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What should I do if the potential supervisor copied my email to another potential supervisor who has already rejected me?
I contacted potential supervisor A (UK university), and A told me he is not sure whether he could supervise me. He copied my email to potential supervisor B (UK university), and the very awkward thing is that B has already rejected my application before I contacted A. So awkward! What should I do? Do I need to send an email to A to say something?

Oof, that does sound awkward. Not much you can do, though ...

Why is this awkward? What did A ask B? Should B be co-supervisor or comment on the topic? Or does A propose that B becomes the supervisor?

You may also find that B always rejects applications unless they come with a recommendation from someone else

I disagree that this is all that awkward: students are expected to correspond with multiple professors looking for a PhD position, and most of them will not have space for the student or will choose someone else (or the student will!). In this situation, both supervisor A and the student thought supervisor B might be a good fit for the student's interests - that validates both supervisor A forwarding the message to B and the student's original contact to B.
I think it's fine to do nothing, but I think it would also be fine to reply-all to the email thread between professors A and B and say both 1) a brief one-sentence 'thanks' to A for considering you and for helpfully suggesting professor B, and 2) acknowledge briefly (one sentence) that you've already heard from professor B that they do not have a position for you.
This accomplishes two things at once: it shows you are gracious, as you'd like to be seen by both A and B as they are professors in your field and will be your peers in the future if your plans work out, and it lets professor B off the hook for needing to respond to A.
No need to apologize for awkwardness or go overboard. Focus your remaining energies on other opportunities.

is very good but I would not do 2). Prof B can change their mind, OP suggesting that it is over already may be premature and closes the door. B may want to respond or not.

@WoJ and it might be the thing to tip B's opinion over. Perhaps he values A's viewpoints and might stumble into something he didn't notice upon his previous contact with the Student. Or he might reconsider his position. B might see A's forwarding of the mail as A believing that Student is a good fit for B's research team.

@Woj I do not think that A redirecting to B is meant to be an endorsement or anything like that; rather, the student probably contacted them with research interests that A recognized overlapped best with B's interests. After all, OP reached out to B first, anyways, probably because they seemed to be the best fit initially. Surely B is capable of determining who is a good fit for their own team, and they have already reviewed the student's application.

The scenario @WoJ describes actually happened to me: I thought joining Prof A was ideal for a postdoc and wrote him, and he didn't respond. A little later, I wrote an e-mail to collaborator Prof B saying I was looking for a postdoc in subject X, who simply forwarded my e-mail to Prof. A. Prof. A responded with an interview request, saying that B prompted him to take another look, and quickly thereafter I received a position with A.

@user71659 Seems a bit different here, where B has already had a look and rejected (which is a stronger behavior than merely failing to both looking and responding). But yes, I suppose if one really wants to keep all doors open you could hold out hope that this mention from A will suddenly change things... I'm doubtful. There are lots of other supervisors out there.

It could be that A was not aware that B had already rejected your application. So, maybe, A was trying to help you by forwarding (CC) your email to B to see if B is interested in being your supervisor.
For now, it seems that both A and B have rejected your request to be your supervisor. Is it true ?
If yes, then you should probably move on and look for a different supervisor. There is no need to talk to A about the fact that B already rejected you.

There is no need to contact A about this issue, but no reason not to stay in contact unless actually rejected.

@Buffy. OK. I've just updated the answer to better reflect my original intention.

Person A has not rejected you. They were, perhaps, trying to be helpful, possibly thinking B would be a better choice. While the situation seems awkward to you, it may not seem so to them, if they are friends/colleagues.
Person A hasn't said why (unless you omitted it) that they "may not be able" to supervise you. Perhaps it had to do with themself, not with you. Perhaps they could change the balance. If they hadn't seem something positive in your request, then they wouldn't have passed it on.
I would continue to try to get A to supervise you, provided that you believe they would be a good choice for reasons you've looked in to and not just a random ask. Give them a good reason to overcome their potential reluctance.
But, pursue all other options in tandem. There is no reason to step back from other possibilities.

You should do nothing.  B will probably say thanks but then ignore the suggestion.  You both already know B is not interested.


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How should I answer a question asking to compare the applicant to students previously sent to the university, if there are none?
One of my students is applying to Caltech for a PhD. He asked me for a recommendation letter. I haven't written a recommendation letter before. He is a bright student and I want to help him.
On Caltech's website, there are five questions a recommender needs to answer. The last one is "How does the applicant compare to any previous students who have come to Caltech for their graduate work?"
However, no one from our department ever applied to Caltech. My university is a well-reputed one, but the department is small. Most of the students either choose to pursue a PhD domestically or go for industry positions. Applying for PhD in the US is unheard of. That's why I'm very keen on recommending this student as he is breaking barriers and is the first in our department with such ambitious goals.
I do know that on a letter, it wouldn't look good if I mention that none of our students have joined Caltech. How should I answer this question in a positive light that would be helpful for my student?

"I can honestly say that I have never recommended a more brilliant, energetic, or talented student to pursue further studies at your institution."

"Most of the students either choose to pursue a PhD domestically or go for industry positions" What country? OECD, or developing nation? Do you have any students that have gone to other famous, top-tier universities like Oxford or Cambridge, or to the top university in your country, to compare them with?

Perhaps give comparables?

You can turn it on an sort of advantage perhaps. His/her motivation should be emphasised by this unprecedented decision. How to find the way is your task, but I hope you get what I mean.

Answer it honestly. You won't be the first to just say that no one has applied before.
You can then say, if you haven't elsewhere, that you expect they will be highly successful and are proud to recommend them.

The question quoted by the OP is "How does the applicant compare to any previous students who have come to Caltech for their graduate work". Rather than interpret this as being about former Caltech graduate students from the OP's own institution, the OP could write about other students known personally to the OP who were graduate students at either Caltech or PhD programs with Caltech's reputation or higher: UCLA, Berkeley, and so on. I think that might be a better reply than answering essentially with ¯_(ツ)_/¯ .

@KCd, that would be an impossible question to answer. I have no idea about Caltech grad students, my own or any others. Georgia Tech (etc.) I could say something about and the university I went to, but not otherwise.

Buffy is right. It is impossible for me to compare my student with other Caltech grad students as I don't know them personally.

It's a silly question to begin with --- academics giving recommendations should be comparing the student in question to other students they know/have taught (at same level, etc.), not students at an entirely different institution they have never met.  Just answer honestly and resist the temptation to tell them how stupid their question is.

CalTech has a reputation to maintain. So they presumably want to admit students who are comparable to (or better than) previous students. That makes it a reasonable question, even though it may be difficult for the recommender to assess.

@Barmar On the contrary, the question implies that CalTech only wants to admit students that come from institutions/departments that have already provided students to CalTech in the past. That reduces the pool of candidates (considerably, if we are talking in the departmental/chair level) and is probably detrimental to the goal of getting the best students/maintaining a reputation.

@Barmar: It also implies that Caltech has so little regard for the time of outside academics that it seeks to impose on them the task of attempting to research the quality of students at Caltech (instead of just asking them to write a standard reference like every other university in the world).  So to the extent that their question gives any information about their reputation, the inferred reputation is that they are assholes.

@ben It's a somewhat common question in America from my limited understanding

@Ben I think you're overblowing this. The point of recommendations is that the professor knows the student better than the school can discover through their own research. If the professor knows other CalTech students, they should be able to compare them. They're not asking the professor to do research, just provide their opinion.

They cannot really have an informed opinion unless they know other graduates who have gone to Caltech, which is very specific information (and even if they do know a few, their personal sample size meeting that criterion is probably going to be small).  Hence, asking them to make this comparison is asking them for a comparison they usually cannot provide (as in the case of OP).

The committee will likely know that no one from your school has gone to grad school at Caltech (at least in that department).  That was the case for me (I don't think they had this question when I applied), and I was accepted.  The issue was that they weren't familiar with my undergrad program, so they didn't know how to interpret me being a top student at my university.  In the end, they took a chance on me, and I can tell you I wasn't the worst student there.
Consequently, of course you should be honest, as Buffy says, but if you can compare this student with students who went to grad school at other top places, or even how the student compares with undergrads at well-known schools, that will likely be helpful.  (In general, even without this question, you should do this in your letter if possible.)
If not, hopefully the other letter writers will be able to.

See if you know anyone who has gone to Caltech for graduate study (e.g. someone who is an alumnus). It doesn't have to be a former student, it could e.g. be your professional contact. If not, see if you know anyone who has gone to a similar US university for graduate study, preferably a university of a similar stature.
If that's not possible too, the best you can do is probably comparing with PhD students at your university. Fortunately your university is a well-reputed one.

