is: Talk to your professor. He may have a plan and can advise you on how to proceed. Or he hasn't thought the issue through and talking to you about it will make him articulate what his expectations are and match them with the ones you will have an opportunity to elaborate on this occasion. Or he doesn't have enough money to pay you for 40 hours and that's just the best he can do.
So many possibilities we all just can't know here but that a short conversation with the person in question can resolve!

You will most likely get paid for the 20 hours and the rest of hours unpaid. Honestly you can spend even more than 40 hours in the lab no one cares. This is very common practice. It is good that you at least get a funded position as an undergraduate student since most of this kind of position is non-paid.

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text:
I entered a PhD program out of fear of being unemployed and regret it. How can I gracefully undo my mistake and switch fields?
I want to switch careers from PhD in chemical engineering to data scientist. How can I go about doing this without having everyone hate me?
It is one year after I started and I am feeling miserable. I really hate the lab work I am forced to do (my summer lab work was better). I didn't like any of the chemical engineering courses. I didn't like my undergraduate courses either. The courses are just dry and pointless.
I took one probability elective and I really liked it and I wish I had moved into data science or became a developer. I really like programming and I am naturally good at it.
I also have a great girlfriend for the first time. We've been dating about 8 months now. She has made me more confident and more aware of how distorted my thinking and decision making is. She is just getting a masters in chemical engineering. She is graduating in one year, so I don't mind being around her until then. I would love to move with her to Seattle post graduation and live with her up there.
I want to move away from chemical engineering and become a data scientists or C++ developer. I know I am capable of achieving these things as long as I have some motivation. At the end of the day I just want a high paying job.
How can I go about undoing my mistake of applying to graduate school and switching to a more promising career field?
Edit: Removed  personal details and added updates
UPDATES: Started my data science career!
What I did:
1) Talked to my advisers and quit.
2) Found a new adviser who allowed me to get a masters in 1 yr doing data science things related to Spectroscopy.
3) Played up research experience and coding and landed a data science internship in silicon valley (pay is 27 K for summer).
4) Took a grad level probability theory courses to improve math background
5) Continued learning data science by working on my masters thesis
6) Continued to get a free masters degree because department is short chemE TA's and by TAing my tuition is waved.
7) I no longer have an assigned office so I now work in the library, and am ultra productive.

Do you know C++? What background do you have that would allow you to work in data science? I am not saying you don't have these things, I am just trying to figure out what your background is.

I have taken a C and a C++ course before and got an A in both of them. I really liked the details of the language and I like the challenge of making code run fast and detailed. I'm not too much of a fan of virtual functions, though.

This may be better off at reddit than here, due to much of it being personal. Do you have any ways of assessing how much of your disappointment about the PhD program relates to chemistry and how much is biased by your anxiety issues? As for the latter, changing the job will likely just kick the can down the road and you'll be posting a very similar question on workplace.stackexchange.com in a year. Ask others who know your situation (including your gf) for opinions, as they might see things from a better vantage point.

@dantonio If you like C, I would look into jobs in cyber security. Embedded systems is a growing field if you are interested.

@Vladhagen  For data science, I really love linear algebra and probability and statistics. I have always been good at linear algebra, enjoyed inverse problems, probability, statistical genomics.  When I went back to graduate school I had the vision of getting really good at these two things on the side, and applying them to my project, but that was overly optimistic. I will take a look at cyber security with Embedded systems.

@dantonio Keep in mind that loving something (viz. linear algebra, data science, probability theory) does not get one a job. I hear many candidates proclaim a love for data science, big data, programming, etc. Employers are not hiring candidates based on what the candidate is interested in learning more about. Employers expect competencies in those skills already. They do not care if you love it or not. They care if you can do the job.

@Vladhagen I have a very solid undergraduate level understanding of those areas. I have not taken any graduate courses. In terms of programming, I have already been good at it. I was better than my friend who, crammed 5 computer science courses into his last year and got a CS job at amazon.

@dantonio Is this solid understanding from formal classes or self study? Either is fine, of course. I am just trying to vet whether this is a matter of "Engineers are #1 at math, chemistry, physics, programming...." or if you actually have studied these subjects. It does sound like your programming abilities are certainly sufficient to find a good junior level programmer job.

@dantonio If you have interest, I would look at the national labs. I work for a lab in the East, but there are labs all over the US. They often want programmers with some engineering background. You would do mostly programming, and would just need some content knowledge about engineering.

People drop out of their PhD program like all the time. Don't sweat over it.

Congrats on making a decision and moving your life in the direction you want. That's awesome!

These are my thoughts as someone who is a data scientist, but also someone who used to teach and advise students at the university level.
Becoming a data scientist

I want to switch careers from PhD in chemical engineering to data scientist.
At the end of the day I just want a high paying job.

