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Planning a PhD project in mathematics
I am obliged to hand in an an exposé outlining my PhD project in mathematics, including some kind of working plan. Since it is answered here and since it can be easily found on the internet, I have some understanding about what such a working plan should look like.
However, when it comes to fleshing this out, I have large difficulties. But I am sure that I am not the first would-be mathematician writing a working plan in the world, so how do others do it?
What I struggle with. For instance, I have no idea of what I want to achieve within the (expected) three years of my studies, and apparently, since we fixed a very broad working title for my thesis, neither has my supervisor.  My Master's was in a different field with only minor connections to the one I am about to start my PhD in.
Therefore, I expect that I spend the first weeks or months getting used to the field, reading literature, working on small problems of which hopefully one turns out to be interesting and fruitful enough to build a theses on.
But I have no idea how to foresee when I will be done with spending most of my time on literature, when I will have solved which problem and finished the proof for what theorem, when I will start compiling my results into a thesis, when to write which chapter of it or when I will hand in a paper with what title to which journal.
How I've solved the problem in the past. To my shame, I have to admit that when writing my Master's thesis, I had not made any plan either. I just worked into the day and in the end, there was a thesis. I am aware that this is a very inefficient working style, but apparently, expectations towards my thesis were low enough such that it worked out. I expect that for a PhD, working in such an unstructured fashion does not work out any more; therefore, I am actually motivated to give my work more structure.

Your advisor should have answers to all your questions. That's what "advising" means!

Either of the words "proposal" or "summary" would be much better than the word "exposé". The term "Exposé" is typically used when writing about something unknown (in the sense of having been intentionally hidden by some person or group of people) or scandalous.

You don't say whether you have a problem (research problem/question) or not.

@Buffy What counts as a problem? I certainly have no problem of the "prove conjecture X" kind. But I think "work on something from subfield Y" does not count as a problem. In this sense, no.

Is this in the UK by any chance, given the short expected length of the period of PhD study? If that is the case then there may be a bureaucratic rather than academic reason behind the instructions you have been given

A key thing with such plans is to not overthink. Such a plan is always only a rough outline. There will be no one that forces you to actually follow it in any detail. In fact as long as you don't completely change subjects, no one will even notice and even then you can always blame some unforseen circumstances.

@YemonChoi No, in Germany, where this duration is common as well. But you are right, the instructions are mainly due to regulations.

If you don’t have at least one research problem, you can’t write a plan.
That’s the core of your difficulty (based on your comment in which you explained that you don’t have a research problem). A plan is the articulation of what your objectives are and how you think you might achieve them. But you don’t actually have any concrete objectives. So the idea of writing a plan is unattainable - you’re not even in a position to get started doing this. It is a classic case of putting the cart before the horse.
Now, let’s talk about what a research problem actually is in pure mathematics. You mention proving a conjecture, that’s certainly a type of research problem and the most concrete and well-defined one. If someone asks you to come up with a research problem, stating that you want to prove someone’s conjecture is the easiest type of problem to come up with, but on the other hand it’s probably the hardest to actually solve since presumably other people are also trying and have not yet succeeded. So for a PhD project it’s perfectly acceptable (and usually advisable) to be a bit less ambitious and have slightly less concrete goals. Such goals can be along the lines of:

Improve a known result from the literature, by weakening the hypotheses and/or strengthening the conclusion.
(E.g., if Jones proved that all infinitely differentiable frombloids are magnabulous and you manage to prove that it’s enough to assume only seven times differentiability, you’ve improved on Jones’ result.)

Prove an analogue of a known result
(E.g., “all p-adic frombloids are semi-magnabulous in the Smith topology”, when you are the first to study p-adic frombloids but are guided by Jones’s ideas in the differentiable case.)

Prove a variant of a known result with stronger hypotheses and stronger conclusions, or weaker hypotheses and weaker conclusions, or hypotheses that are neither strictly stronger nor strictly weaker than the original.

Sharpen a numerical constant in a known result
(E.g., “the fractal dimension of a magnabulous frombloid is bounded by 17.781”, when Jones proved the bound 27.13)

Prove (or disprove) a converse to a known result

Etc etc.

Now, the point here is that research problems exist on a spectrum of vagueness-concreteness. It’s okay to not have a completely accurate idea of what it is that you want to prove when you get started (as someone said, that’s what makes it research). Very experienced researchers even sometimes start thinking about a research area with a completely vague goal of the type “I want to understand [research area/class of objects/etc] better” (I know that I sometimes do this myself). But there’s a strong caveat here: you are a PhD student. A goal that is suitable for an experienced (not to mention tenured) researcher is not necessarily suitable as one that a PhD student should be given to try and solve with the expectation that there will be a reasonably high likelihood of success. And specifically, for a PhD student I think it’s pretty essential that the goal should be fairly concrete. Just “I want to understand X better” is not a recipe for success at your stage, and in fact even for experienced researchers it often leads nowhere.
So what should you do? Talk to your advisor. Explain to them that you think the project should be fleshed out some more before you begin writing your exposé and that you need some actual, specific problems. It is their responsibility to help you find problems that are suitable to work on; ideally you should have not just one but at least three or four fairly concrete goals, of a more or less realistic level of difficulty for your level of training when you start out. If your advisor isn’t able to help you come up with some ideas like that and bring you to a point where you can start putting a plan on paper, sadly they are probably not a very good advisor, and you might have more serious things to worry about for the future of your project than just the current difficulties with writing the plan. Anyway, hope this helps and good luck!

This may seem like a joke, but it isn't intended as such. I'll give you an algorithm.

Find a problem that seems suitable.

Work like crazy to try to solve that problem, either establishing a proof of correctness or a counterexample. Spend enough time and effort at this to determine whether it should be successful (either way) in a reasonable amount of time.

If you succeed at step 2 determine whether the result is significant (again, either way). If it is not significant, go back to step 1.

If you don't succeed in a reasonable amount of time, go back to step 1.

You were successful in establishing a significant result, either positive or negative. Write it up. End.

Along the way use your advisor as necessary and consult the literature as necessary. This is especially true for step 1. Others can help as well if you have a math seminar available for general discussions on problems and ideas.
My own doctorate in math required three passes through step 1. The first pass resulted in a lot of insignificant theorems. The work was abandoned. The second pass was a total block. Nothing could be learned. Back to step 1. The third pass got me to step 5 and my degree. Quite a nice result if I do say so myself. My advisor was helpful in step 1 (each time) and in validating my judgement about the three attempts.
And note that step 1 can be the hardest step of all, since you take it at the time you know very little. Things that seem to be one thing turn out to be something different.
While I called this an "algorithm" it has some indeterminate parts, especially the time and effort part. No one can schedule "success" in research. It is a dive into the unknown. A voyage where no one has gone before. It might also fail to be an algorithm if you fail at some step, such as 1 or 2. Some people refuse to give up a problem when they should.
To make step 2 reasonable, work on some schedule that is fairly intense but includes breaks so that it doesn't negatively impact your mental or physical health. Or your personal relationships.

At step 4 write up what you think you have learned in a notebook that you can return to later if you get some inspiration.

How structured is your step 2? I guess, the research plan I am asked to provide is supposed to be written after the first iteration of step 1 – at least, I have enough time for handing in the plan to come up with a problem. Do you just work like creazy until you think that this leads nowhere, or does your craziness have more structure to it?

I think the whole concept of planning research is misleading. If you can make a detailed plan, maybe even including the results, then it's craftsmanship and not research. E.g. try to devise a plan for proving the Collatz conjecture.
But as your PhD program seems to have a fixed run time of three years, it's good to create a schedule for yourself, how much time you want to spend for literature survey, for pinning down the exact thesis topic, for research, for writing down the thesis, and so on. You can see this schedule as a friendly reminder before you get into trouble for e.g. spending too much time on preliminaries.
But don't be too surprised if your progress doesn't match your schedule. After all, doing a PhD means researching something that hasn't been done before.
And always keep in contact with your supervisor.


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What is the timeline for using arXiv in computer science?
In mathematics, the timeline is typically as follows.