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Should I contact arXiv if the status "on hold" is pending for a week?
I submitted my research article in mathematics (number theory category) on Thursday. It has been seven days since my paper status was "on hold". I have submitted several papers before, but this time it took a long time.
I always submit my articles from my supervisor's account (through cross-connection), since I don't have an arXiv account. But I have not seen so much in my previous six articles.
Why is arXiv not taking action further? Should I contact arXiv about the delay?

I am not sure, but I think that the arxiv email response always gives a reason why the paper is on hold. Which reason was could well be that action on your side is needed.

Since mid-2022, ArXiv takes longer to make papers public. The reasons were not explained. Perhaps, it has something to do with a large number of papers written in relation to Covid-19, and the fact that some preprints were used as "scientific evidence" in public/political discourse before the results were peer-reviewed and "officially" published.
At the moment, it is quite normal for a preprint to be on hold in ArXiv for 2+ weeks. Sit tight and wait patiently.

Thank you very much for the recent information. I was not aware of it.

That's interesting, but definitely not normal in my arXiv categories.

I don't think this is accurate for OP, who specified math.NT. All the preprints in that category in today's (June 2) release were submitted either on June 1 or late on May 31.

@EspeciallyLime, I submitted my preprint through "differential geometry(DG)" category mentioning the cross connection in number theory (NT). This procedure I have been following since last 3 years.

@learner I had a quick look at math.DG and papers don't seem to take noticeably longer than for math.NT.

*arXiv

Your information seems correct. Finally, arXiv accepted the paper on 13th day from submission. i.e., within 2 weeks

Let me tell you that I always submit my articles from my supervisor's account

This doesn't sound like a good idea. I can't remember the exact rules regarding submission, but why can't your supervisor endorse you to submit to your chosen arXiv category?

Why is Arxiv not taking action further?

Who knows why.

Should I contact Arxiv about the delay?

If you want to know why, then yes. They may also be able to advise you about how your advisor can endorse you so that you can handle the submissions properly.

Indeed, my supervisor is always a coauthor, so I submit from his account. He can not endorse me in "number theory" category because he has different "default" category. Thank you for answer.

@learner AFAIK categories one can endorse depends on whether one has published in those categories, it doesn't have to be the default category

@GoodDeeds: Presumably by "published in those categories" you mean archiving something in ArXiv in those categories? My understanding is that regardless of how much one has formally published (peer review journals), someone without an institutional address requires endorsement even for acceptance in categories one has formally published in.

@DaveLRenfro Yes, that is what I meant (archiving on arXiv in those categories), sorry for the confusion.

@GoodDeeds, to my knowledge one can endorse to a specific category if he/she has at least 4 published papers. My supervisor and I have one published article in a journal in the number-theory category, but the other 5 preprints are in arxiv. So I think my supervisor can not endorse me in the number-theory category. Of course, he can endorse me in his default category, on which I don't work.

@learner I am not sure that is how it works, according to https://info.arxiv.org/help/endorsement.html, the number of submissions needed to have been authored varies by subject but only requires that they have been submitted to arXiv, with no requirement of journal or other publications.

You do not need an endorsement if you open an account with the university domain email address. That is what I did.

I strongly recommend that you absolutely do NOT contact arXiv about why your submission is "on hold". When I did this (e.g., cs.LG, cs.NE, cs.AI), via the suggested support channel that arXiv suggests, I found that doing so leads to a rejection of the paper. I believe the reason for this is that it is annoying to the team/support team to receive queries related to the delay/on-hold status. [Sadly, this quite readily leads to paranoia given that one never really ever knows why their work will be put on hold or is rejected -- you are receiving a peer review without access to the peer review thus you never correct for whatever reason lead to the rejection. Bear in mind that arXiv does explicitly state on their page that it will not provide reasons for rejection.]
Note that it can take 3+ weeks for work be on hold for the cs categories (I believe this is more likely for interdisciplinary/transdisciplinary research). Be patient and just hope for the best.

Anyway, it was accepted later

"it is annoying to the team/support team to receive queries related to the delay/on-hold status" Well, it is annoying to the AUTHORS to now have to face lengthy delays because the moderation team doesn't have their act together. Since the authors are the ones supplying the product, I feel "Be patient and just hope for the best" is an insufficient response. It looks to me like arXiv is strangling itself with poor management.

I agree with you; however, in some disciplinary domains arXiv holds the monopoly on preprints that are taken seriously. Preprints on alternatives like OSF aren’t viewed as much (sadly) and others are looked at as non-legit while viXra is looked at in some domains as work for crackpots, pseudoscience, and alchemy (not true but dominant public perception matters most in science/academia today) thus not leaving other viable options with wide audiences for scientists and students. This means you just have to worry care the moods of the moderators and serve their whims else be banned/backlisted.

I have generally witnessed long waiting time if I upload a word-file converted to PDF (rather than pure latex), which correlated with the fact that the work was not 100% technical but more interdisciplinary (The same observation as made by @gw109).

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Do university rankings matter for research?

Possible Duplicate:
University rank/stature - How much does it affect one’s career post-Ph.D?

Do rankings of universities matter while pursuing research or should I be more concerned about finding a suitable supervisor irrespective of the university or institute rankings?

See my answer to a related question

I'd strongly endorse JeffE's answer he linked to above.  You can find excellent supervisors at some lower-ranked universities, but you typically won't have nearly as strong a cohort of fellow students.  (There are far more student positions than faculty positions, so the strongest faculty get spread out over more schools.)  You'll spend a lot of time talking and working with your peers, so this makes a big difference.  Rankings don't predict this perfectly, but they are highly correlated with it, and these peer effects matter more than the university name on your diploma.

I think the importance you have to attach to this criterion (university ranking) when finding a new research job (from your question, it appears to be a PhD) is limited, because:

What counts if our research output: your results, and how you communicate them to your community. You want people in your field to recognize you as someone who can tackle difficult problems and design creative and efficient solutions.
Of course, your research may not be so stellar that everyone has heard of you. So, coming from a well-known group with a proven track record is important. You want your research group to be famous, because it reflect well on you.
But it's not that simple… not all group leaders are superstars! Failing that, it is better to be affiliated with a well-known department (or university). You want to be in a university/department that people think is good.
But not all people know all universities well enough to be able to judge them. Those who don't rely on externally published rankings.

See how rankings are introduced only as item #4 in the above list. Thus, even considering only the career advancement side of your question, university ranking is not a primary concern. Sure, it plays a role, but lots of students overestimate that role compared to, say, the importance of your own work and results.

In terms of employers, you will face two types of them:

One is interested in only good universities and will make it as a negative point if your university ranking is not that good. Usually those know nothing about your research. It is also subjective and vague for what is a good university ranking? is there any threshold to specify good and bad rankings?. Things are not clear here.
Another type of employers (specially in academia/research positions) they admire your research (if you did good research) and have zero weight on where you come from.

The bottom line here is: if you see your supervisor is going to help you to be better researcher (and thus publish in good journal/conferences) then why not?
There are plenty of good professors affiliated with not-so-good university ranking.
If you could make the two (good university ranking + good supervisor) then this is the perfect solution.

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I have stack-exchanged through my undergrad math program. Am I likely to succeed in mathematics PhD programs?
I'm currently a third-year mathematics student at a top-20 private research university in the US (though mostly known for the humanities). We have a small undergraduate mathematics department, but we were offered the option to take many graduate courses. I’m always passionate about studying pure math, specifically algebra, and I’m very seriously considering pursuing a PhD degree in mathematics. Nonetheless, I’ve not been able to participate in mathematical research of any kind so far – getting undergraduate research experience is impossible due to personal status issues, and my department has no resource committed to undergraduate research.
Indeed, as of my course load, I’ve finished the three-semester algebra sequence by my second year (i.e., group/representation, ring, field/Galois, category theory, commutative algebra, and homological algebra). Though I started late, I'm also working my way through the analysis and topology/geometry sequence, taking differentiable manifold and complex analysis now. I maintained all As in the graduate courses I’ve taken.
Regarding this, I do have one important confession to make, and it is in fact the reason why I’m asking this question. Math SE is a very robust community with respect to algebra. This worked very conveniently for me as there are very few peers at my school to discuss math with. As a combined consequence I actively seek ideas on SE whenever I get stuck on homework. (Please note that I'm not in violation of any collaboration rules set by my department: I understand and then proceed to write every proof myself.) This happens in about 30% of the assignments. I have no problem with exams since they are usually much easier than assignments.
Only after having recently talked to graduate students and professors at a conference, did I realize this is a terrible approach. I vividly remember one said something like: “unless you went through a textbook and attempted to prove every theorem yourself first you won’t truly understand the subject”, which is, the exact contrary of what I’ve been doing. I’m seriously in doubt about my aptitude over these subjects, fearing that I will be subpar on the level of understanding as well as the ability to conduct research, to approach open questions when I reached graduate school. I fear I never try/explore “hard enough” to come up with proofs like others have suggested. I managed to do most just by familiarity of common methods/tricks and theorems, but those things can be forgotten over time.
So here comes some specifics of my question:

Is searching SE for homework problems common for math students?
How will doing so affect a student’s understanding of the material?
In what ways does doing so tie to one’s ability to do research?
What are some possible ways to remedy this, besides completely re-learning the material?
How much do I have to pay in the future for stack-exchanging through my courses?