If you want to be a data scientist and earn a lot of money, you are either going to need to start your own company and hit it big, or get a graduate degree. (Or both).
Being a (well-paid) data scientist requires much more than programming. (That is still part of it, of course. But it is necessary, not sufficient). High end data scientists usually have a pretty extensive background in statistics and probability theory. I used to work for an engineering firm as a data scientist. They converted several mechanical engineers into "data scientists" because they could program. This ended up leading to many wasted months of work when I informed them that the test they were using required certain assumptions on distributions of the population they were sampling from.
Making an impact as a data scientist is much more involved than people think. Online classes and boot camps make some people think that they can get a certificate in Python and land as a data science lead at Google or something. It doesn't work like that.
Essentially what I am trying to tell you is this: I would probably not look at someone with a 3.5 GPA in chemical engineering and very little formal data science training for any sort of high paying data science job.

I had to take a bunch of online courses and I lacked the motivation to complete them.
I know I am capable of achieving these things as long as I have some motivation.
At the end of the day I just want a high paying job.

Avoid telling a future employer this.
Ask yourself if your motivations to become a data scientist are the money or the subject. Part of any job is being self motivated by the subject matter itself.
The money in data science is not guaranteed. Some of the very high paying data science jobs also require extensive education and immense dedication to working 60 hours a week.

Leaving the PhD program

If it didn't harm my lab, I would just drop out now without even bothering to complete my masters. Because I care about my lab, I don't want to drop out and harm things.

I would not feel obligated to waste 4 years of your life so that your lab mates don't feel bad.
If you are not enjoying yourself, do not feel bad about dropping out. You will be doing yourself a large favor in the end I think. There is no shame in dropping out to do something different. People drop out all of the time from graduate programs in order to pursue something they enjoy more.
Let me absolve you of overall guilt: Your situation is much more common than you think. I think there will be many people who will support you in pursuing a career you will enjoy and be productive in. Take confidence in yourself and don't let others discourage you.
Especially don't become your own worst enemy by tearing yourself down.

Overall advice

If you are not enjoying your PhD program, your first priority is yourself. Drop out. Now. Tell the program administrators your thoughts. You do not need to ask their permission to do what is best for your psyche and career.
Look into becoming a software developer if that is something you will enjoy. A BS in Chemical Engineering and demonstrated aptitude in C++ or Java can usually set you on a pretty good career path.
Don't look back.

You can also make a lot of money as a data scientist by joining a company, doing amazing work and making yourself indispensable, and getting raises. But this is harder and slower than first getting a graduate degree.

@PeterShor. Sure. That's the pathway for anyone to get a high paying job (in theory). But there is usually a certain level of "entry cost" to get into a field. People with a BS in Chem Eng and little statistics background usually will struggle to get into the track that leads to high level data science jobs. We do not place every possible candidate in a position and see how they develop. We select the candidate that is most likely to succeed. Based on the limited view I have into the OP's resume, I would not hire him over someone with a PhD in computer science emph. machine learning.

I actually know a few data scientists who don't have advanced degrees. It's doable, but won't be as easy (e.g. one might need to go through a company's graduate program).

I think I should clarify that "a lot of money" is double or three times more than the 30k/yr I am getting paid currently.

@dantonio You easily can get a job paying $75k in Seattle. Now, the cost of living is pretty high there, but.....it's livable. Your expectations for salary are pretty reasonable though.

@Vladhagen Thanks for your advice. I am still in graduate school but now pursing a chemE-datascience related project. I have landed a data science internship over the 2020 summer and am now just working on my master's thesis. I have also taken a grad level probability course. What else should I do to bolster my datascience skills?

@alluppercase Internships are great! Develop your Python skills (sk learn, pandas). I would also look into developing skills in data visualization. I've had people ask for Plotly, Tableau, ggplot (R). Great visuals of data help with non-technical management buy-in.

@Vladhagen Thank you for your advice. I will look into those things. I guess the one thing chemistry degree has given me is experience making graphs and presenting data.


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How do I find a supervisor for PhD studies?
I am thinking of doing a PhD. Problem is, I am not a student and the only professors I do know are the ones from the university I took my bachelor and Master's degree. However I was thinking of changing institution or even moving to a relevant scientific field and thus I do not want to contact one of those professors.
I have located some institutions and faculties I might be interested in following a doctoral programme. Question is how can I contact one of the faculty professors, since I do not know them either personally or academically? Is there any other way except of spam emailing them?

The difference between "spamming", which you should not do, and a completely acceptable contact is how targeted your emails are. Make sure you know what you want and what the professor you are contacting does their research in, and that these two things align. Explain in your first email why you want to work with that specific person, what your background is, maybe also include your university transcripts. You do not need to know the professor personally before contacting them.

You should email them and arrange to have a call. Many times, they’ll agree but a big thing is to make sure your research interests align with their work. Why them specifically? Heres a couple pointers: (1) you clearly convey drive and conviction, (2) clearly can explain his/her field and the lab’s general expertise, (3) what are you interested in advancing thats important? (But say you’re open to exploring new ideas too!)
Remember that they must also support a PhD student’s stipend, so it really depends on their funding and pending grants, so ask whether could support you or not - after the main talk.