Upload a completed draft of the paper to arXiv.
Wait a week or so to see if anyone suggests changes, then submit to a journal.
Once the paper is accepted or major revisions are made, update arXiv. The final arXiv version is the journal version but minus any journal-specific formatting.
When the paper is actually published, add the "Journal ref" to the arXiv entry (this updates some data without creating a new version).

How is this done in CS when there is both a conference version and a journal version of the same paper, which nonetheless may be rather different? I know that the journal version is submitted after the conference version, but what is the timeline, and are the papers different versions of the same arXiv entry?

Step 0. Make sure that the journal you want to submit to permits author uploads to arXiv.

Indeed, feel free to add that to the question if you'd like, though I'd say in math that step shouldn't be necessary.

Step 0.b if it is not allowed: decide to not publish in such a [expletive removed] journal. We are scientists. Science should be open and accessible. Do not contribute to hiding scientific results behind paywalls! Especially in a time where there really is no reason to anymore. There are always open ways of publishing available. And arXiv can even be your main and only publisher. This goes doubly so if you have tenure, but really in most fields great results will stand out no matter where they are published and things are shifting more and more towards "open science" not hurting your career.

I have submitted papers to arXiv, subsequently submitted them to journals which forbid arXiv, added a note to the submission that they had already been published on arXiv and this could not be revoked, and it didn't seem that anybody cared. I suppose they could subsequently "unpublish" it from their journal but legally copyright has been granted to arXiv first, and the journal has no right or ability to override that. (IANAL)

In theoretical computer science, a fairly common way to do it is roughly this:

Prepare a nice, complete, readable version of the paper and upload it to arXiv. This is usually known as the "full version".

Prepare a version suitable for conference submission (e.g. move some proofs to the appendix, save space here and there to meet the page limits, change layout if needed).

Revise both versions based on the reviews & comments if needed, and repeat.

Eventually the paper is accepted to a conference. Edit the accepted manuscript it so that it has the right length, the right layout, etc. Often there are page limits, and hence some details will be omitted. Refer to the "full version" in arXiv for the missing details. The publisher may or may not do additional edits before the paper appears in the conference. This is now known as the "conference version", and it is typically fairly different from the full version in arXiv.

For many papers the timeline ends here. However, some papers will also eventually appear in a journal, in which case we continue:

Using both the full version and the latest conference version as a starting point, prepare a paper for journal submission. If there are relevant changes, update the arXiv version.

Revise both versions based on the reviews & comments if needed, and repeat.

Eventually the paper is accepted to a journal. The final published version may be very close to the arXiv version, or there may be changes in the journal version e.g. due to the reviewer's comments that are not incorporated in the arXiv version.

In brief, there is just one arXiv submission (with potentially many revisions), and it is usually much closer to the journal version (if one ever appears) than to the conference version (which tends to omit some details due to lack of space).
Publishers may also have restrictions on how much of their "added value" (e.g. changes made based on reviewers' feedback) can be included in the arXiv version, and because of this the arXiv version may also be an early draft.
Conferences play a big role, they have strict deadlines, and people organize their work based on the deadlines, so it is common to see papers first appearing in arXiv roughly at the same time as when they are first submitted to a conference (± a few days).

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Double thesis or double topic in thesis?
This is a pretty hypothetical scenario, but it could apply to me based on how the next two years of my PhD go.
Let's say a PhD student in math/applied math has two ongoing projects, both of which are potentially thesis quality, yet only tangentially related to each other. As is generally true in research, it's not clear how impactful or successful each of these projects will go, and the student wants to keep working on both.
Is it possible for a thesis to be split over two unrelated topics? And what happens if both of these topics end up successful (i.e. end up being developed into a full thesis)? Would we pick only one of them to end up as the 'official' thesis?

This is a question for your advisor and your department.

Some related questions: PhD Thesis based on published articles on different topics, Has a "portfolio" of orthogonal projects ever been acceptable for a PhD thesis, instead of a single large project?, Can a (stapler) PhD thesis comprise multiple unrelated papers?

@Anyon Ah thanks!!

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How to thank letter writers
I am nearing the end of my PhD and am now applying to postdoc positions. I have had to have my three reference writers submit their letters to a multitude of different application portals, and I feel bad every time I ask for a new submission. How does one thank the letter-writers after everything is done? I plan to send a thank-you card soon after the applications are all in, and then send an update after I accept an offer, but I feel like I should do something more. Are gift cards or other actual gifts acceptable?

This question is similar to: How should I phrase an important question that I need to ask a professor?. If you believe it’s different, please [edit] the question, make it clear how it’s different and/or how the answers on that question are not helpful for your problem.

@AzorAhai-him- I feel that my question is significantly different. It's not about asking for the letter (or asking for anything else); it's about how to express gratitude. If this is unclear, feel free to offer an edit.

Did you read the accepted answer?

@AzorAhai-him-, I don't see an accepted answer.

Oops sorry, clicking around too fast. The top answer.

Gifts of small monetary value are acceptable, especially if there is no possibility of a hint of bribery for actions not yet taken. That is a possible but unusual situation, of course.
But gifts of sentimental value, assuming modest cost, can be meaningful and valued. Over the years, I've been given small presents by foreign students that represent something meaningful to their own home culture. They are "treasures" of the mind and soul, but not expensive for the student.
Yes, thank-you cards and such are fine. Hundred dollar bills within them are not fine. I assume there are some places with rules about such things and you need to be aware. In particular, passing gifts "upward" in some hierarchies is forbidden. But a card is still fine.
Probably the best time to thank your letter writers and other supporters is when you have finalized the position you were seeking. You can bring them up to date on the situation as well as thank them.
It is also a good idea to keep contact with such folks for at least several years after they have helped you. It opens many possibilities both personal and professional.

Thank you. I will refrain from giving gift cards. A related question is that I am not sure what to give my advisor after I graduate, but I figure that will be similar?

Yes, similar, I think.

I like to give people hand made thank you cards in this kind of situation. I gave my previous supervisor a hand made thank you card when he left for a new job at a different institution, and wrote a short note inside expressing my appreciation for specific things he'd done as my supervisor. I like this option because it feels more meaningful than a store bought card when someone has put in a lot of effort on my behalf, but it doesn't have any monetary value so couldn't be perceived as a bribe.
Academics are generally overworked and underappreciated, so writing a bit more inside a card making it clear how much you appreciate the effort they have put in for you is likely to be much more meaningful than a gift! I know my supervisor has held onto cards given to him by previous students for quite a long time.

Writing reference letters is part of my job, and as such I'm paid for it through my salary. Nothing particular is needed to thank me for it. Don't feel bad about it. Chances are you pay university fees, and these pay for recommendation letters as well. I'm not going to complain about a thank you card and a situation update, but I don't expect anything, and for sure nothing more is needed (certainly nothing of material value).


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Bringing advisor into summer internship project
I have a summer internship in the research side of a big tech company. I already know the project I will be working on, and it has some relation to my advisor's research. In fact I believe he might be more knowledgeable than some of the researchers I will be working with over the summer.
I've already shared what I know of the project with him, and he gave me some general thoughts about it. I'd like to continue getting his input, but signed a form for the company saying I forfeit any results to the company. (I think this just means that they get credit for any resulting papers).
Is it possible/typical for an advisor to get involved in a student's summer internship project?

I think this situation seldom arises, so wouldn't call it typical. There might be university regulations that govern it, since your relationship to your advisor would change somewhat.
But I fear you are being a bit naive about the company's ownership of your results. It probably means that you can't publish without permission (and specific approval). It might mean, or imply, non-disclosure of what you learn. In the latter case, the company would need to establish a formal relationship with your advisor so that everyone understands and adheres to the ground rules.
I don't think there are problems necessarily, but you need to make sure that everybody in the process understands what is happening.