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I got to say, this post makes me feel like I'm doing pretty bad in my math major. I'm barely through basic undergraduate math as a third year and have nowhere near all As. Oof.

Obviously user115896 can't see this comment, but for future readers, I would assume that to mean a top-20 research university that is also private.

First of all, I believe this is extremely common these days. More and more I notice students neglecting to develop important problem solving skills and instead developing great “google-fu” and “stack-exchange-fu” skills to achieve the same goals.
Now, don’t get me wrong, SE-fu is a terrific skill to have. Just like you are worried about using the internet too much and coming to rely on it as a crutch, some people genuinely ought to worry about having the opposite problem of obstinately trying to figure everything out themselves even if it takes them weeks or months and refusing to ask for help. This is just hugely inefficient. These people may in fact become excellent problem-solvers given enough time, but it’s just not a practical approach to covering the large amount of material a modern mathematical education requires.
So what I’m saying is, there is a right amount of stack-exchange usage that can be really good for you. Someone who makes the right use of math.SE and other great online resources can really boost their ability to master complex topics and speed up the learning process compared to their peers who don’t use those resources. And then... there is definitely also a wrong amount of stack-exchange usage. It is certainly possible to rely on it too much, or more generally to rely too much on asking other people to help you figure things out when you get stuck (before SE was around, people with such tendencies also existed, they would just nag their friends and class mates with lots of questions instead of using google/SE).
So, is this a fatal flaw or an indication you’re unlikely to succeed? Absolutely not. From your description it sounds like a slightly bad habit at worst, but one that you likely share with a lot of other students (I mean probably something like 70% of them, if we interpret your habit to include heavy use of google and not just SE).
I do advise you however to actively work on shaking this habit and investing more time and effort in trying to solve problems by yourself before you give up and ask for help. Getting yourself unstuck when you get stuck is a skill in and of itself, and involves important sub-skills like learning how to identify when you have a serious misconception about a problem, learning to believe in your ability to solve problems by yourself, learning to be attentive to small details, and probably other things that are equally important but that I would have a hard time articulating in words. When you look up the answer or ask for help on SE, you end up solving a specific short-term problem (figuring out the answer to the specific question you need solved), but deprive yourself of broader opportunities to acquire these very valuable problem-solving skills. It’s certainly not too late to start though, and your tendency to over-rely on help sounds fairly mild in any case, if it even exists. Good luck!

Exactly this. Related to getting help when you believe it is currently beyond you. =)

I really like the balance this post strikes. The people telling the OP that every serious mathematician works through every text by themselves are being absurd, but I also think that the OP has real reason for concern.

@DavidESpeyer thanks. I hope readers here consider that your opinion is all the more meaningful coming as it does from a very successful professional mathematician.

+1 for SE-fu and Google-fu as in kung-fu. Solve problems. Don't flex your muscles out of subject.

Yes! In fact, I think you're well on your way to doing better than your peers! Taking longer to understand something isn't something to be proud of! There's no need to reinvent the wheel. If someone can help you understand something, you would be well-advised to make use of them. In the same way, you would be well-advised to attend the lectures, thereby getting help from the professor, instead of staying at home with the ZFC axioms and attempting to derive the whole of mathematics from scratch.
My experience asking questions on Stack Exchange also indicates that simply writing the problem in a form which others can understand is a great help in clarifying my own understanding of the problem. Indeed, I've solved some of my problems simply by beginning to write a (never asked) question.
Of course, this doesn't mean you should outsource your understanding to others. You should make it so that you can explain the concept to next year's students without help (answer some other SE questions while you're at it!). But even then you should feel free to ask for help with next year's problems.

When you say "taking longer to understand something isn't something to be proud of", do you mean "isn't something to be ashamed of" or "is something to be proud of"? What's written at the moment seems to contradict the otherwise encouraging tone of the answer, so it looks like a mistake.

In this case he means that deliberately spending hours trying to work it out for yourself is needlessly masochistic when you have other resources (i.e. StackExchange) to help.

I get where you're coming from, but I disagree with this answer. A large part of studying is learning how to deal with frustration and push through. It's like training a muscle. When I jog the point isn't to get from point A to B, but to make my heart and legs strong enough to carry me fast for long periods of time. Otherwise I could just call a cab.

@E.T. yes, so one should also make a serious attempt to solve the problem first. However, if it feels like one has run out of ideas and cannot make progress, one should also feel no shame about asking for help.

Would those be the questions you have had closed or the others?

@E.T. Continuing your analogy, what do you do when youre farther out that you can return from? When your legs collapse? Call the cab, of course.

I don't want to discourage anyone from asking for help, but I do think there's a big difference between asking a professor for help in office hours or asking a peer to work on a problem with you, and looking up answers online.

the comment on the benefits of "writing things out" is so true. A classic rubber ducky scenario: https://en.wikipedia.org/wiki/Rubber_duck_debugging

I think this answer could be improved if there was a direct reference to the work of a PhD program, and maybe some justification of how the asker will be prepared to make a novel contribution.

"...simply writing the problem in a form which others can understand is a great help in clarifying my own understanding of the problem" - YES!

I don't have any disagreement with this answer. Just wanted to mention something I read on twitter - "When you reinvent the wheel you understand all the reasons why it is round. It is a very educational experience."

@NoahSnyder It's not just "looking up answers online", as SE answers tend to elaborate about the process and how the answer is reached, rather than just replying with x=5

I wouldn't worry too much. It sounds like you are making excellent progress. You are still an undergraduate, you have tons of time ahead of you!
There are lots of good ways to learn mathematics. Talking with others (including over the Internet) is one. Allowing yourself to get stuck, and trying hard to come up with your own proofs is another.
If you feel that your study habits have skewed too much towards the former, I'd recommend trying out the latter approach. (Which does not mean you have to change to it permanently.) For example, choose a course or book and try to get through it without SE. See what happens!

There are some techniques the OP may not have learned such as sleep on it, take a walk, write down several alternative approaches, and rubber duck. For proofs, you explain to the duck, in full detail, why there is no way to prove the theorem.

Writing a question on Stackexchange can be like talking to a rubber duck. Many times, I found the answer to my question in the process of writing it up.

I too have found writing questions to be an excellent exercise to help understand a problem better, and I too have sometimes ended up with a solution from an hour or two of just question-writing.

I hope that people who wrote a good question and then found the answer themselves still took the time to post both. A good answer is good regardless of who wrote it. Also, someone else may have an even better answer.

@usernumber - even better, answer a question somewhere where you know the technical vocabulary well enough but have no idea what they're talking about. The OP verbed 'SE' but really they should've said google-fu. To stack exchange something is to employ the scientific method to solve empirical problems, so the only thing you need to learn how to do is take a flippant question, turn it into an empirical one so that it can be answered, going down rabbit holes until you can get back to question as asked. AKA, research.

@MSalters Often enough, I discover while writing up a question that my mistake was a typo in my code. In those cases, I prefer keeping the question and the answer to myself :p

"... unless you went through a textbook and attempted to prove every theorem yourself first you won't truly understand the subject"
Nonsense! This is anxious, perfectionistic thinking, and internalizing thoughts like this ultimately caused me to leave academia. I felt that I couldn't pursue my research unless I fully understood everything from first principles. I would get stuck for weeks trying and failing to get my head around a particular tiny nuance of probability theory. Needless to say, it was exhausting, and I barely managed to finish my master's thesis.
The thing is that learning is a continuous process, and you don't have to understand everything perfectly to move forward. You can learn as you go.

Well, it likely depends a bit on your personality type. Personally, I have always read textbooks from the very first page to the very last, not leaving a page until I have felt that I've understood it well (or memorised it well, if applicable to the subject/situation). And that approach worked very well for me during my 10 years at the university (physics, mathematics, and then medicine). For me, it was a very efficient and enjoyable experience, and I did feel that I understood "everything" very well. But I also understand that we are all different, and I suspect I am the "unusual" one here...

@AndreasRejbrand That's fair! I'm not that type of person, and based on the OP's post I don't think they are either, but I realize that it could be a natural way of learning for some people.

No-one really knows the educational effects of reliance on SE yet, mostly because you, and your generation, are the canaries down the coal-mine.  Most of the experts who answer questions on the technical SE sites are people who completed their graduate education before SE existed, and some before the Internet was even in regular use.  Those of us who answer questions on these technical SE sites rely on the students who use this facility to have good judgment about when reliance on this assistance is helping them learn, as opposed to being a substitute to learning.  From our perspective, we certainly hope this assistance will help your understanding of the material, and we try to frame our answers in this way, but we are relying on you to let us know how it all works out, not the other way around.