Recruiting PhD students is part of their job, so you are not spamming them by expressing interest in receiving supervision. But make sure that you keep it concise and that you know their area of expertise.

A short discussion of how to choose a PhD advisor is given in the book "A PhD is not enough" by Peter Feibelman (chapter 3).  See this link for an online PDF.  Before sending any messages out I would recommend you make a list of advisors that you really want to work with (and knowing yourself the reasons why), rather than spamming a whole bunch of professors in the hopes that one will finally accept you.


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Math PhD in US vs Master + PhD in Europe
I'm currently doing my bachelor's degree in mathematics in Germany (Heidelberg to be precise) and I'll soon be applying for master programs / grad school. I basically consider two  options:
I) First do a master's degree and then a PhD in Europe and try to get a postdoc position in the US afterwards
II) Go to grad school in the US now and then look for a postdoc position in the US
Concerning I) I really like how math programs at universities in Germany (and other European countries) are structured and if I decide to stay in Europe for now, I will probably do my master's degree at Bonn. However, I am afraid that I'll have a hard time finding a postdoc position in the US having done my PhD in Europe, both because my experience (for instance regarding teaching) might not be what US universities are looking for and because European universities might not have as good of a reputation as universities in the US. I suspect, at least a PhD from Oxford or Cambridge might have some prestige in the US, however, I really don't like the 9 month master system there, as I feel like the material is rushed through and as I've heard, in order to get admitted to a PhD there, it is strongly advised to also do your master's there.
Concerning II) Since I prefer the European master/PhD system, for me to be happy with moving to the US now, it would be helpful to get a position at a top university. I already (successfully) did the TOEFL test but I would have to do the GRE (both general and math) test. Together with application fees this would probably add up to about 1000$ which is a hell of lot of money.
So I guess my questions are:
1) Are my concerns regarding I) justified? How hard is it for someone who just completed their PhD in Europe to find a job at a university in the US?
2) What is the reputation of places like Heidelberg, Bonn, ETH Zürich,... in the US? Is a PhD from Oxbridge prestigious enough for it to be worth it to overcome my aversion towards their program?
3) Do I even stand a chance of getting admitted to a top US program? I took a lot of courses and managed to score between 1.0 and 1.3 (if I looked it up correctly, this should be between 3.7 and 4.0 GPA?) almost everywhere. However I haven't participated in any REUs and don't have anything to offer besides the courses I took. Having read what people that got admitted to Harvard, Princeton, Berkely... have done prior to grad school, I don't think I can keep up with them.
4) Having said that, do you think it is even worth applying and spending such a huge amount of money in the application process?
5) Do you have any other piece of advice or experience to share?
Thank you so much for your help!

Is there any particular reason you want to end up with a job in the US? Understanding that seems instrumental to giving advise as it helps understand where the question is coming from.

@JJJ Well, I think I would like to get around and make connections and also I feel like there is more math going on in the US in the sense that there are way more places where active research is seriously done.

I guess it depends on the branch of mathematics. For example, AI, while maybe not strictly a subfield of maths, is actually booming in Germany. Even the Americans settled there to get a taste of the action. Remember that if your plan is very narrowly focused on the US, you may miss out if things (even out of your control, like geopolitics) make the US less important you might be better of in Europe (maybe with connections to Asia rather than the US).

You don't need to worry about Bonn's reputation in mathematics. It was very strong even before Peter Scholze was awarded a Fields medal last year. I would, however, recommend that you try to get some teaching experience. Many mathematics departments, including mine (University of Michigan) take teaching into account when hiring postdocs, and I know of one very strong candidate who was not chosen by my department because he had absolutely no teaching experience.

Is it true that German universities have low or no fees for doctoral students? US universities can be expensive, and their PhD may take several years longer than in Europe.

@Owain Somebody correct me if I'm wrong, but as far as I know, yes this is true. When doing a PhD in Germany, you no longer count as a student and therefore don't have to pay fees. Instead, you're employed by the university and get payed (depending on how much you teach)