Good point, I didn't think about confidentiality. Will figure that out


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Low ranked master's before PhD
Is it a bad idea to do a Master's at a low ranked university before doing a PhD, if my undergraduate record is not strong enough for me to be admitted into a good PhD program out of undergrad?
The university I am considering is low ranked in my subject field of interest (70-80). However, the university itself has a strong overall reputation and would be considered a household name (top 30 undergrad USNWR).
I know that I would have some decent research opportunities in the master's, as well as the chance to write a two-semester thesis. However, I am not sure about the prestige of the faculty, and the program is somewhat small.

Ranked where? Worldwide?

This would be in the graduate subject ranking according to USNWR.

Would you be happy to live at that place (especially during Covid times, with probably not to many contacts?)? Feeling happy where you live ia much important than any ranking.

Who or what is USNWR?

US News and World Report. They do rankings for undergrad as well as many grad programs. I believe when people refer to the "top X schools" in a given graduate discipline they are referring to the USNWR rankings (or just common consensus). At the graduate level I believe the rankings are generated by surveying professors in the field for their impressions of a given program's reputation, so I am pretty sure they reflect the common consensus among the academic community either way.

@user111388 Yes, I would be happy to live in the area.

Hmmm, 70-80 is not a low rank. But more important, how do you know that you aren't already qualified to apply to a doctoral program - assuming US? A small program might be more of a problem, giving fewer options.

@Buffy The interesting thing is that I had 0 courses in the discipline I would be doing the master's in in undergrad. Plus 0 research experience. So I don't think I could have put together a convincing doctoral application even if I tried. This program admitted me with a few undergrad prerequisites.

I'll guess that the university in question is still an R1 university (and in the US) and is about mid way through the rankings of those. From that I assume that the standards are high and that you should get a fine education.
And, from comments, you probably need a solid grounding in the new field, so I don't really see any down-side.
A small program can be a bit of a problem, however, if it gives you fewer options. Alternatively, it might also give you the opportunity to work more closely with a faculty member or two rather than being part of the "mob".
However, don't make assumptions about what is required for admission to a US doctoral program. People frequently choose a different field than their undergraduate major. The typical program is heavy on coursework at the start and often not a lot different from what you do in a masters. So, I'd suggest that you get a solid understanding of the real requirements.

Thanks for your help. Yes, the university itself is R1. I'll continue to look into the program further to make sure that I would have good research opportunities despite the size.


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Authorship of alternative or fictional personalities
Let's say I'm a student with a dissociative identity or imaginary friend situation that's not going away no matter what, and I feel they contributed to my research and don't want me to take all the credit. Revealing their identity would be awkward if not impossible. What should I do in terms of academic integrity?

Could you add Camille Nous as an author? https://www.cogitamus.fr/camilleen.html

@astronat Cool idea! But what if they do have a name? Especially if the name is already used and will have consequences if disclosed.

In general, there is no problem with including a fictional co-author. It has been done in the past. As long as there is no intent to defraud, which is unlikely, there aren't any serious issues, except...
There is a danger that, unless you are already well established in your field, it will be taken as a joke. There is no problem with jokes, in fact, but that may not be your intent.
And, I hope you are working with a professional on any issues with your identity. And if doing this reinforces what may be a disorder (not my field, so no judgments) it might not be wise. Talk to a professional.


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Timing a career switch from math to TCS
Short version: Is it better to switch focus as a postdoc or wait until after tenure?
Details: I'm a PhD student in math (combinatorics) graduating next year. Let's suppose that I'm a strong candidate for research-oriented, tenure-track positions in math, but my long-term research program is interdisciplinary with TCS. If I have a really productive 1-2 years of postdoc in TCS, will I have a shot at being hired in a good CS department in the US?
I'd rather be in a CS department, but many people in my area don't share that enthusiasm (or are located in Europe). I'm worried that I'll end up with papers in both general math journals and STOC/FOCS and still be unhireable. Should I wait until after tenure?
Edit: Here's why I'm asking. I have postdoc offers in both math and CS departments - I want to take the CS one, but all of my publications are in math journals, and the CS postdoc won't make me a stronger candidate for math departments.

I thought the question was specific enough to TCS to post here (are math publications valued in TCS hiring or am I too far gone to have a reasonable chance of switching now?) I think that's too specfic for Academia.SE.

I am not sure where this would be a better fit; but in view of the downvote and votes to close, it's not clear CSTheory.SE is the best place, so you may want to try there if here doesn't pan out.

Thanks for the suggestion!

@Anonymous Yes, mathematics publications are valued in TCS hiring. It's not like there's a sharp boundary between the two fields.

@JeffE I'm under the impression that this is especially true at your university ;). I've spent my undergrad & grad careers at such universities, and I was curious to see how typical that experience is. In the end, I'll follow what I love anyways and apply to both departments.

It depends a lot on the kind of research you do and the CS department you are applying to. But my guess is that getting a tenure-track position in TCS will be harder than in math. There are some reasons for this:

I think that even if you do a postdoc in CS, people will likely see you as a math person (by background and training). In my experience I am not sure that is a positive: while there are lots of strong CS candidates getting hired on interdisciplinary research agendas, usually it comes in the form of applications of their research -- applications to medicine, biology, etc. Even in TCS, it looks really good if you are applying your TCS research to some specific problem domains (say in computational biology, machine learning, systems, whatever).
To get hired in CS, you have to not just convince the TCS person who is fighting for you, but that person also has to convince the rest of the department. So even if your research is getting published in STOC and FOCS, you also need to have a clear impact in computer science as a whole and that impact needs to be unquestionable.
Usually part of the hiring process in US universities is a talk that you give to the entire department. These talks are very general-audience and need to have a clear focus on specific applications and problems, with minimal mathematics (aside from boiling technical things down to some very simple ideas that are digestible, and maybe a few slides where you explain some proof in detail but no more than that).
I have found in these talks that it can be a bit harder for TCS researchers, compared to those who work on systems, security, etc., because you just need a lot of clear applications. This is where it depends a lot on your research; have you worked on finding applications of your research to some other areas of CS?

I'm worried that I'll end up with papers in both general math journals and STOC/FOCS and still be unhireable.

I think here what matters is how to make yourself the strongest candidate, not the specific journals and conferences (assuming they are top journals and conferences). If your research agenda is interdisciplinary, no one will be surprised that you are publishing in both and that should be seen as a positive.
But I think the "interdisciplinary" pitch is likely to work a lot better in math departments than in computer science departments. So if that is the road you are going for, I would stick to math for now (depending on the impact of your work in TCS course -- if you are proving P = NP, your background won't matter).

I'm interested in TCS broadly, at least - computational geometry/combinatorial optimization/logic and descriptive complexity/approximation algorithms/parameterized complexity/quantum computing/etc. I intend to take the TCS postdoc but with the advice I've recieved here, I will stay heavily involved within the mathematics community. Thanks!


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What does a reference letter for a postdoc/tenure-track position in math look like?
I find myself in the unenviable position of having to draft the body of my own reference letter. I trust the recommender in question to actually treat it as a draft, and I know that they think highly of me as a researcher, but I'm totally stumped. I'm currently a postdoc and for this reason none of my mentors have been willing to share a sample letter with me. I also cannot find one online after trying for several hours.
So can anyone help by providing a specific outline of what such letters usually contain? Is it really almost entirely about research as suggested by my mentors and here? This is for postdoc fellowships and tenure-track positions in research-oriented universities, in math.

Writing your own recommendation letter? Sounds fishy.

I am aware, and I'm sure it has something to do with this person being outside of the US. But they did make it very clear that it was a draft that they would change. Anyways, my mentors recommended I go through with it, and now I have to.

Here’s an example.

Joking aside, based on this question your writing skills seem quite good enough to come up with something reasonable on your own. The premise that a recommendation letter has some sort of rigid structure that must be confirmed too or the letter will look fake is simply not correct. And as you said, your letter will be merely a draft and the official letter writer will make sure to edit out any obvious faux pas that you make, in the unlikely event that you will write something that clearly doesn’t belong in such a letter.

Haha, ah yes, my mistake - I saw the John Nash letter a couple of years ago. Thank you for the feedback!

Oops, I meant “conformed to”, not “confirmed too”. Must be an autocorrect.