So here comes some specifics of my question:
• Is searching SE for homework problem common for Math students?

You are probably in a much better position to judge this than most of us.  Ask around the students in your faculty and see if they use this resource, or if it is just you.  There are certainly a reasonable number of student questions on SE.math, but the volume is still far below the number of mathematics undergraduates presently studying.  This suggests that only a small proportion of math students are using SE to ask questions, though many may be looking up answers to existing questions on that facility.

• How will doing so affect a student's understanding of the material?

This really depends on the exercise of good judgment by the student, so you tell us!  Has SE helped you or hindered you?  Have SE answers functioned as a tool to assist your learning, or as a substitute for learning?  Have there been any instances in which you used an SE answer to substitute having to learn to understand a piece of material?  Was this common?

• In what ways does doing so tie to one's ability to do research?

Unless the use of SE answers has hampered your previous learning, there is no reason to think it will impose a limit on your ability to learn to do research.  It takes a long time to learn to do research, which is why we have PhD programs, but if you are able to get into one of those programs, there is no inherent reason that you should lack the ability to learn the material and ultimately succeed in this area.  You mention your professor's comment that you won't truly understand a subject unless you attempt to prove every theorem in the relevant textbook yourself.  I would say that is rather aspirational, and it assumes that the textbook is some kind of golden-tablet that perfectly delineates all necessary knowledge in the subject.  In practice, this level of engagement wouldn't necessarily occur, and it is not a necessary condition for expertise.  As you acquire expertise in a subject, you are naturally going to be curious to check and re-check all the foundations, so you are probably going to find that at some point you will learn to prove all or most of the relevant theorems yourself.  That might occur slowly, as you learn more about your subject and relate it to other relevant areas of mathematics.
In regard to research trainnig, it is worth noting that the major difference between undergraduate mathematics, versus research mathematics, with respect to SE, is that the latter is going to involve problems that are sufficiently difficult that it might be hard to get answers on SE.  At the level of graduate research, you are expected to be developing into someone who is becoming an expert in your topic, so at that point the pool of people that can help you diminished substantially.  Some researchers do ask questions on SE.math pertaining to research topics, and sometimes they get useful answers, but often the complexity/obscurity of the topic is such that it is difficult to get assistance through this medium.

• What are some possible ways to remedy this besides completely re-learning the material?

You haven't really told us exactly what deficiencies you feel you have that you're trying to remedy.  Presumably you have learned something in the courses you passed, so even if there are gaps in your knowledge, plugging those gaps would require only a partial relearning of the material.  Certainly, if you feel that there are areas of your mathematics education where you did not acquire the relevant knowledge, go back and have another go at them, and try out some practice problems until you gain the understanding that you missed.

• How much do I have to pay in the future for stack-exchanging through my courses?

As I said at the start, you are the canary in the coalmine here, so we are waiting to see the results, and then you can tell us.

Instead of me looking through your questions on Math SE like Ethan Bolker suggests, let me tell you what I would look for and evaluate instead, and then let yourself do the self-evaluation (which is also an important skill to develop as a researcher!).
Basically, I would look at if your questions are well received. If you hit the  hallmarks of a "good question" (as defined on many SE sites), you are probably benefiting from your interaction with Math SE. To list some of these characteristics of good questions:

shows that you have put thought in the problem,
shows that you have attempted to solve the problem yourself,
shows that you understand the material.

If you had good guidance and supervision, you would probably be able to discuss these things with your advisor. If you had many peers with similar interests, you would be able to discuss these things with your peers. Neither your advisor, nor your peers, nor the community at Math SE would value if you came asking for help while showing you had put no effort into understanding the problems yourself.
So if your questions are not well received, SE might be pulling your weight, and the same way the community does not appreciate questions showing low research effort, a prospective adviser would not develop confidence in your understanding and dedication if you expected them to serve you with all the answers.
Additionally, and excellent way to deepen your understanding of mathematics (or any topic, really) is to start answering others' questions. You need a deeper understanding of the material in order to explain something clearly and concisely. This would be similar to explaining a topic to one of your peers asking for help.
Finally, I'd like to note that not everybody has the same learning style: some people benefit more from sole studying with a textbook, some people benefit from using visual aids or drawing, and some people (me included) work and learn (and come up with new ideas!) best when interacting with other people.
To summarise: if you are asking well-received questions and providing well-received answers on Math SE (or a similar technical SE) you are probably benefiting from it similar to what you could get out of a good adviser and peers with similar interests. This is especially true if you have an interactive learning style; you were simply looking for the most effective learning method fitting your learning style which was possible in your situation.

On a personal note: I used to be much more active on Stack Overflow during my BSc and MSc. My activity and reputation graph pretty much follows my project and seminar schedules: they had required me to think about more than we had to do for class, or to combine the course material in new ways. Being able to get feedback on my ideas and approaches was invaluable for my learning and understanding.

That is so much ignored: Different people learn in different ways! You will meet plenty of people who think that if you don't learn in a particular way, you are useless. In reality, if you find one way that works for you, you're fine. (Myself, I have to write something down, and it enters my brain and stays there. Without that step, I don't learn. )

There are a lot of aspects of training to be a mathemtician.  For example, you want to learn:

Mathematical theory (definitions, key theorems, key constructions)
Literature search (figuring out what's in which papers, finding results in books, using google to find relevant ideas)
Mathematical tricks and proof techniques
How to struggle with a difficult problem that takes hours or days to solve. What kind of techniques do you use to get unstuck? How do you deal psychologically with being stuck?  How do you decide when to give up on a problem or approach?
Writing math papers (dealing with writer's block, making diagrams, organization, clarity of proofs)
Collaboration (learning how to solve problems together with other people, figuring out how to learn from and explain to your peers, etc.)

The bad news is it sounds like you've focused exclusively on the first two bullet points at the detriment of the other ones.  Getting stuck on 30% of problems suggests that you're pretty far behind where you should be in terms of mathematical tricks and proof techniques.  If you go to a graduate school that has a preliminary exam you're likely to struggle with it.  Not having the experience of really struggling with questions you're stuck on, means you're underprepared for the psychological experience of research, and for figuring out how to work on problems to which no one knows the answer.  It's important to try to learn the difference between being stuck and close to an answer, and being stuck and far from an answer.  By turning to stackexchange exclusively instead of talking with your fellow students and your teachers in person, you've fallen behind on learning how to collaborate.
The good news is that you have time to learn these things during the rest of this year and during your first year or two of graduate school before you move on to research.  But you really need to start thinking about the aspects of your mathematical training beyond just learning mathematical theory.  You need to stop giving up on problems early, and you need to talk to people in person about problems you're stuck on rather than just finding answers online.

From the question it seems that the OP does not really have many peers to discuss and collaborate with, and the number of faculty members might be quite small too (humanities-based university). I think the rest of this answer is nice, but I wouldn't say that he neglected the collaborative answer by participating in SE

@penelope: Whether or not OP had good opportunities to collaborate, OP hasn’t learned collaboration skills and would be wise to try to develop them.  But you’re right that sometimes this isn’t a student’s fault if they don’t have peers.  In OP’s case there’s a graduate program, so the faculty is at least medium-sized.  I can’t think of a school fitting OPs description that has a genuinely small department.  But at any rate you may be right that the lack of collaboration isn’t OPs fault.

For one thing, OP probably isn’t the only student googling through their homework, so there may be few opportunities to work on hard problems with other students since they’ve also looked up the answer.  I think the rise of googling for answers has coincided with a huge decrease of students working together.  It’s hard for one student to buck that cultural shift.

I would actually say that posting on SE does develop collaboration skills up to a point... now, whether we chose to believe the OP that they didn't have any better opportunities or not is a different question, but I firmly believe that communicating your problem, giving clarifications etc in a good SE format does require (and develop) at least some collaboration skills.

Great answer! It says a lot of the things I was trying to say in my answer, but in a different (in some ways better) way.

Really, the answer to this is very simple.
Everything that you can find on the internet has already been done by someone else.
What you are required to do in PhD research is something which has not been done by anyone else yet.
Of course, the web may still give you good ideas about techniques, etc. But SE or (any other web forum) isn't actually going to "do your PhD for you" in the same way it can "do your homework for you" - even if you have been avoiding straightforward "copying" of what you discovered from web sites.
You will also eventually hit the problem that there are very few people in the world who are working on anything very similar to what you are doing - and that handful of people might not hang out on SE, or anywhere else you are looking on the web for advice!

I think this is probably the correct answer, but could maybe be tempered by pointing out that the OP is unprepared, not necessarily inept, and many other undergraduates are in the same boat--even if they don't use the internet, knowing that the problem is expected to be solvable with tools-to-date certainly leads to a different experience. (Plus just having the ability to do research is not sufficient, hopefully you also enjoy it...)