I got my PhD in Germany (Heidelberg) and then did a postdoc in the US. I think that was the right choice: In the US, you will have to spend a couple of years taking classes, satisfying your breadth requirement, and you will likely have to teach alongside your research. There is much to be said about this system -- including that it teaches you to teach, and that you get a broader overview of what mathematics is -- but it all gets in your way of doing research. On the other hand, in the German system, you will most likely have relatively light teaching duties (if any) and have time to specialize. This will help you find a research area, and it will likely mean that you are better qualified than many American applicants once you apply for postdoc positions.
What is going to be important is that you form the personal connections on the other side of the pond to get a postdoc position there. Postdoc positions are not just awarded by accomplishments alone -- much as we would like that to be the case -- but also based on who you know, who your adviser knows, etc. This is so because when you apply for postdoc positions, your resume is still relatively thin: A couple of papers, a couple of conference presentations. In essence, every applicant on paper looks equally good, and so things like what university you come from, who your adviser was, and what the letters of recommendation say all have influence. The biggest influencer is if you know someone at the university you apply to. In other words, build these connections: go to conferences in the US if you can, contact people there to see whether they want to collaborate with you, see if your adviser knows people there and can support you for a 4-week stay. All of these things are going to matter.
Second, see that you can teach a course for a semester. Almost all US graduate students teach courses, and postdocs generally have to do the same. As a consequence, having taught (and having letters of recommendation that speak to your abilities as a teacher) is a criterion that is often considered when evaluating postdoc candidates. Try to make the selection committees job easier by providing them something in this area.
Finally, make yourself knowledgeable about the application deadlines in the US. These days, they are often at the end of October or November, for appointments that start in August or September of next year, at the beginning of the next academic year. (One can think that that is crazy, but that's how it is.) Most applicants will not yet have graduated at the time they apply, hoping to graduate at the end of the spring (May) or even summer semester (August). In other words, don't wait until you have your PhD to apply for a postdoc position -- you might have a gap of nearly a year if you do!

Thanks a lot for sharing your experience

In comparison with someone who is completing a PhD in the US, a candidate who is completing a PhD in Europe will have a few issues to contend with in trying to get a job in the US.

Bringing you to campus for an interview will be much more expensive.  Many institutions simply won't pay the travel expenses of interview candidates who are outside the US.
You won't have direct experience of the US higher education system, which can be quite different from systems in other countries.  Teaching experience is generally expected of new Ph.D.'s in math and any teaching experience that you might have outside of the US is likely to be discounted as "not the same."
Someone who has completed a PhD in the US on an F1 student visa can work for one year (any discipline) or longer (Science, Engineering, Math) in the US under "Optional Practical Training" before having to get an employer-sponsored H-1B or J1 visa.

Yeah, I have heard of these issues. Thank you for your input!

I think you should choose this based on personal preferences only. I see no career advantage either way. Bonn is a top level university by any standard as is ETH Zurich. You will find no feeling here that they are inferior in any way. Bonn, has, for example, several Nobel Prize and Fields Medal winners.
Whenever you do it, you will have to deal with visa issues in moving to the US, but you should have no academic problems with a good European doctorate. Language is unlikely to be an issue for any educated German today.
Not all postdocs require teaching, of course, or not a lot of it. Ability to advise grad students is a plus.

That sounds very reassuring. Thank you so much!


text:
Sharing referee/AE report online to point out a grievous error in refereeing
I submitted a short note to a math journal providing a counterexample to a result in literature that had first appeared in that very journal.
After eight months, I heard from the journal. It was a rejection. The associate editor based his rejection on one referee who had clearly misunderstood my counterexample.
I framed a polite email to the editor-in-chief (EIC) arguing why the referee was wrong in claiming that my counter example was not valid. I don't have high hopes of hearing back from the EIC. He never responded to my emails asking for status updates in months 4, 6 and 8.
For the sake of science (the algorithm to which I propose a counterexample is used by folks in my area of applied math), I intend to upload my paper, the referee report and the covering letter of the associate editor (all of whom are anonymous) on my website and on Research Gate. Alongside this, I plan to upload an explanation explaining why the journal was mathematically wrong to reject my work. I essentially plan to simply upload the letter that I have written to the EIC where I argue why the referee/AE are wrong.
Is there any legal reason why I should not upload the referee/AE reports?
How else can I handle this messy and depressing situation?

Calm down. I got all kinds of wrong or terrible referee reports. The solution: Go to another journal.

For legal advice, consult a lawyer. Any advice you get here cannot be trusted in any legal proceeding.

@J.FabianMeier Even if everything after the first two words of your comment is good advice, why chuck in the personal insult at the start? Nothing in the OP's post suggests that they are not in fact perfectly "calm".

@MarkAmery "Calm down" is not an insult. I got the impression that the OP takes this issue very personal ("messy and depressing situation"), and I tried to tell him/her that is not necessary.

Is there any reason why you can't submit this article to any other journal?

@J.FabianMeier On the other hand, "calm down" is pretty patronizing. It can be justified, it can work really well, but it can also be quite aggravating. I don't mean that as criticism of what you said, just as something to also keep in mind.

https://arxiv.org/abs/hep-th/0208093  http://sites.math.rutgers.edu/~zeilberg/YuriT2.html  http://sites.math.rutgers.edu/~zeilberg/RefTipesh.html

For the sake of science [...], I intend to upload my paper, the referee report and the covering letter of the associate editor (all of whom are anonymous, BTW) on my website and on researchgate. Alongside this, I plan to upload an explanation explaining why the journal was mathematically wrong to reject my work.