@cgb5436 Ironically, "fishy" might be more applicable than one might think here (well not necessarily here but still): in Russian, the initial draft often provided by the side "requesting" the thing is called a fish. It happens all the time with recommendation letters, contracts and whatnot. Moreover, they're typically not confidential but profs have little issue trashing students nonetheless :-) The culture of references differs by country a lot.

Pure mathematician here. I've written several letters for graduating PhD students, for folks finishing one postdoc and looking for the next, and for visiting professors at my university looking for a tenure track job at a liberal arts college. I've also read thousands of such letters when we are hiring.
Broadly speaking, I agree with the answer the OP linked to, that there is an expectation to explain the person's results. There are several reasons for that. First, presumably a senior person is better at explaining the results in terms the hiring committee can understand (thanks to the experience of grant writing for example). Second, it's important to show an understanding of the candidates work, before commenting on its quality. Third, the candidate will likely have some unpublished preprints and the hiring committee wants an opinion about the quality of those and the level of journal we can expect them to be published in.
My template is as follows:

This is a letter of recommendation for X. X is a talented and personable young man who is currently in the final year of <>. For the past three years, I’ve interacted with X via ... X is a strong researcher, an excellent teacher, and a great colleague. X's research touches on several areas that have lately been attracting a great deal of attention, including ... I am very enthusiastic about X’s research, so let me start with that.

The basic idea of algebraic topology is ... X's research connects to these questions via ...

Here you have 2-4 paragraphs explaining the big ideas, X's specific papers, where they were published, and the quality of the preprints. Usually candidates have at least one thing published, and I can say that their preprint should be published in an equally good journal. I try to emphasize that X is a good writer, well-organized, has a track record of bringing things to fruition, is likely to be grant funded, and has lots of promising ideas that are likely to lead to many publications over a productive career.
If I only know about X's research then I conclude with something like:

In summary, X is a bright and talented mathematician, who has already proven many excellent results and has plans to prove many more. In my conversations with him, I’ve been impressed by how quickly X digests new mathematics, with his creativity in solving technical problems with slick arguments, and with his meticulous attention to detail in his writing. I think this skill will serve him well in publishing and grant-writing. X’s research is strong for a homotopy theorist just finishing his first postdoc. In a postdoc with you, I am confident he would produce several high quality papers, could plug in to others’ existing research program, and could expand his expertise in the direction of ... I recommend him to you without reservation.

One might also get a recommendation "in the strongest possible terms."
Because I'm at a liberal arts college, if the candidate is apply to such a place, I include a paragraph about undergrad research projects, reflecting my conversations with the candidate, their interest in such research, and the fact that they have good ideas for suitable projects. If I have seen them give a talk, then I include a paragraph about their teaching abilities like:

Turning now to teaching, service, and colleagueship, it seems clear to me that X is ready for either a research postdoc or a tenure track job at a small liberal arts college. While I’ve never seen him teach, I have seen him give several seminar presentations, and all have been clear and well-prepared. He is an engaging speaker, with excellent board work, and he has won several teaching awards. His teaching statement echoes our discussions over the years, with his emphasis on active learning, empathy, being approachable, encouraging students,  and helping students build up their confidence. I note that one course X taught, .... X's empathetic, relational, and encouraging approach greatly helped his students in this course succeed. X is also an excellent departmental citizen. He served as a peer mentor for new TAs, helped in the summer training for incoming TAs, has run reading groups and helped with the seminar, and stepped up to supervise undergraduate research even in the middle of the COVID pandemic.

I modify this and fill in the blanks based on what I know from the teaching statement, CV, and conversations with the candidate. Most likely you will have a separate teaching letter and there's no real expectation to have teaching mentioned in a research letter, but I do it because it might help a little bit, coming from someone like me at a place known for an emphasis on quality teaching.
Then I put it on letterhead, include my email address, sign it, and send it on time.
I agree with opinions in the comments to the OP that, if you were drafting your own letter, you'd want to leave the subjective judgments to the senior person. It's a real shame if the senior person isn't willing to write the letter themselves, because I think it adds a lot of value to have a second perspective on the research, other than what is already in the research statement. Having the candidate write both seems pretty suboptimal.


text:
How to get recognition of research as an independent autodidact?
I have done my own research independently from any academic institution.  The theses are mainly biochemical, and aquaculture.  I would like to have the work peer reviewed.
I tried to use researchgate.net but they have created a barrier to entry for autodidacts, and non-institutional researchers.  The question answer format for stackexchage is also unsuitable.
Are there other web-portals specifically for independent, non-institutional, autodidact researchers?

"I would like to have the work peer-reviewed." Why not submit it to a peer-reviewed journal then? That's generally better than finding some random, potentially untrustworthy website to upload your work to.

@astronat which journals accept independent work?

I've no idea, I'm not a biochemist. A better approach would be to look at the literature you cite most often and see what journals those articles are published in. Then go to the website of those journals and see what their submission criteria are.

Virtually all journals will accept submissions from unaffiliated researchers. See Does one need to be affiliated with a university to publish papers. It seems like this was mentioned already in answers to your previous question.

Do you have any professional associations that might lend credibility?  For example, are you in an R&D department or do you do technical work related to the field?

As a thought, you might want to think out your big-picture objectives (rather than just "get a paper reviewed" or something little like that) and focus on achieving that goal.  As you're correct to note, academia can have a significant barrier to entry, as hard as it can be for academics to notice it.  The best approach to this barrier is to attack it directly; for example, attending a conference (as I'd written up in an answer) is one way to go.  I mean, if you literally just want to publish a paper, then okay - but you probably want more, right?

You need not have any institutional affiliation to submit your work to the usual peer-reviewed journals. The only downside to lack of affiliation is that people might wonder "who you are". But there's no rule against anyone in the world submitting...
The "gotcha" is that if your writing style, formatting, referencing, and so on do not approximately conform to the standards of the milieu, people will almost surely reject your submission out of hand. That is, it is critical that you not communicate any sort of "crackpottery", which is often signalled simply by extreme, random non-conformity to simple professional standards.
So you might want to try to get advice from a seasoned professional, who knows the "parlance/standards/prejudices" of the profession. This may not be easy, especially if you approach them with a snarky or combative attitude, but I'd wager that you really do need this help.
That is, to get any kind of hearing, you "need" to demonstrate that you can comply, to some extent, with the implicit conformity demands of the milieu. Otherwise people won't pay attention to you at all. No, of course, this is not any official statement, but it is obviously the mechanism in almost every human activity.

Note that a number of journals are also blinded, which means reviewers won't even know you don't have an affiliation.

Join an organization
Most major fields have at least one major organization for academics, professionals, students, teachers, interested industrial representatives, etc..  For example, if you're in the US or other country where they're active, you might be interested in the American Chemical Society (ACS).
Professional organizations can help you meet others in your research area, publish your work (for example, ACS runs several major journals), and potentially find employment.
Attend the meetings
Once you're in the relevant organization, you can try to attend a conference (and some allow you to attend without membership, but often with a higher entrance fee).  Major organizations tend to host at least 1 major annual conference that people come from around the world to attend, plus a bunch of smaller regional conferences and special conferences devoted to particular subtopics.
For example, ACS's next major meeting is the "255th ACS National Meeting & Exposition: Nexus of Food, Energy & Water", coming up in March.  From their landing page:

Why Attend?
Discover new research, network, advance your career.
Learn More

16,000 attendees

11,000 papers presented

16% of attendees are International

22% of attendees are from Industry

47% of attendees are from Academia

22% of attendees are Students

They're taking abstracts now.  If you want to present, you can go ahead and write up a proposal.  In my personal experience, it's not too hard to get a proposal accepted - but whether or not people happen to attend your talk is another matter, so you'll want it to be interesting for that.
Once some of the abstracts have gone through, they'll post a schedule online where you can read about what everyone's doing and plan which talks you want to see.  At larger conferences, there'll often be lots of talks going on at the same time in different conference rooms, so you'll want to plan out your schedule in advance.
Then, network!!!.  Ask questions after others' talks; meet up with people doing research similar to your own and industrial representatives looking to head-hunt talent.  Print off some business cards in advance if you'd like; mostly with your name, contact info (ideally email, possibly LinkedIn/etc.), professional association (if your career is related to the field), and some quick reference to what you're there about, just so they can recall what your topic/area is when they get back home after the conference.
Also, if you do present, you'll often have an opportunity (or obligation, depending on the organization) to post an abstract on their website.  If you're looking for exposure, this is a good option.  You might even post your other work on a pre-print server and reference it (assuming that it's related).
Once you get home, add people to your professional networking.  Put them on your LinkedIn or other professional media.  Try to get involved in the organization; talk on its forums, etc..