You can just carry on with this approach through graduate school and well into your career as a professional mathematician.
For instance I have at least one series of papers that started because of answers I got to a mathoverflow post when I was confused about something.

But should they continue to do so? I spend some time on MathOverflow dealing with (a small number of) people who are essentially asking others to do all the mathematical thinking

I intended to answer after looking at the kinds of questions and answers you posted on Math SE. I was surprised to find none linked from your profile.
Stack Exchange can be a good place to "discuss mathematics", but if all you did was lurk, reading other people's entries, you have not discussed much, and may not be as ready for further study as others here suggest.

The profile for this question is marked "new contributor". The OP may have another profile that is active on Math SE.

@PatriciaShanahan That thought occurred to me. Perhaps we'll get an update.

I was wondering about that myself a few hours ago when I first saw this question, and suspected what @Patricia Shanahan said, but still wondered why this obviously easily checked and seemingly inconsistent issue wasn't at least briefly addressed. Also, getting through 3 semesters of graduate algebra by second year (when usual is maybe multivariable calculus and elementary linear algebra) and working on "analysis and topology/geometry sequence, taking differentiable manifold and complex analysis" sounds ultra-accelerated to me (for an undergraduate at a U.S. university).

@EthanBolker Thank you for your answer. This is indeed a new profile created by me like Patricia Shanahan suggested. I have chosen to enjoy the anonymity of the internet in this case mainly because my math.SE account is easily recognizable by people I know and this topic can be potentially controversial. My motivation behind asking this question is to look for ways to "self-diagnose" and ways to improve as needed. I'm sorry if I cannot provide links to questions I've discussed on in the past :(

@FunnyMorphism That makes sense. But it does make it harder to give you advice. I think you'll be OK. Good luck.

If you are looking up the solutions to the exact (or trivially similar) questions you are being asked in your homeworks, then that is cheating. It is bad for all the reasons that cheating is bad:

you are not doing the assignment the professor wants in the manner they want you to do it; you are side-stepping the challenge.
Your performance in the assignment is incorrect feedback to the professor that you understand the problem, potentially causing them to accelerate or at least not bother reviewing and circling back as much. At the very least you should cite the online sources you used so they will know. This provides a good opportunity to test your theory that it is perfectly kosher to use those sources.
Your grade will not represent your abilities as it was meant to, and potential grad schools and employers will be misled into thinking you are better at math than you really are. This is also blatantly unfair to everyone who did not look up solutions.

As for rewriting the theorems after you understand them, this is better than nothing sure, but couldn't you claim the same after "collaborating" to get the answers? That doesn't make cheating ok. Many other answers here focus on the question of learning, but you could also learn wonderfully while plagiarizing fellow students' work, hacking the profs laptop for the solutions, and performing other forms of overt cheating, as long as you did it "properly". Hey we can't expect you to solve every problem in the book yourself right?
When I made this point in a comment it was met with a surprising amount of alarm and the comment was even deleted. To everyone with such mindsets I'd suggest you consider the problem viewed from a higher level of moral development. See here: Kohlberg levels of moral development. What matters is the universal principal underlying the rules against cheating, which I listed above, not what you can get away with due to less-savvy profs and outdated student handbooks.
As for re-doing every proof in a textbook, this is creating a false dichotomy. There are more alternatives between the extremes of cheating through all problems versus re-writing a content-packed book with your eyes closed. That middle ground is the job of your instructor to find for you. You don't really understand math unless you can redo it yourself without first knowing the answer. Yes, that's a fact. You may or may not need to understand every theorem in a particular book. Depends on the book, most aren't even peer-reviewed and have some mix of key topics and the author's personal preferences. Your instructor's job is to feed you material and challenging practice work a little at a time so that you can follow along and keep up.
As for your specific questions, yes it is very common as is all cheating. The modern view of students seems to be that a college degree is worth millions as some kind of job ticket, while merit is practically irrelevant. It will hurt you far more than you realize because your tendency will be to seek help at precisely the times you shouldn't; while you are motivated to do problems yourself when they are easy and you aren't challenged. Expertise requires Deliberate Practice which means increasing challenge, not just working easy problems or reading how others solved problems. This also provides the framework for answering the rest of your questions. Yes working through an entire book is one way to get this increasing challenge. But a better way is to do just certain key parts in a good order from a really good book. Use stackexchange to find these superior resources. Another way of course is to take a class with a good instructor that leads you through the material and provides assistance when you are stuck, rather than you looking to the internet for assistance.

@Heutl So then I suppose they also give out the answers at the same time as the assignment? if not, why not? Personally I tell students they can use the internet but they must cite what they used or run the risk of a plagiarism or collaboration accusation (since multiple students might use the same source). Plus I am very careful not to ask a question that has a available solution elsewhere. When I fail at this, I just get multiple copies of the stackexchange answer. Then I give the same problem on an exam and almost no one can do it. The main victim of cheating is always yourself.

@Heutl That takes complete care of it actually. I personally have stopped "caring" about cheating because I just give minimal credit for homeworks and the cheaters fail the quizzes and exams. Doesn't mean I stopped thinking it's cheating. Do the exams include questions about "answer finding skills" such as the best source of pirated solutions manuals, or which nerds are the most willing to share their answers? Just kidding.

@Heutl that was merely a side note, that even when the prof says its ok, they still could very likely consider it cheating. For my definition of cheating however, read the answer above.

I imagine that this is one of those situations in which far too many people have this "not invented here" mentality. It is something every one of goes through at some point in our lives. For example, a beginner programmer might insist that he or she has to write their own code for any and all functions that they wish to implement, including shunning the use of open-source, freely-available or otherwise acceptable to use libraries, functions, plug-ins or other assists. By the same token (and this is something I have personal experience with) a 3D beginner might insist on refusing to use any texture art, mesh data or keyframe information that they had not explicitly created themselves, even if it served the purpose to flesh out certain areas of a concept they might have been going for in the first place.
There is nothing wrong with properly-attributed work being used to support your case, and examining other people's work (and collaborating with other people) is often a fantastic and accelerated way to learn how to do things. I greatly enjoy 3D modeling, animation and rendering, but I absolutely suck at mathematics. I learned just enough to be able to work on my 3D stuff, and I use computational tools that simply didn't exist 30 years ago to provide me the assistance I need any time I work on anything requiring calculations.
In my experience, you will not be treated poorly by the academic community for using other people's work to support your own, just as long as you are open and honest about doing so. That's the key issue here. Academic dishonesty is severely frowned upon for very good reason, but so long as you do not engage in such shenanigans, I think you'll be fine.

As students read textbooks and solve exercises, but do not have access to them while writing the actual exam. So is the case with StackExchange. You don't have access to it while writing the actual exam. Whatever case you follow, as long as you did well on the exams, why should it matter?
BTW, if you do join PHD, please use mathoverflow.

BTW, if you do join PHD, please use mathoverflow. --- Why? I don't know what "join PHD" means (Enroll in a Ph.D. program? Graduate from a Ph.D. program?), but there are plenty of people with a Ph.D. who participate in Mathematics StackExchange, probably more (by actual number, but perhaps not more by percent) than in mathoverflow.

@DaveLRenfro I am suggesting OP to gain from mathoverflow.com as well during his graduate studies, just as he gained from stackexchange during his undergraduate studies.

I've found mathoverflow to be much more limited in topics, so if the OP is interested in topics emphasized on mathoverflow (and this might very likely be the case, given his extreme advancement in algebra), then certainly mathoverflow should be looked at. Probably scan over both groups, but since questions to Mathematics StackExchange have increased so much in the last few years (from 2011-2013 or so), I no longer bother trying to scroll through all the questions each day (also not the OP). Sometimes I'll pick a tag I'm interested in, or can often help with (e.g. Reference), and look at those.

authors: Bob Jarvis - Слава Україні


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Data used for analysis is not free. What should I do as a reviewer?
I'm doing a review of a paper (very well written, I think) for a journal with a fairly good reputation.
This is my first review, and I have a question regarding data availability which is, according to the journal policy, a necessary condition to publish:

The data, code or other digital research materials must be publicly accessible and clearly indicated as such.

The problem is that the dataset used in the analysis can only be retrieved under the payment of a fee from a link provided by the authors.
How should I behave in this case?
The journal asked me if data was accessible and if it was adequate to allow replication. The honest answer is "no", but the authors could not have done otherwise, since the data has a license and is not free to share.

Actually it is not completely clear that "the honest answer is no." The policy is probably intended to require that the data are available for free, but it doesn't say that. I think you should ask the journal to clarify: do the data have to be available for free, or is being available for a fee sufficient?

must be publicly accessible, doesn't mean it is free. As a side note, the GPL license requires source code to be provided to any binary user that asked and a fee is allowed although it is required that fee to be something reasonable to cover the expenses of posting and data storage device. For sure journal has to clarify what counts as publicly accessible.