Besides possibly being a copyright infringement and coming across as immature, this isn't really going to contribute anything to science.  Your paper is not going to attract a significant audience if it's only on your website and researchgate.  arXiv would be slightly better, but not much.
Your contribution to science is the paper itself, so the best way to handle this situation is to revise your paper to make it more clear, particularly to a reader who may have the same misconceptions as the reviewer did.  Then submit it to a different journal.
To be clear, I do not think it is a good idea to post an explicit rebuttal or criticism of the referee's report,  with or without the report itself, on your website or in any other public forum,.   It is unprofessional, and it will cause people to focus less on the content of your work and more on your negative reactions.  You can rebut their concerns indirectly within your paper itself ("it may appear that X, but in fact this is not true because Y"), but do not "call out" the referee or the journal.

Yes! Revise for clarity and submit elsewhere. Many math journals won't consider a paper after rejection.

I disagree that arXiv would be slightly better. It would be actually much better. These days, I’d guess there are more people who read their daily arXiv fix than those who regularly browse through printed journals.

@EmilJeřábek I agree that you're more likely to come across it when you're perusing, and likely many would see it through the arXiv. But when I'm digging through older literature, I don't really consider non-peer-reviewed work to be reliable enough to depend on, and I'd be concerned that after a few months (or etc.) the paper would disappear.

@RichardRast To clarify my comment, I absolutely agree that it is important to get the paper vetted and published in a proper way. I’m just saying that putting it on the arXiv (rather than just a personal web site) already makes it reach a large audience.

Note, though, that posting referee reports and responses to same to arXiv is not allowed.  I remember a situation on arXiv some years back where the author tried posting a version of a paper including a referee rejection and his response to it, and the arXiv editors ended up scrubbing that version from the system somehow.

I read elsewhere in this site "referees are always right, even when they are wrong", meaning that if they misunderstood your paper, there is a high chance that readers will have the same mistake, so clarification is in order.

I'm sorry about your bad experience. However, your proposed course of action makes you look petulant and childish. You're not going to make any friends or impress anyone. Trying to tell the world that the editor and referee were wrong is just a waste of your time. Everybody has misunderstood a paper at least once in their life and, sometimes, you get unlucky and misunderstand a paper that you're refereeing.
Wait a few days, then see if the referee doesn't actually have a point. Communication failures are rarely 100% the fault of either party and, even if it's mostly the referee's fault that they misunderstood, you can probably still make your paper clearer, so other people don't misunderstand it in the same way. Do that and resubmit the paper somewhere else.

Is there any legal reason why I should not upload the referee/AE reports?

As mentioned by @Buffy, seek a lawyer for legal advice, not this website. But honestly, this would look really bad on your CV, as it is very unprofessional. Furthermore, what if every prospective employer/advisor/grant manager came across this piece of work and after a quick and careless reading, this person sided with the referee?

How else can I handle this messy and depressing situation?

Insist a bit more on the same journal, you might have been unlucky enough that the referee was the author whose mistake you were pointing out. If they chose another referee or if you clarify your work, you might get accepted. Or, as others said, publish somewhere else.

"this would look really bad on your CV" Nobody's proposing to put it on their CV. But I agree that it would damage the asker's reputation.

@DavidRicherby : I considered saying "this would look back on your background check". I wanted to convey the ideia of things you are judged from, by a person whose judgement matters to you.


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For a first year math PhD student, should the student read their graduate level math textbooks page by page, sentence by sentence?
Question is: For a first year math PhD student, should the student read their graduate level math textbooks page by page, sentence by sentence?
I often hear professors say that that's a bad idea, and that it's better to look at problems first, and then go back to read as necessary.
From undergrad training though, I like reading math books and working through them methodically, namely, going cover to cover (e.g. for calculus, linear algebra, introductory analysis, probability, etc.)

Different approaches work better for different people.  Why not try it one way or another for a period of time, and see how it feels to you?

I think you'll find that you simply won't have enough time to read through your textbooks sentence by sentence.  This means you will have to figure out what you can get away with knowing more superficially.  Keep in mind that your eventual goal is to produce a piece of original research, not to know everything that's already known.

While it may be good for something, it isn't really the best way to learn anything. To learn, you need to get practice (reinforcement) and feedback. The exercises in the book will do two things for you if the book is a good one. First, they will exercise the more important ideas, giving you the practice, but also giving you an outline of the chapters. Second, the problems will point you, indirectly, to the examples, theorems, and proofs that are the most important to study.
The big idea here is that not every word in a math book has equal weight.
Trying to "memorize" the textbook is also a terrible way to prepare for exams. Find more exercises and solve them.
Your brain isn't like a thumb drive that you can pour information in to an then expect that you have "learned" it. Think of a novel that you read a year ago. How much of it do you really remember? If you read a lot, then it is unlikely that you will have retained very much about that old book. A few people can do that, but they are very rare. Chances are slim that you are one of them.
Finally, if you can't solve an exercise you know what you need to ask the professor about. Hopefully the prof will give you feedback on your work - the other essential to learning. That way you are less likely to develop misunderstandings that need to be corrected later.