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text:
Can I delete figures on accepted manuscript?
I am now in panic. One of my paper got accepted by journal. However, I am stuck with the copyright from two figures I have used in my research paper. These two figures ( these two from open access internet source and free to the public). I just simply thought that I will acknowledge/reference their organizations in my paper and that's it. After I read the copyright requirements from journal, I realize that I need to write and ask for permission from third parties. I already write emails to them but it might take a long time or even they don't answer my email. In there website, it is said that :"All materials that appear on ADB's official website, adb.org, are its exclusive property unless otherwise indicated. ADB encourages users to print, download, or copy information, documents and materials from the website exclusively for personal and non-commercial use".
my research paper is now in the production stage ( pass all review processes) and needs the last step of proofreading.
Is there any chance that I remove these two figures from my accepted manuscript? Or what should I do now.
I know it's my mistake and this one is my first research paper, I don't have any experience in publication. Please help me , I really appreciated for your advice.

I am not an expert once I've used two figures from NASA and togheter with the editor we found out that basically a citations was all that was needed. I can't judge if commercial use extend to the profit that the journals are making. I would check with the editor, as well as try to contact the source. At the end, a proof read paper doesn't necessarily has to go public. Of course redrawing is possible by mentioning it.

"I realize that I need to write and ask for permission from third parties."  That's the answer.

Normally, this is something you would normally arrange before the submission. There may be no perfect solution at this stage.
Deleting figures from an accepted manuscript is not advisable, as it may make your conclusions unjustified. Normally, journal's won't allow significant modifications after the review.
However, a few ideas to consider:

If figures are simple sketches, you can make your own and submit them.
If figures are plots, you can redraw/reproduce them.
Depending on the copyright laws in your country and copyright policy of the publisher, you may be able to reuse a small portion of text/figures from the original publication under a fair use policy.

Thanks so much for your answer, Mr. Dmistry. Can I email to people in charge of production stage and said that I make a small change of two figures by redraw them? Is there possible? I really appreciated for your help and wish you all the best

Normally, it is a good idea to inform both your editor and your publisher (production team) of changes, explaining the reasons for the change. They may suggest another solution, e.g. acquiring a copyright for you, if they think it is worth it.

You probably need to cite the original figures even if you don't use them but draw your own, as plagiarism is also a possible issue.

I suggest that you inform the editor immediately of the problem. Some publishers will act on your behalf to obtain (and possibly pay for) copyright license. It is worth an ask.
But the editor needs to be informed in any case. Don't delay. You would need their permission to delete as it may affect the readability of the paper.
And the solutions suggested by Dmitry Savostyanov may be open to you of course.

good answer.  These things happen all the time.  Let the Journal help you get what you need.  No reason to panic, and no reason to eliminate figures.


text:
Paper Suggestion/Recommendation Tools
To make literature search simpler and more efficient, I'm looking for a good tool that would come up with a list of publications based on a given set of publications/research areas. So far, I've found Mendeley Suggest but it does not seem to work all that well. I was wondering if someone in this community might know about a better tool or an altogether better approach for pursuing efficient literature search.

Hmmm. The one we used to use was called a Library. If a tool is too specialized it will come with an assumed set of both false positives and false negatives. The latter is more problematic.

The low-tech way will be to check in google scholar who cites each of your papers. You list will be ranked by citations number, so you can immediately see which paper is more important.

This doesn't seem to answer the question about how to find papers.

This approach would simply find papers that cite a reference paper. I'm looking for other papers that are related to the reference paper, perhaps published even earlier.

The old school way would simply to read a review article on the research topic or field, that is what they are there for - to provide efficient access to recent literature! Note that using Google Scholar combined with a good review article can help you search both forward and backward in time. The review article itself summarizes the past literature. If the review was published some years ago, the citations to that article on Scholar will help you quickly and efficiently learn the recent progress.
A related minor suggestion is that I also find that investing some time building a profile on a site such as ResearchGate can pay dividends, as it will show you recent papers by authors you follow, and also help surface papers you might be interested in. However, this is a longer-term strategy for keeping abreast of the literature.

Thanks for the suggestions. I was hoping that there are some standard machine learning tools out there that can help classify papers, and possibly save me the work of manually searching for the papers :D


text:
What are the benefits of serving as a reviewer, initially as a PhD/PostDoc and later as a faculty member/research scientist?
The very first thought that comes to mind is that reviewing a paper is like giving back to the academic community. After all, one's own work is published after the efforts of some anonymous reviewer.
But what are the primary incentives that motivate so many researchers to voluntarily serve as reviewers? Does it make a researcher more established/reputed? How does it differ in the case of PhD students as opposed to faculty members?

Related: To what extent is reviewing work beneficial for young researcher's career?, Should I agree to review papers as a postdoc?

An important recent development is that publishers can now provide recognition to reviewers by confirming the refereeing work on ORCID and Publons.  Previously there often wasn't any way to confirm the reviewing work of a researcher.

This varies quite a bit by stage of career. For a senior academic it may just be seen as service to the community that provided service to him/her along the way.
For a mid level academic or even a student, however, the opportunity to get the earliest view of new research may be compelling. It can be a source of "hot" new areas that they can explore in their own research.
And for a beginner, seeing a lot of academic writing in your field might help you develop a compatible style that will be viewed favorably in your own writing.
The actual incentives are small, of course. Your name may get mentioned for some sorts of reviews, such as reviewing after publication for something like Computing Reviews

The primary advantage of peer reviewing is that you are ahead of the researchers in your field by a margin of several months. Second advantage of getting a bad paper for review is that you get an idea "what to avoid" in your own future work. Most people do not realize this because it is not a paid service, nor there is any public acknowledgement on the paper. Several journal editors have mentioned to me that they have difficulty inviting reviewers. I asked an editor of a pretty good review-type journal and he mentioned that at times he has to write to 10-12 people and only a few respond. It is a also common complaint among editors that people from certain countries don't commonly accept peer review requests because the academic promotion is based on paper publications rather than article reviewing.
In short, we should accept review requests, if we feel we are qualified to do so, as a service to the community as well for your own education.

The aspect of being ahead is rather field-dependent. In my field, most would post a preprint around the same time as the journal submission.

Yes, pretty common is mathematics and physics as well, but this pre-print phenomenon is quite recent.

Something that may be more anecdotal, and relevant only to some: in the United States, reviewing for established venues or journals can bolster* your application for a green card, citizenship, or some visa statuses. In particular, it is something to mention on your CV/in your application.
*Maybe not a lot, and I don't have first-hand experience; but I have been told so by several people applying for such statuses.

I've heard the same from an immigration lawyer specializing in such applications for scientists. However, I've also heard that USCIS recently (last year or so) started giving less weight to reviews at least in green card applications "because everyone reviews papers". To bolster your chances now, you need to review an unusual amount of papers, or, ideally, receive personalized invitations to review appealing to your specific expertise, i.e. not just form letters.


text:
How do search committees judge the publication list?
As I understand, the search committee held a meeting to shortlist a few candidates from tens (or even thousands) of applications received. Thus, they should decide by a quick look at the CVs. The list of publications is the most important part of a CV, but how they can judge the quality of publications?
Many of the committee members are not expert exactly in the applicant's field to know all the high impact journals. On the other hand, by the growing number of open access journals by unknown publishers, there are similarities in the name of high and low impact journals.
A committee member spends a few minutes to read an application, how he or she judge if this list of publications justifies being shortlisted?

The list of publications is the most important part of a CV. That is not unequivocally true. The university reputation and advisor counts as much if not same.