Have you asked the author (via the editor, if reviewing is being done blind) to purchase another copy of the data specifically for the reviewer(s)?

You asked, "How should I behave in this case?" Concerning completing the form, the answer is straightforward: No, the data is not freely available.
However, I suppose that your question is asking more than that. If your concern is that you, as a reviewer, do not have sufficient material to adequately review the article according to the journal's standards (that is, you do not have access to the data), then you should email the editor who assigned the review to you and explain the situation. Either they will tell you to proceed with the review taking the authors' analysis in good faith, or they may contact the authors to ask them to provide the data as a condition to continue the review. I suspect that the editor would most likely just ask you to proceed with the review, but I do not know the journal, so they might actually ask the authors to comply with their stated policy.

"publicly accessible" is not the same as "freely available".

"[take] the authors' analysis in good faith" I thought the point of peer review before publication is precisely so that we don't have to just trust that a given paper is correct/true.

It's not clear to me in from the original post that the issue is not being able to adequately review the piece, but rather whether there is an out and out violation of journal policy.

@TylerH Exactly; it is not only about did the authors commit a fraud, or accidentally erred on a detail by tunnel vision (e.g., EuSpIRg). Possibly contributions to OrganicSynthesis in chemistry go beyond the typical milage, it includes could the results replicated with one team submitting, and an other checking (example), names below the reaction scheme serving as abstract.

@CrisLuengo That is a claim that needs a source.  There is no commonly accepted legal definition of that term so it will depend entirely on the language of the contract or context in which it is found.  Where no explicit definition exists I don't know that it would be unthinkable to interpret "publicly accessible" to imply "accessible without cost".

@J... Just like museums have the mission to make collections accessible to the public, but nobody bats an eye when they have to pay an admission fee.

@TylerH Maybe in some fields, but in my field (physics), it is definitely not expected that reviewers, or anyone, will reproduce the analysis, when usually a paper is the result of years of analysis by a large team. Peer review is more to verify that the steps the authors claimed to use are appropriate for the type of analysis presented.

Since different journals and different editors might have different precise expectation, my basic answer (in bold) is "ask the editor".

@thegreatemu It's not necessarily about reproducing the entire experiment, it's about having access to the data and the methodology so you can determine if something was done incorrectly.

@TylerH I think that's explicitly not what it's about here.  There is a strict journal requirement that the data be publicly available.  I expect a reviewer's responsibilities to include ensuring the data can indeed be accessed with the provided method and that it follows expectations regarding formatting, documentation, etc. I find it highly unlikely that most reviewers have the time to reproduce enough of the work to "determine if something was done incorrectly."

@CrisLuengo Sure. But extending the museum analogy, this might be the Smithsonian of journals, and be chartered in a way that forbids charging admission.

I doubt this is a problem. I suggest shooting an email to the editor of the journal with this question. It might be the case that the author(s) will be required to provide a local (downloadable) copy of the dataset that they worked with upon approval for publication (supplementary materials). Even if that's not the possible, I wouldn't necessarily interpret "publicly accessible" as "free."
It would also be helpful to know what type or journal / research project / data we're talking about here. When the authors conducted the analysis, did they do so on a local file or through something like an R server with restricted access? If they performed analysis offline, then they should have no problem providing an anonymized copy.

If the original data is behind a fee-wall, I doubt the authors have a license to redistribute it in any way, not matter how they analyzed it.

Yeah could be. It's not really clear at this point where the data came from, so we're all speculating here. Still I doubt the intention of the journal with this rule is to prevent the publication of good work based on data that are behind a paywall.

I would question whether it was good work, if the data necessary to evaluate it is inaccessible.  Sounds like a scam.  Like all of the ads for good health where they tell you about all of the great results from their method/product, and if you pay $99.99 they will tell you what their product/method is.


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Reconnecting with a previous professor then asking right away for a reference letter
I am in the process of applying for a Ph.D. and the application process requires several reference letters. Since I only have done significant work with only one supervisor so far in my Master's, I would need to ask from previous professors during my Bachelor's.
Fortunately, the previous professors have already written me reference letters, and therefore the effort would be minimal. What would need to be done is just translate and then maybe change a few words to match the description of the ad.
Nevertheless, I cannot help but feel bad about reconnecting with previous professors with more than two years of no communication, only to ask for a reference letter and to get their permission to list them as referees in my CV.
What is your take on this? How should I approach this without being seen in a bad way?

If you had been a good student, I wouldn't mind writing a letter.  If I have nothing to say, regardless when you were a student, I would say no.

They were a grad student trying to get into PhD programs once themselves, they will understand.

You are not “reconnecting”. You are emailing someone to ask for a letter of reference. This is normal and expected. It’s not guaranteed that they’ll say yes, but no one will think any less of you for sending such an email. The people you’re emailing have themselves likely sent a number of such emails to people they don’t know very well over the years. So they will have no issues at all with such a request.
By contrast, what would be a genuine thing to feel bad about, and likely unwelcome, is if you email a professor expressing an inauthentic-sounding desire to “reconnect”, asking some inauthentic-sounding questions about how they are doing, and then emailing them again a few days later to say “Oh, I forgot to mention I’m applying for grad programs, will you write me a letter?” Such a strategy is transparently dishonest and likely to upset people, so don’t do that.
The main thing is to be straight about your intentions. Then you will be fine, and should have no reason to feel bad.

I'll even amplify "this is normal and expected": this happens all the time. OP you're all good!

and please remember to give them a copy of your current CV or some document that lets them know what you've been up to. (and also helps remind them of who you are/were).  It helps them 'remember' you, also, and by placing you better in their memory, can also end up reminding them of the past interactions that they had forgotten (but are to your benefit that they recall them).

Normal and expected is putting it mildly. This could literally be in the job description for professors

Students do sometimes ask me for references several years after I have worked with them. I  have no problem with that request, even if I have heard nothing in the interim. It's particularly easy to grant if I have written for them before.
That said, I do tell them that letters about current work are more useful than letters from the past.
You might include in your request that you know current references are better but that you have too few of those for your purpose.

The connection itself is useful and fun if they mentored you in any way. I've reconnected just for that and it was appreciated that I thanked them for their early help. I didn't need letters, though.

In my opinion, you lose nothing by trying. We have a saying in Spain: "El no ya lo tienes" (you already have the "no", you just have to win the "yes").
I'm applying for postdocs and last week I contacted a professor I've barely worked with. She is a great reference in the field. To my surprise, she accepted very quickly and very kindly.
Just explain the situation, make the request and take the opportunity to greet the professor and get to know their current situation.


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A potentially trans student is misgendered in university records. What should I do?
I have noticed* that an undergrad student in a course I teach has "female" written in the "gender" field in the university intranet database (used for course enrollment, grading, etc.), although they present themselves as male in terms of appearance and pronouns.
I would have chalked it up to a simple clerical error, but then I realized that the student's name also is of a somewhat unisex character (it's common for men but not entirely rare for women as well, think "Andy"), so there is a small but nonzero probability the student is actually trans.
Of course I could just ignore the issue completely, but that would mean the wrong gender would keep being shown to dozens of other teachers for years to come, and that might put the student into all kinds of uncomfortable situations.
I'm thus trying to balance the invasion of the student's privacy by bringing this up in some way vs the invasion of their privacy caused by the problematic gender field in the database.
I was thinking about sending them a short e-mail along the lines of:

Dear Student, I have noticed the university records show your gender as female. Should you want to have that corrected, contact the Department of Student Affairs. Feel free to ignore this message if it is not relevant, I don't expect a reply.

Is there a better (read: more respectful, safer, less likely to come across as super creepy) course of action?
*: Noticing this didn't require any investigation whatsoever. When I open the teacher dashboard for my course,I am presented with a list of students. One entry in that list looks like

Andy Smith (F) (photo of a bearded dude)

That's not really easy to miss in a list with less than 30 rows.

Comments are not for extended discussion; this conversation has been moved to chat. Please read this FAQ before posting another comment.

If you must do something (an assumption I would encourage you to question), then probably the best way to help the student avoid uncomfortable situations, without actually putting them in exactly the kind of uncomfortable situation you are trying to spare them, is to alert your university’s registrar to the potential error. The registrar would be in a better position to check whether this is in fact a clerical error or something that is in accordance with the student’s wishes. And the student would probably perceive an email from an anonymous registrar staff member discussing the option of correcting an incorrect entry in their university records as a lot less creepy than a similar email coming from their professor.
Edit: see also the comment by @niemiro, who said that “The registrar could send an email containing every field in the database for that student and ask for confirmation that it’s all still correct”. If/when you email the registrar, you can suggest to them this approach to minimize any creepiness factor and avoid a risk of accidentally outing the student.
Other than this idea, doing nothing is a viable, and, in my opinion, completely satisfactory approach to handling a “problem” that you neither know with certainty is actually a problem, nor falls anywhere near your actual professional duties with respect to the student in question.