The generic answer to this question is: it depends. Textbooks are written in such a way that both instructors and students can use different approaches to teach and learn the material, respectively. There is no one “right” way to use a textbook.
Professors who recommend certain approaches are likely speaking from experience and their own personal preference. It can be a good idea to follow the advice of those who are familiar with the material (because they learned it themselves at one point) and who have been tasked to teach it to students; they will likely have good suggestions.
If you personally feel that you can learn better by using a particular method (even if it is unpopular and not genetically recommended), you should use the book in that way.
The bottom line: if you are actually learning the material and are motivated to continue studying in that way, you should do that.

I would stick with the process that worked well for you before, until, you find it doesn't.  As far as glancing at the problems, before.  I don't think you have to--think you can use your old practice (doing the problems after).  As long as you are reading the text in an engaged manner (working examples, doing skipped steps to the side, etc.) you should be fine.  Of course, do the problems after.
One other answer mistakenly thinks you are talking about memorizing the text, but I don't think that was your question, just if you should pre-look at the problems.  I don't think it matters that much, especially if the pre-look is reasonably fast.  But in any case, there will be some recursion.  Because as you work the problems, it will force you to go back and look at the text again.
P.s.  Good pedagogical question.  Might also be of interest on one of the math forums.

Not the question, no, but too many students think that memorization is the key. It is not. Just a warning.

The answer to your question depends not only on your style of learning but also on your professors and the textbooks they choose. Some professors regard the textbook as just a convenient source of homework problems or a reference for details that don't fit into the class schedule. Other professors regard the textbook as the first place you should learn the material; their lectures are not so much systematic presentations of the material as commentaries on the textbook. This difference in professors' attitudes affects not only what they do in their lectures but also which textbooks they choose for their courses. In particular, some but not all of your textbooks are likely to be appropriate for self-study. (I found that some textbooks, from which I was unable to really learn anything as a first-year Ph.D. student, were excellent references later when I needed some more detailed information about those topics.)
So I suggest you see (or ask) how your professors view the textbooks and then use the books accordingly.
Of course, if you have the time, it's never a bad idea to read more, to attack more problems, and generally to do more mathematics than your professors require. But your first priority, especially at the beginning of your Ph.D. studies, should be to learn thoroughly what your professors want you to learn.

I am a second year PhD student in statistics (I know, if mathematics at all it is applied maths). I like to have books around me. I consult them all the time.
Sometimes I realise that for my particular research problem I need to understand some point in complete detail, so complete that I could explain it to a first year undergraduate. In that case, for someone with my learning style, there is no alternative but to slog through every line, in detail, and do all the exercises.
But sometimes all I need to know is that at some point in my thesis I will find myself writing "it can be shown that ..." and just applying the result.
My experience so far in my PhD research is that it is not always easy at first to identify which of these two options is right. But I do know that if I chose option 1 as my default, I would not have got as far as I have with my own research. So my adivce would be: try to understand the main results first until you know which of them you will need to examine in such detail that maybe you might overturn them or add significantly to them.

There is lots of good advice in these answers. I think it is also helpful to try a method that is in between yours and your professors' suggestions. Go ahead and read the textbook line by line, but whenever you get to a theorem or lemma, try to prove it yourself before you read the proof. This can give you a chance to test your understanding in a way where you can get immediate feedback. If you have no idea how to start the proof, read the first couple lines and then try to finish it on your own.
Of course, there will be several times that you can't do the proof on your own, and you shouldn't be discouraged by this! Trying it first will help you better understand the proof when you read it, though.
Along a similar line, whenever you read a definition, try to think of some examples and non-examples that you're familiar with already. For example, if you were reading the definition of a group for the first time, you might think about how the integers under addition are an example, but the natural numbers are a non-example.

Depends on the book. Undergraduate-level textbooks tend to be easier to read cover-to-cover. After a while books end up being less self-contained and are better as references, like encyclopedias. That suits research-level work which revolves around research papers. Encyclopedic references are not meant to be read page by page.


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Journal standards vs. personal standards
I am currently reviewing an applied math paper that I don't think is great; indeed, I am hesitant to accept it even with major revisions.  The language is poor, I'm not convinced by the arguments, and the numerical results are difficult to interpret based on how they are presented.  However, based on other work this journal has published (in particular, other papers by the same authors), I think the quality of the journal I'm reviewing for is a bit lower than my personal standards.
Should I based my final recommendation on my own standards, or the journal's?

Too much nonsense is published. If the paper has poor language and is not convincing, it just should not be published, even if the journal published other similar papers before.

Rather than consulting the journal's previous publications or Stack Exchange, consider the instructions the journal provides to reviewers.

If you don't think a journal has appropriate standards, you should not review for the journal.

There are many different notions of quality of a paper:

accessibility of the presentation,
soundness of the arguments and conclusions,
relevance of the research.