@mystupid_acct when the list of publications is considerable (should be the case of the OP), the applicant is not at early stage. Thus, his advisor or education is not as important as his ability in conducting research and attracting research funds.

This also depends on the field. I've never listed on my CV who my advisor is/was.

First of all, you should not presume that a committee member spends just "a few minutes". Even for large volume searches, a huge number of applications fail some very basic filters (Do you have a PhD or equiv.? Did your cover letter show some flicker of recognition as to what you were applying for?, etc.) that affords the committee more time on the actual applications that may or may not make the short list. In my experience, searches are massive expenditures of time on the part of the committee and are taken pretty seriously - after all, they're talking about spending potentially hundreds of thousands of dollars and having to work with someone for 5+ years.
And while search committee members may not be experts in the exact subfield in question, there's good odds one of them has a notion of the broad strokes of what's a good journal and what's not. It's also possible to look these journals up if it's unclear - or to ask colleagues closer to the field in question "Hey, have you ever heard of the International Journal of Epidemiology, and is it any good?" (For reference, the answer is 'Yes, and Yes').

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text:
What to include in a Festschrift (memorial publication)?
A now deceased professor would have turned 100 year this year. What is the best way to honor his achievements?
Should a Festschrift (memorial publication) include:

Personal anecdotes on how you first met his thoughts in university
Personal reflections on what his thoughts has meant for your career further on in life
Review of publications
Links to others reviews of his publications
A detailed paraphrase of his most important works, step by step
etc

A couple of memorial papers in particular stick in my mind, from my field.
These are:
"A tribute: Professor Dr. Paul Hoffmann (March 28, 1931–July 10, 2008), a scientist with a great collaborative spirit"
and
William A. Arnold by Govindjee and Srivastava (2014)
If you can't find either of these then I'll link you to them. What sticks out for me when reading them is just how personal they are. They can go into quite a bit of family history and life history, telling some anecdotes, whilst showing happy, relaxed photographs of them. At the same time, they can cover the most important achievements of that person's scientific career.
There are plenty of examples out there for you to draw from but at the end of the day, this is your tribute to the person so make it how you think is best fitting to them and their legacy.


text:
Taking vacations days in the middle of a semester
Context: I am an assistant professor at a small institution in the US.
Question: My significant other has the opportunity through work to travel to an exotic location over a long weekend in February, and I would very much like to join.  That said, it would require that I miss both my Thursday and Friday classes before the weekend.  Would it be unreasonable and/or unprofessional for me to join her on this trip?
I can easily structure my content schedule in such a way that I could cancel these classes without losing anything significant, but I'm concerned about how such an absence would be perceived by my colleagues.  I have an excellent relationship with those in my department, my department chair, and my dean.
I would also be curious to hear how dependent the answer is upon my tenure status.  I am tenure-track and plan to apply for tenure three years from now.

You need to discuss this with your chair.  In many places, taking personal vacation during the academic term is considered unacceptable, although canceling class to participate in a conference might be OK.  Ultimately the answer will depend on local norms and rules.

I am not a professor, but it would seem to me the best/expected solution would be to find a substitute instructor (perhaps a graduate student) for those two days instead of cancelling outright.

Some have colleagues who always move classes on Fridays without good reason except they want a longer weekend...

In the departments I have worked in, it would probably be considered unprofessional to leave on a pleasure-cruise in the middle of the semester. I suspect that that is universal.
In other words, this is not the image you want to project as someone who will still have to go through the tenure process. On the other hand, it's a fairly small thing -- people are gone all the time, although almost always for professional reasons: at conferences, workshops, for collaborations. So the mechanics of being gone are all appreciated in any department, such as moving classes around, giving out reading assignments instead of in-person classes, or putting a midterm exam on such a date and having someone else proctor the exam. Students also understand these things. In the end, it will be a judgment call: It comes over as "frivolous" to leave for a vacation and cancel classes over it, but it's also not a huge deal and I'd be surprised if anyone would think that you'll lose tenure over it. It's just a bad mark in your peers' perception of your professionalism.

First of all, I’d suggest leaving questions of perception aside. It is much more helpful to think whether your suggested behavior is unprofessional than to worry about how it will be perceived by your colleagues. But for the first question, don’t just think about superficialities like whether you have the technical ability to reschedule or cancel class or ask a colleague or TA to give it in your place. You need to go deeper than that. Ask yourself:

Am I potentially inconveniencing my students by redesigning my class schedule to fit my own personal vacation plans? Can I really claim to have my students’ best interest at heart when I say I can “easily structure my content schedule ... without losing anything significant”? (The word “significant” here suggests to me the answer is no.)
Is the TA or colleague whom I’m thinking of asking to cover my class while I’m on vacation equally qualified as me to give those lectures? Will the students benefit equally from hearing this lecture from the TA/colleague as they would if I were present to deliver it? (Again, I’m guessing the answer is likely no.)
Will my absence also inconvenience my students in other ways because I’ll have to cancel or reschedule office hours, and be less available to answer their questions over email while I’m on vacation?

You can go even deeper and think about second- and third-order effects of the vacation plan:

Will my behavior contribute to a healthy departmental and institutional climate? Do I feel comfortable with the thought that my behavior might push norms in the direction of faculty members generally doing whatever they want based on their own convenience, without oversight, without regard to university policies, and without considering the larger picture of the students’ interests? (E.g., perhaps you are acting in a thoughtful way and making sure you’re not hurting the students, but a colleague who sees you behave in this way and might be tempted to behave similarly in the future may not be as thoughtful as you.)
Will taxpayers in my state feel happy hearing about my behavior, should it get covered by a local newspaper? Can my behavior conceivably cause reputational problems for my department or university?
Etc.

The bottom line is that to behave professionally is to show yourself as a person who understands that they are being paid to perform a job, and that that job entails certain responsibilities that must be taken very seriously. If you can consider all the questions I listed above and come up with serious, sincere, well-thought out answers to all of them that demonstrate convincingly that your vacation plan is not going to create any inconvenience or negative effects for your students or anyone else, I for one will be more than happy to say you’re acting professionally and to wish you a fun vacation.
That being said, based on how you phrased your question, I feel it’s premature to conclude that you’ve really taken all the effects of your vacation plan into account in the way I’ve suggested.

In the departments I have worked in, this would be completely fine (provided there is no additional work to your peers). So if you need someone to cover your classes (which probably looks better than cancelling them), let it be someone who is familiar with the material and is sympathetic to you and pay the favor back. People generally understand if you take a short vacation because of a one-time-opportunity like it is in your case. This is especially the case if you are "friends" with your peers.
You might want to consider if there are any rules against this and if other people also did this. But don't be afraid to ask, especially given your good relationsship to your superior.

This is a question for your colleagues and chair. A couple of days probably isn't going to be much of an issue, but it will be frowned upon if only a bit. But people go off to conferences for similar amounts of time.
But even better if you can be available to your students via something like email or a mailing list while you are away.
I would say the equation would change if it were a week and both week ends. Now it starts to be a disadvantage for student learning.
You can also offer to do a makeup for anyone who wants - evenings or week ends or virtually somehow. Or extra office hours.
But first, ask those whose opinions you value. Especially as an assistant professor who will be judged by your peers, partly on your commitment. You might just raise the "opportunity" in the coffee room as a possibility and listen to any opinions that are offered.


text:
Do PhD students get the 3 year contract in the beginning in Germany like they do in Sweden?
I am about to finish my masters from Sweden and have a PhD offer from Germany and in Sweden. I recognise the pros and cons of each offer, but I would like to have a more generalistic view on doing a PhD both the countries.
P.S. The university in Sweden is: Chalmers university of technology
The university in Germany is A research institute and with collaborations with industries.

Can you clarify what it is you want to know? In the title you refer to "the 3 year contract", but in the text you state that you "would like to have a more generalistic view". So – is your question about contracts or about doing a PhD in general?

I want to know about the contract system in Germany and also the difference in doing a PhD in Sweden and in Germany

You need to ask the person offering you the position in Germany about your initial contract time. This vary quite a bit, as far as I know.