I don't think I must do something,just that doing something might be the decent thing to do. If I were a trans student, I think I wouldn't want something very private about me to be shown to every single teacher. I would want to know this was happening so that I could put an end to it.

The student not knowing is by far the least likely scenario. Much more likely that he’s not out to his parents or that your school, state, or country has trans-unfriendly policies.

@TooTea understood. Well, it’s reasonable to do something, and it’s reasonable to do nothing. I’ve given a suggestion for what to do if you want to choose the “do something” path.

If this is indeed a clerical error, contacting the registrar directly would also alert them that they need to double-check the rest of the information for this student as well.  Some student profile data (grant/funding information, emergency contacts, etc) could be disastrous if incorrect. Stuff like that doesn't always get audited unless someone lets them know there might be a problem.

If the student prefers the current situation, then the registrar will probably also be aware of this case.  In that case they may not even bother the student, but this question would be "taken care of" in OP's mind.

This. The registrar could send an email containing every field in the database for that student and ask for confirmation that it's all still correct and up to date.

Do not do this. You risk outing the student in the case that employers and/or family have access to their records.

@LShaver which records? Outing how exactly? I’m confused about what sort of scenario you’re imagining exactly.

For example, their parents might read their official email. Or maybe some letters are mailed to the students permanent address with a gendered title. Or the parents just open any letters sent to the student at their permanent address. Or maybe gender is mentioned somewhere on financial aid information. Lots of ways this can go horribly wrong.

@NoahSnyder while I personally think doing nothing is the best option, your objections don’t make sense. The “official email”, if such an email is ever sent, will be an email from the registrar asking the student to confirm that the details of their profile are correct. And if the student is worried about the gender being mentioned in official communications, all they need to do is not change their “parent-safe” gender in the university profile. The student will remain 100% in control. I still don’t see how the action I’m suggesting can lead to outing.

@NoahSnyder: The question now says the student's photo is "of a bearded dude".  Maybe I'm incorrect here, but that seems unlikely to be someone who maintains a female appearance when seeing their parents.  Without that info, yeah I agree there's more concern that the student isn't out to everyone yet.

I don't understand how passing the buck to the registrar solves this problem or even addresses the spirit of the OP's question. Suppose the registrar notices the potentially erroneous gender—then what should the registrar do? (And I second @LShaver's concern about potentially outing the student to family or others.)

@Max I believe these concerns are addressed in my answer and the long discussion in the comments. I don’t have anything to add beyond that.

an undergrad student in a course I teach

Your job is teaching this student.  The gender in the university records has no relevance to that job that I can think of.  Don't do anything unless the student asks you for help with the record.

wrong gender would keep being shown to dozens of other teachers for years to come

That's true, but I do not see what is has to do with your responsibilities to the student.  Sensible faculty know that student records are full of errors, and quite frequently lack student's preferred names, such as Andy instead of Andrew.

Is there a better course of action?

If you want to address students by their correct pronoun, invite all of them to identify their pronoun at the start of the course.

The student uses male pronouns,so at least in that regard I'm safe. And FWIW this is the first case of an error in student records I have seen. They really have to be correct as the data is used directly to issue diplomas,grant scholarships and so on.

If the gender was not relevant it would not have been displayed in the report the teacher sees.

@WoJ In my experience student records displayed to the instructor have loads of irrelevant information.

@WoJ Please elaborate on what relevance does it has? Presumably the OP isn't in charge of arranging housing, university students are typically capable of choosing which restroom to use on their own, and pronouns are best established by just asking... So what are you actually doing differently based on M or F?

@user3067860: I have no idea, I am not American. This does not make any sense in Europe and this kind of information never appears on any report. The US being the US it may make sense there and since it is explicitly mentioned I assume it is there for something.

@WoJ Sorry,when did the US enter the picture? My original question is about the EU (and tagged as such).

As an American, I find the "it does not make sense, therefore it must be American" syllogism rather amusing.

@TooTea: ah, that's a game-changer then :) Which country if I may ask?

@Kevin: no - this is not that. From all I read (and having worked 15 years for a US company)  the US is much more, say, aware of race, sex, etc. Problems that do not appear in Europe (or at least in France) do pop up in the US. There is nothing derogatory in my sentence.

@WoJ I work in Czechia and the Netherlands. I'd prefer not to be more specific because this question is now on the HNQ and I don't want to risk deanonymising the student.

@TooTea: I understand, thanks. In that case, things have changed a lot in the last ~25 years since I left academia. Now that I counted and  wrote it I feel old and not that surprised anymore that things changed. Thanks for the question anyway!

@WoJ Possibly the list was typed by hand 25 years ago? These days the list is digital and generated using off the shelf software that is sold to thousands of different schools for all ages...and, most importantly, purchasing decisions are made by some administrator who doesn't actually have to use it and probably tries to make sense of competing software packages by comparing nonsense statistics like "number of fields shown".

Assuming that a student's gender identity is irrelevant to the course, AND that the professor has no particular authority or skill for correcting the database, then doing nothing is the best course of action.

By the use of the word "corrected" you are making an assumption. If they haven't made any declaration then don't act on such assumptions.
You could just leave it alone, and if the student wants it changed they will probably act on it. But at most, tell them that they should (might want to) review their student records with the appropriate office to decide on any desired changes.
I'd guess there are students of university age struggling with who they are. To some extend we all experienced that, perhaps.

Right, "corrected" is probably a mistake (although it would be okay if it is a clerical error, which I think is the much more likely explanation). Perhaps "changed" or something would be better? The whole reason I'm even considering doing something about this is that the web form with these basic personal data is quite well hidden from the perspective of a student (it's filled in once by the administration when enroll in the university and then probably never touched again), but the data from there is shown to every teacher as a part of the list of students enrolled into a course.

I'm with @buffy here. You make the assumption that something needs to be changed or corrected. That may be true, but it may also not. The student may very well like to keep an ambiguity about their gender, and it's not your job to point out that the record does not reflect how they present today. I've known a person who showed up as a woman one day at a conference, and as a man the next.

Sometime every year, the central admin at my university asks me (faculty) to check the correctness of the various bits of "information" they have for me. Sure, address, phone, next-of-kin (in case of accident?), and mostly mundane-though-personal things. This also includes expressions of preference about whether bits of info will be publicly accessible, or not. In the past, the default seemed to have been that lots of stuff was public, but not so much now.
Assuming that students have the same option to adjust/update their "personal information", you should just give a blanket encouragement to students... for gender-related but many more... reasons, to be sure to look at the univ's "personal info + preferences" file for them, and update as needed.
I think this approach would avoid a lot of the invasiveness and potential insensitivity/presumption about dealing directly with the specific possible issue-at-hand.

This approach feels like a good start, but I feel are 2 things missing: 1) tell the students where to find the information that is held on them, we have had lots of questions here that amount to students not being good at finding information in university computer systems. 2) Explicitly say that gender is self determined and need not match their passport/id card/whatever. Lots of organisations are pedantic about that, so students may not realise they have a choice.

The intent is good.
I would find a way to do it that’s less likely to be professionally dubious and to the student, alarming/creepy/distressing, though.  Which is the likely outcome, handled that way.

I have noticed that an undergrad student in a course I teach...

This is the key, and it’s all that is needed.
If you teach in person, then good, ask them to hold back a moment after a class or supervision session. If not, consider if it’s better to email or ask if you can have a word (adding also "it’s nothing bad, a course admin thing I need to check").
Then simply say something like this:

Hi! It’s nothing big. I wanted to double check what pronouns you want me to use when we talk [or work/during supervisions/whatever, pick one as appropriate]. It matters to get them right and I’d like to be sure rather than make a mistake.

That way you’re using a legitimate reason, that they are your student and you will at some time have to communicate to them, or with them, or about them, to someone or other, be it written course correspondence, exams, informal, educational Q&A, discussions with other staff, whatever. So you want to double check what's right, to not make a hurtful thoughtless mistake.
That’s legitimate. It comes over well. And it doesn’t sound like you trawled records. They’ll probably like and appreciate the care involved, which indeed you show.
If you feel this could be an issue affecting others, it’s also not a bad thing to ask all your students at some convenient time, and let them know its okay to advise of pronouns if they wish. Treat it like any admin thing, as routine as letting them know next class time or handing out coursework.

Hi!  Before we start, I have a small administrative thing. I'm updating my records, and I like to check along with names, if anyone has pronouns that they want to let me know. For reference, mine are [whatever]. If anyone wants to make sure my records are correct, please catch me some time or drop me an email. And now, back to (subject).

The people, to whom it matters, will very much notice the invitation.