Ideally, the level of journals only differs in Point 3. Realistically, there are some differences in Point 1 as well (ironically, I find that middle-level journal score best here, but that’s a different story). However, even mega journals aspire Point 2 – and outrage ensues if they clearly fail.
I would therefore not let the level of the journal influence assessment of deficiencies with respect to soundness, i.e., if I consider a paper unsound, I recommend to reject it, no matter the level of the journal.
Also, think for a second what would happen if all reviewers would recommend to accept all papers that are better than the worst paper in the journal in question:
Due to the variability and laziness of reviewers (and the abundance of bad papers), the threshold would decrease perpetually.
Nobody wants this.
Also, irrespective of the journal’s level, I note everything I see wrong with a paper, and let the editor decide whether this is a sufficient reason for rejection. As language problems (and some other presentation issues) can be fixed by a copy editor or similar, I would not even let them influence my main recommendation, but just recommend heavy copy-editing or similar to the editor.

Minor language problems can be fixed by line-editors. The big problems (clarity and flow, calques, organization, poor notation, etc) cannot. These only authors can fix. In these cases, I would recommend major revision or even rejection (on 2nd/3rd iteration in absence of improvements).

Actually, it is the editor's decision to accept or reject. Give an honest recommendation according to your best judgement.
I suggest you make your best effort to help  the author(s) improve the paper. Your recommendation to the editor can be whatever you think best. But don't give it a higher rating than you think it deserves (or lower, for that matter) as that will skew the information the editor has to work with. If you think it has low quality you can certainly say that to the editor.

I replaced "decision" with "recommendation." ;)

As a reviewer, your role is to provide sufficient information to the editor that they can make a decision about how to proceed with a manuscript (accept, accept if major amendments are made, reject). I have reviewed some manuscripts, and used many more in research. From my perspective:

manuscripts should have been peer reviewed prior to submission, particularly if there are multiple authors. This solves most manuscript problems.
language should be clear. Everyone has their own writing style. I don't suggest changes to language in a manuscript unless there are major problems in my understanding of the prose, and I therefore assume that the journal readers will have the same problem. I don't edit prose, my edit is a comment about what precisely is unclear with a request to amend the text to clarify the content. I do not know if this is what you mean by "the language is poor" or whether you mean that the person does not have English as a first language and therefore their translations into English are poor. See how clarity is good?
state how the arguments are unconvincing. Also, your interpretation of how the arguments are unconvincing may not be at the same standard as those of others. Sometimes this has little impact on whether the manuscript is published.
explain exactly how the numeric results are hard to understand. You may be the only reviewer with expertise in how those numbers should be reported.

"whether you mean that the person does not have English as a first language" When peer reviewing, please try to avoid the appearance of bias or discrimination on the basis of language background.

@AnonymousPhysicist my point is that the OP did not clarify what they meant by "The language is poor". If it was due to ESOL, then the OP is suggesting that one reason for recommending rejection is due to the ESOL.

Just explain the strengths and weaknesses of the paper without judging, give constructive critique where possible. Also try to be concrete, e.g. say that theorem 3.5 is not obviously true as claimed, in fact you don't see how XYZ follows trivially, instead of just saying that it is not convincing.
In the end, you can give a recommendation and you could base that on the level of the journal, yes. However, the final decision is made by the editor, and for them, your observations about flaws and good points are much more important than your personal opinion (unless, of course, you are the most famous researcher in this area^^).

One kind of has to judge though, because one has to check "revise" or "reject".

That's a completely unhelpful answer from an editor-in-chief's perspective: We want the reviewer to judge. That's the role of a reviewer.

One thing that would be good to know here is the exact meaning of "accept with major revisions". The emphasis may be on "accept" or on "major revisions". In many (probably most) journals I'm familiar with (I'm from statistics), a "major revision" actually means that the reviewers get the paper again and can still reject it if issues are not appropriately addressed. This is however not everywhere the case (and may in any case depend on what other reviewers think).
My understanding of the question is that there's nothing clearly wrong about the paper, and that there is a contribution with at least some originality and some use to somebody. Such papers should in my opinion be publishable somewhere, and whether the standard of the current journal is low enough is ultimately the editor's call, although you may have your opinion. However it seems that things are unclear, so that currently it cannot be appropriately evaluated whether the paper is correct and/or a contribution of some value.
Many journals offer "reject with encouragement to resubmit" as option in cases like this, in which from the current version it isn't quite clear whether or not a revised version will be publishable, whereas "major revision" in my view implies that my subjective probability that this will be OK after (maybe more than one) revision is substantially larger than 50% (in case "reject with encouragement to resubmit" is not offered I'd cut out the "substantially").

I don't think I've ever seen "accept with major revisions" as an option; usually the distinction for requiring major revisions rather than minor is that in the former case you will need to see the revisions before deciding whether to accept.


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ratemyprofessors' alternatives for francophone or German-speaking countries
Are there some equivalent/alternatives for the sites like ratemyprofessors.com for francophones or German-speaking countries?

Are you sure you can't use that site? Some UK schools are there, at least.

Since it says in the "location" drop-down, "I'm looking for a school in" and the only options are US states or territories (including DC), my guess is it wouldn't be worth trying to hack it for that.