Small warning though - when you ask, I would frame it as important for visa or housing matters. Just asking whether you get a 3-year contract immediately without context may give the impression that you are not very confident in your fitness for the position, and want to know whether it will be hard to get rid of you if you don't perform.

Your question is unclear to me. On one hand, you said you recognise the pros and cons of each offer. On the other, you would like to have a more generalistic view. Your question title is about the length of the contract. What exactly do you want to ask?

In Germany, there are many possibilities for funding PhD studies:

Scholarship: The research group can offer a monthly scholarship, but this depends on the financial power of the group, and his interest in the candidate. Otherwise, many programs offer scholarships to young talents (e.g. DAAD)
GRK position: The German government ( Represented by the DFG) supports some field in some universities by introducing a limited program called "GRK: Graduiertenkolleg". This program offers full/half positions to PhD candidates to finish their studies.
Project position: If a research group has a research project (German or European) with a budget for positions, it is possible to hire PhD candidates. However, their work must be within the project purpose. Usually, PhD candidates employed by projects write their dissertations in the same context of the project. Otherwise, it is tough to work on two different projects.

Almost in all the above cases, the duration is limited to 3-to-4 years. However, people can get another contract to finish their PhDs and in the same time help in other projects.

I'd break down #2/#3 in a quite different way. There are (a) faculty positions with obligation to teach and opportunity to write a thesis (initially limited to 3 yrs, with extension option), a so-called "Landesstelle", because the money comes from the state. And there are (b) project positions usually with obligation not to teach (funded by any 3rd party, like DFG, which is interested in the project only, not in upholding teaching). In the latter case, contract duration depends on whatever the professor negotiates with the PhD student (within the limits of  project funds being available).

"However, their work must be within the project purpose. Usually, PhD candidates employed by projects write their dissertations in the same context of the project." - these statements should be qualified with an extremely bold and large "in theory".


text:
Chicago Manual of Style - notes in footnotes
When using Chicago Style Footnote can other notes (i.e. asides and not references) be used in the footnotes as well or should footnotes be kept exclusively for the references?

If mixed (references and notes in footnotes), how is citing then used in a 'note' footnote?

If kept separate (references and notes) where should notes go?

The overwhelming majority of journals that use the Chicago style allow you to include "asides" along with source material references. In fact it is quite a common thing. For an example of how references and extra comments can be mixed together into a single footnote, just read any article from Monumenta Nipponica, or JSAH.
Nevertheless, do be sure to double-check the specific requirements and instructions provided by the journal in question, and confirm if they have any problem with including general info in the footnotes.
EDIT: here is an example of several mixed references together with additional comments within a single note, taken from the following paper:
https://online.ucpress.edu/jsah/article/80/1/12/116120/The-Architectural-Origins-of-the-Parthenon-Frieze
(Note that endnotes can be written in the same manner as footnotes, there is no difference except in their placement within the paper itself)

Thanks for the confirmation that mixing the two is generally acceptable. How then does citing in an "aside" footnote occur i.e. does one footnote refer to another for the reference? Word/OpenOffice/LibreOffice etc. don't allow the use of footnotes like this.

I have edited my response in order to address your comment. Please check it.

I thought of this but thought it seemed too messy. Good to have a visual confirmation. Many thanks.


text:
Does arXiv prevent your work from getting scooped, or the opposite?
On the one hand, it seems like a preprint can discourage dishonest reviewers or editors (who get to see new work before anyone else) from running off with ideas since you have proof of originality with a preprint. On the other hand, a preprint puts the ideas out there to the world at large. What do you think is the safest approach, submitting to journals with or without a preprint?

Assuming you are dishonest person, I'd advise that the vast majority of what's posted on ArXiv or in journals is simply not worth scooping.  Scooping is not something one really needs to worry about in practice.

It may allow others to start to build on your work earlier. It depends on you whether that is a good thing or not. Is it a low-hanging fruit that still needs some milking? Or are just afraid of loosing the priority for your current work?

Preprint services prevent scooping.
Every preprint service puts a date stamp on every document that is published there (and in many cases a DOI as well). That's an effectively unmodifiable record of the time when something went live, at which point nobody can republish your result elsewhere with an earlier date stamp with any reputable publisher.
That said, preprints will not prevent competition for the generation of follow-on research based on a result, nor will it prevent somebody from claiming independent discovery of the same result. Those, however, are just a normal part of doing business in science.

ChemRxiv does assign DOIs

@FedericoPoloni You're right; I'd forgotten that for arXiv the DOI comes from the journal later. bioRxiv assigns the DOI immediately, as do all of the others I've recently interacted with.

If I submitted a paper to arxiv, and it produced tons of follow-on research that cited my paper, I would be generally quite pleased.

@puppetsock Typically yes! Some people are much more fearful or greedy, e.g., believing that a particular paper opens up a lot of "low hanging fruit" results that they want to gather themselves as well. I believe that such views are typically short-sighted, but I can see how people come to hold them.

authors: Vladimir F Героям слава


text:
Is a software-simulated experiment enough?
My ideal experiment to test my hypothesis would involve launching a large apparatus into deep space - and would cost millions of dollars, which I dont have.
Instead, if I develop a software model/simulation to test my hypothesis, is this an acceptable alternative? (in order for my ideas to be published and accepted by the scientific community).

I'm voting to close this question as off-topic because this is a question for your scientific community.

"would cost millions of dollars, which I dont have" - Sounds like you need a backer with deep pockets

In general, you can use a numerical model if you can also demonstrate that the model works with something that is testable, and explain why the model should be relevant to the thing in question.
But in practice it depends totally on the field you're in and what the norms are.

This is highly dependent on what field you're in. I'm guessing physics from the question, but even so it depends on your subfield.
Still, as a general matter of scientific methodology: there have been plenty of papers - including many good ones, and many famous ones - that have raised hypotheses and presented models, without also including experiments. This may be because the experiment would be extremely difficult, because the topic itself is inherently theoretical, or simply because the authors are not in an experimental department. There are plenty of journals that specialise in such theoretical results, where such a paper could be submitted.
However, what you almost certainly can't claim is that by running your model you have tested the hypothesis. If your hypothesis is about something that would happen in the real world, then it's not tested until someone has done the experiment to test it. That doesn't mean you can't publish the hypothesis, and use the model to back it up. The model may suggest the hypothesis is true, but by the standards of almost every subdiscipline, it wouldn't count as testing the hypothesis.
(The only exception I can think of is if your hypothesis is about how a particular type of model will behave when simulated, rather than being about the real world per se. In that case it can be reasonable to say you tested the hypothesis by running the simulation. But since your said your hypothesis could in principle be tested experimentally, I assume that's not the case here.)

This is impossible to answer without reading the actual paper, but I will do my best to give you an indication.
If the hypothesis is exciting and the simulation is well-executed and also gives the expected results: probably publishable. Otherwise, probably not.
Given that you need to ask this question here, it looks more like a "no", but don't let me (or any other random person on the internet) stop you: if you think it is publishable you should definitely try it. In the worst case it does not get published and you have learned something.
Also, you should ask this question to your supervisor (if you have one), or try to find someone to work with who has experience publishing papers: support from someone with experience publishing will probably be very helpful (read: necessary) to get your paper into a journal or conference.


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Can I do experiments on humans without a degree?
I have several ideas for research that I believe would advance our understanding of psychological priming. It won't involve anything extreme - just reading non-offensive words on a screen.
But I have only a bachelor's degree. Will that preclude me in anyway from doing research of this type, and publishing?
I know I'll have a greater challenge finding participants, and designing the experiment, and correctly formatting my paper without guidance, etc. I can work with that.
But is it even possible to get IRB approval without being affiliated with a university?
Is there any way that my current affiliation status will formally prevent me from going forward?

"you might miss it" - No reputable journal will publish the work without an IRB review, so the researcher will almost certainly miss it.

@Roland - Both.

It is possible to get IRB reviews without an academic affiliation.  Commercial IRBs (companies that, for a fee, review trials for third parties) exist; that's one way that industry manages to perform clinical trials.