"What pronouns do you want me to use?" and "what should I have in my own records?" are not the same question as "do you want the university's official records changed?"

The difference is, they are legitimate and valid questions that don't cause issues, and tell you whether the official records have a problem in the first place.  Which is what the OP actually wants to know, a non creepy "better course of action". ......

...The answer obtained either confirms the official records are right, or allow the OP to legitimately follow up internally by correcting them without distressing or involving the student further: "Hi, I noticed that X appears to be incorrectly listed as female on our official records but he's just confirmed he's male. It came to light as I was checking my own records. Can we correct this? Thanks!"  Additional benefit, its fixed without emotional labour on the part of the student, rather than demanding they jump extra hoops

Or, if so desired, by asking them, "okay, I've noted that on mine. Do you want me to chdck/make sure the official university records say the same?

"Follow up internally without involving the student further" is a very bad idea, when the student hasn't actually indicated that they want OP to do this. As discussed in my answer, it's not safe to assume that changing the record is the student's desired course of action. It's also very unlikely that university admin would be willing to change a student's recorded details just on the say-so of a teacher, without documentation or a direct request from that student.

Yes, check. For sureBut it solve the OPs actual problem which is identifying if there's actually an issue related to recorded gender vs desired use-gender, without creeping out the student.

I suspect that what has happened here is that your student doesn't realise that their registered gender need not match their passport/ID card/birth certificate. So when they filled out the form, they put down the gender they thought they were obliged to use, even though actually they could have picked the right option.
There is also a non-zero chance that some years ago, when they filled out the form, they weren't sure, but now they are more settled. Statistically, an undergraduate is right in the age band where that can happen, and testosterone acts very fast. It might only take a year to acquire a good beard.
Either way, I agree with the answers that suggest a blanket email rather than targeting this student. Is there an LGBT organisation at the university? Maybe you could ask them to send an email around explaining that;

The university welcomes folks of all gender, and respects the gender that students self-id as.
Any student is welcome to change their gender marker in the university database. It need not match any other documents.
That can be done by going to https://..... and clicking on blah

If your student is actually trans it's reasonably likely they open an email with something like "encouraging gender self-id" in the header. Of course, it may be that they don't read their email much at all, but we must live in hope.

99% of students see themselves as either male or female. Among bearded blokes named Andy the percentage may be higher.
A simple question to the person: “Hi, according to the student database you are female. Is that correct?” will give the student an opportunity to either tell you it’s correct, or to fix a mistake. And there’s the possibility that the wrong picture ended up on the database.
And please nothing like “should you want that corrected” - here you are making assumptions. A simple question makes no assumptions. If I was Andy and you said I was a “potentially trans student”, I’d be very annoyed about you making assumptions. PS. I know a lady whose complete name is the same as mine except for one letter. Had we been at the same university, any mixups wouldn’t have been too surprising.

No way this is a wrong picture. We meet in person every week and the student looks very much like the one in the photo. But isn't directly asking about their gender (which is absolutely none of my business) way worse than just pointing out what I see and letting them decide whether to do anything?

You wouldn't ask about the gender. You would ask "is there an error in the student records"? And excuse me, but for most people you get their gender correctly, and for a large portion of the rest you got the gender that they want you to assume.

I very much agree with @gnasher729 here. Don't assume anything, that's non of your bussiness. Nothing here is strictly your responsibility, the only thing you can claim is a general interest in the admin being correct as a member of the institution. So they most you can do is ask 'Is this correct?' and accept whatever answer you get. It's also the best thing to do because it allows the student to just say 'Yes' and walk away (as is their right).

I was thinking about sending them a short e-mail along the lines of:

Dear Student, I have noticed the university records show your gender as female. Should you want to have that corrected, contact the
Department of Student Affairs. Feel free to ignore this message if it
is not relevant, I don't expect a reply.

This is a good approach, but I might tweak the wording a little, e.g.:

...You may already be aware of this, but if not, Student Affairs would be the department to talk to about updating that information.

You're right to take this to the student first and only. Never ever out somebody as trans or maybe-trans without their consent. Let Andy decide whether to take this further.
For a variety of reasons, it's possible that Andy is aware of the record and either doesn't want to change it, or isn't able to change it. Sometimes it's hard, expensive, or even impossible for trans people to get gender markers changed on official docs (e.g. the university requires amended birth certificate, but issuing state refuses to amend).
There can be safety considerations here — Andy might not feel comfortable having such a request on record, or might not want his parents seeing letters addressed to "Mr. Andy Smith".
There can also be administrative reasons, e.g. I know of trans men who've had insurance claims for health services denied because the insurer had a hardcoded rule saying that men couldn't have pap tests.
So, by all means let the student know what's on the record, but don't assume they haven't considered changing it.

I know a person whose father was completely drunk when he arrived at the registry office to record her birth. She didn't get the name that her mum and dad agreed on as a result. She's lucky she was registered as female, that was probably a 50/50 chance.

@gnasher729 I recall at least one case where an immigration official misspelled the family's name and it was easier for the entire family just to change to the misspelling than to get it fixed.

Very hidden in the comments to the question, the OP states

"the student uses male pronouns."

There you go. You absolutely do not need any other information, and if you feel the urge of taking actions, simply write to the maintainer of the database or to the relevant office and point out there is a typo in that database field, but as other already pointed out, it is best to leave that to the student themselves.

No investigations, no typical male physical attributes, no creepy direct question to the student, really noting else is needed.

Sorry, but this isn't going to work. The standard procedure is for students themselves to request any changes to their personal data, and it would be extremely awkward for me to request changes to somebody else's record. It will have to involve the student and the whole point of my question is how to do that.

Actually, whatever pronouns you use, and what gender you identify as, do not need to be linked. So you can't just draw conclusions just like that.

@IvoBeckers very good point. How offensive would you find a direct question "what gender do you identify with?", from a peer and from a person superior to me in the power-scale? I, and I speak for myself, respectively "a bit offensive" and "very offensive".

@EarlGrey for me personally I wouldn't care, but I can imagine a large percentage would find it offensive yeah. I also do not claim to know the best course of action here, I merely wanted to make that remark

@IvoBeckers I totally agree, but in the academia english speaking world, it is common to self express how to be addressed (his/her/their) and it is assumed that such expression clarify the gender (especially with his/her).
Your remark "whatever pronouns you use, and what gender you identify as, do not need to be linked" was true until some years ago, nowadays less and less.

You are seeing the tip of a tree, but there is a forest that you need to burn down as fast as possible: why are students' genders recorded?
The student can take care of themselves. Maybe it has already been done, and maybe they will be a female in three months, who knows. Maybe they already are, and this is none of your business.
You can start a movement to ban the recording of gender in students' registers.

Quite frankly, this is not a hill I'm willing to die on. As you might have noticed I know very little about the issues of gender and the like. I'd love to be able to help one particular student out, but I'm certainly not going to start a big movement to have half of the university systems and processes overhauled.

@EarlGrey Since you asked for feedback, I downvoted because your answer, while correct, does not address the question.  The asker, as an instructor, cannot change the fact that gender is recorded.

@TooTea "I'm certainly not going to start a big movement to have half of the university systems and processes overhauled." I am sure you have good intentions, but instead of fixing a potentially dangerous system, you give the burden to the potential victims of "saving" themselves from the dangerous system, while you absolutely have the power to move and change something, since you are in the system.

Comments are not for extended discussion; this (quite interesting) conversation has been moved to chat. Please use the chat for continued discussion; comments below this one should have a realistic chance of leading to the answer being edited.

Re "the tip of a tree": Do you mean "the tip of the iceberg"?

They burn down the forests on other planets, but here? Is it the idiom see the forest for the trees that is referred to?

This is a non-starter, because recording data on gender and other protected categories is all but essential for a university that wants to assure its compliance with anti-discrimination laws. For instance, without that data it's much harder to tell whether your recruitment process is unduly favouring one gender over another.

@PeterMortensen thanks.

@GeoffreyBrent and is it necessary to share these informations with teachers&co?

@EarlGrey Often a person's gender isn't obvious from their physical appearance, and providing that information - assuming it's correct! - can avoid some awkward "sir-er-ma'am-er-sir" moments.

@GeoffreyBrent this goes against whatever small steps against gender discrimination we did in the past few years. Gender is not important, can we get rid of archaic way of expressing ourselves? We are in academia:SE, most of the discussion is about research&progress, but we still use wordings from centuries/millenia ago :) ! Why can't you simply say "dear student"instead of "dear sir/ma'am"? I admit in English is super easy, less so in other languages ...

dear @PeterMortensen I am sorry you could not find a correct codification for that expression, but hey, if John Heywood documented the English use of the proverb in 1546, why can't Peter Mortensen document the international use of such an expression in 2022?
Do as many edits as you want, but ask yourself: am I crystallizing the language?