To the original poster: This is a legitimate question, but ... be careful what you wish for!  It's not exactly scientific.

@kcrisman Cambridge UK has some listings. It may be possible to add universities outside the English speaking world. But they would be hard to find as the UI seems to limit to the US. But searching for a university seems to work. Also, as a prof, I found it useful even when I was occasionally blasted there. Other students will come to your rescue if untrue things are said. But, yes, not scientific.

@Buffy thanks, I wasn't aware there were any others there.

For Germany, there is meinprof.de.


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What "soft-skills" does one need to succeed as a mathematician?
My question is about "soft-skills", i.e. knowing how to handle Latex, giving a speech or giving a lecture, or other knowledge that could be useful for a career in mathematics.
Skills that (all) mathematicians need, but which are not necessarily something that one learns studying the mathematics of text books or lectures.
This knowledge should therefore benefit mathematicians of varying disciplines and not only the algebraic topologists or the number theorists.

The term "soft skills" usually refers to interpersonal skills. Things like LaTeX and general writing skills would usually be excluded. All of these are of course useful. Furthermore your premise is not entirely correct: all these skills can be (at least partly) learned from books --- there are excellent books on LaTeX, general writing, presentation skills, and even on how to make friends.

That's the reason why I put it in quotes. I could not think of a more suitable term, so I explained the thing that I am looking for more clearly in the question body.

" Studying the mathematics of text books or lectures". I didn't exclude learning skills from books, but I excluded specific mathematical knowledge. @BorisBukh

A few that come to mind, and are probably valid in other fields also --

Learn how to give good talks.
Learn how to describe your research informally. Say you meet someone at a conference, and they ask you "What do you work on?" Can you convince them that what you work on is interesting?
Learn how to come up with interesting questions that you don't know how to answer.
Learn how to read a paper. Can you figure out "the big idea" without getting bogged down in the technicalities?
Learn how to meaningfully participate in a math discussion when you're less than 100% sure what's going on.
Develop a gut feeling for when a subject will come in useful. For example, "This lemma feels like I could use algebraic geometry to prove it", without knowing initially what that form would take.
Get a sense for what other researchers in your field consider interesting. What is worth writing a paper about, and what is worth giving a talk about?

There are many, many more -- and none of the above are easy.

"how to meaningfully participate in a math discussion when you're less than 100% sure what's going on" I would put it more bluntly: learn to ask questions when you don't understand something instead of nodding with a clever face while not having the slightest clue on what the other person is talking about. The best time to acquire this skill is when you are still a graduate student, but it is never too late :-)

@fedja: I certainly agree that's important when you understand 0%. I was actually referring to when you understand some, but not all of what the other person is saying. I've often found it productive to keep the discussion going -- I get some idea for the big picture, and can fill in details later on my own.

Understanding the research process and how to overcome hurdles and frustrations. Some of these points have already been addressed in other answers, but I think an explicit list of things around this is good. This means:

Knowing how to find interesting research questions.
Knowing how to get started on the research process.
Understanding what it means to put time and effort into solving a research problem.
Knowing how to find collaborators that would be interested in working with you, and then working with them in a productive manner.

... and many other things


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How can I learn to establish good research questions?
My problem is that I struggle with finding/posing questions that are worth researching.
I think the reason is my lack of experience, but I am eager to learn and don't want to only rely on my supervisor.

Hmmm. Muddle. Try. Fail. Muddle. Repeat. Repeat. Try. Succeed (partially). Muddle. Refine. Muddle. Succeed (maybe).
To paraphrase a bit of wisdom from another field: Posing good questions comes from Experience. Experience comes from posing bad questions.
There isn't a plan in mathematical research (or in most other fields) that will guarantee success. You are moving into the unknown, which is, well, unknown.
But there are a few hints that work (sometimes...partially). First, you need to deeply understand the essence of what you are about. This requires insight and insight isn't always gained even by earning a doctorate. Insight is what knocks you off the donkey when you aren't expecting it. Insight is understanding something one moment that eluded  you the moment before. Insight sometimes comes from hard work, but it also sometimes comes from just riding on the donkey to get somewhere.
The hints:
Read a lot of papers.
Think about possible extensions of those papers.
Think about possible variations of those papers.
Think about applying the method of proof of those papers to some other, possibly unrelated sub-field.
Take a lot of notes and update them when you have any small insights. I find it useful to carry some of those notes around on index cards, just to refresh my memory (on the donkey).
Think hard about the essence. What is the derivative? What is the essence of the derivative? Why is the definition like it is? Are all of those parts essential? Can they be changed? What would I learn if I change something there? Derivatives work nicely on nice functions. What if the functions aren't nice.
Talk to a lot of people. Share ideas, don't hoard them. Work together. Ask "what if".
Take risks in your thinking. New sub-fields of math have often arisen from "risky thinking". Algebraic Geometry? What a wild idea.
And, finally:
No guarantees.
Try again. Make notes.