Commercial IRBs have multiplied in recent decades, reviewing and passing proposals for profit. Their creation was spurred partly by an explosion of industry-sponsored clinical trials, but they are increasingly passed business from academic centres, to relieve overstretched in-house ethics committees. There are now dozens of these companies and they will see potential business in the proposed shift to single-IRB oversight of multi-site trials.

--Who watches the watchmen? Nature, 2011
Some of these IRBs are listed at the Consortium of Independent Review Boards (CIRB).
The absence of a graduate degree and of academic affiliation don't prevent you from publishing either, although they may present some complications during the process.  There are other questions in Academia SE that discuss this:

Does one need to be affiliated with a university to publish papers?
How do I go about publishing a paper without a university affiliation?


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Advice about job applications in the US (mathematics)
I did my Phd in mathematics in Europe and am at the end of my second year of postdoc in Europe too. I plan to apply for jobs in the US in the fall (ideally tenure track, but I wouldn't mind too much doing a second postdoc, as I finished my phd early). I think it's the best place for me, as most of the researchers in my field are in the US. But I'm not familiar with the american system at all, so I would be happy if you could help me answer a few questions:

I know most applications go through mathjobs.org and that there are hundreds of applications for a every position. What is the best technique for an application not to be overlooked? Is it common in the US to email a professor at the university which offers the job and let them know that you applied/tell them that you would like to work with them? If yes, is it even ok to email a professor that I don't know personnaly but who I think knows my work or would be interested in it? In Europe it is very common and even necessary, at least in the countries I know, but I wouldn't want to do something that is weird or unethical in the US.
Someone told me that US universities tend to favor people who are already working in the US, especially for tenure-track positions (something about not wanting to pay a flight from overseas for the interviews). Is that true? Is it the same for postdocs?
Is it weird to apply for both a tenure-track position and a postdoc position at the same university? If I did so, would they automatically think that they'd rather give me the postdoc as I'm ok with both, and give the tenure-track to someone who applied only to tenure-track?
Are the chances of getting hired in an university where no one works on the same things as I do very low? Of course I would prefer to be in an university with nice collaboration opportunities, but just in case I was thinking of applying to others too.

Thank you very much in advance for your replies!

Answers to your questions (the numbering is the order you asked them):

You should definitely email people at the university who might be interested in and familiar with your work.  But for tenure track positions it is weird to say you want to work with them.  Instead, I would just send a low-key email just letting them know that you applied to their position and would be very interested in coming there.  The goal is to be informative but not pushy.
It is true that it is both more expensive and more difficult logistically to interview someone who is coming from overseas, but it certainly does happen.  They just have to want you enough.  For postdocs, there generally isn't an interview, so it isn't an issue.  However, some kinds of postdocs are funded by sources like the NSF that only want to support US citizens or permanent residents, so foreign applicants won't be considered for them.
It's not weird at all.  Doing so will not affect your chances at getting a tenure-track position.  Everyone knows that the job market is tight.
There has to be someone at the university who advocates for hiring you, which means at least they appreciate the kinds of math you do.  But certainly there does not have to be someone who works in precisely the same part of mathematics (and in fact often the "needs of the department" involve hiring in fields that are not well-represented there).

My background: I've served on a large number of search committees in pure mathematics at a couple of different private research universities.

For 2, I would add that it's often not a big deal bringing people in from overseas for interviews at research universities, but it does make a bigger deal at more teaching-oriented schools.  I wrote more about this here.

Thank you very much for your answer! Now that I'm actually in the application process, I have one more question: should I only email full professors or can it also be associate or (tenure track) assistant professors if they are closer to my field?

@european job searcher: In all the departments I have been a part of, all tenure stream faculty members are involved in hiring.  Contact who ever is closer to your field.

I've participated in many searches over the years, and chaired search committees in each of the last two years.  My institution is a smaller
research intensive university that specializes only in the STEM disciplines.  Our mathematics department specializes in applied areas of mathematics.  The situation can be somewhat different at other kinds of institutions, but many aspects of this are related to federal employment law and are fairly standardized.

You can contact the search committee if you want to.  However, expressing interest in the position, flattering the committee members, etc. will have very little effect on your chances of getting an interview. The committee will have to justify its selections based only on what is in the official application files. If you have a specific question about the position, then it is appropriate to ask that question. The best way to get your application noticed is to submit a complete and clear application that shows that you are well qualified in terms of whatever it is that the committee is looking for.  The hard part can be figuring out what the committee really cares about- advertisements are often worded vaguely.
Hiring for a tenure track position almost always involves an on-campus interview.  Since travel from outside of the US is expensive, this can be a factor in deciding who to bring to campus for interviews.  Some institutions have special rules about paying for international travel.  For example, our institution won't pay for international travel for faculty applicants.  If you're planning on being in the US for some other reason (attending a conference), then you should mention this in your application cover letter.  At another level, there's often a reluctance to hire applicants who must be sponsored for a visa, although many of the applicants on the market are not permanent residents of the US.
This is very common.  There's a box to check on the application form.  It's not unusual for a search to fail (the top candidates turn down offers.)  In that case, the search committee might be asked to go back into the applications and interview candidates for a visiting assitant professor/postdoc position instead.
Most larger departments want to hire assistant professors to join existing research groups.  However, at smaller less research focused institutions there's often a desire to diversify the areas of mathematics in the department.  The job ad should make it clear what the department wants.

Some further thoughts, as a supplment to the two excellent answers to your bulleted questions. (I've served on multiple hiring committees for a math department in a mid-tier American research university.)
In the US, it is quite typical to submit a job application without: contacting any faculty members there; writing more than a perfunctory cover letter; trying to ascertain how likely you are to be hired by a particular university. This is especially true if you are just finishing a postdoc, as there is no need to explain why you are applying for a different job than the one you have. That said, in your case I'd recommend addressing your specific desire to move to the US in your cover letter.
Indeed, this is what most of the candidates we interviewed did.
By all means, e-mail people or go into more details in your cover letter if you have anything particular to say. It might help you if you can make the case that you are an especially good fit for a particular university. But if you can't think of anything natural to say, then it is okay not to say anything.
You ask how not to be overlooked. One way in which you might help your cause is to try to attend (and, if possible, speak at) as many US conferences as you can. The Joint Mathematics Meetings in January is very popular, especially among job seekers. More specialized conferences are also a great way to get the attention of people who might have the ability to hire you.


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Trouble with editorial manager
I submitted a paper to a math journal last week.
The manuscript was sent back to me 3 times because of the following reasons:

the order of the authors do not match in the manuscript as in the submission step (one time)
there is no item stating the name of the data repository that I used to associate data (two times)

But the order of the authors was consistent and there is no associated data in the paper. I checked several times that I did not make a mistake in the submission steps. There might be a bug in the journal web page.
I explained this situation in the reply, but the editorial manager does not seem to take it seriously. I just received typical emails that seem to be automatically generated.
What should I do in this case? Should I withdraw and submit to another journal?


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I want to go to grad school but don't have personal relationships with any of my online professors. What do I do about the LOR requirements?
I am an undergraduate student expecting to graduate next spring, but i've attended online classes for the past 2-3 years and don't normally have much contact with my online professors. I want to apply for a masters program, but probably not for another year. When I apply next year, I'm afraid i'll have no one to ask for a LOR. I feel like I am supposed to ask for letters of recommendation from professors who know me well, but I don't have anyone who fits that bill. I'm afraid that if I ask for a LOR from a past professor, especially in a year from now, they'll respond negatively to an ask from a random student they don't even remember.
I don't know how I could've (or if I should've) tried to foster relationships with professors online. I am the kind of student to just read the syllabus and do the work. I don't often have questions to contact the professor with and I understand the coursework just fine on my own. I have had especially limited contact because online professors ask you to try every other resource before e-mailing them.
Can anyone give me advice about how to meet the LOR requirements for graduate program application?

Can you apply to the same place as undergrad? For example ASU has engineering BS and MS online and will be happy to admit you to online MS after completing BS but it won't be funded. In fact most distance MS programs are pretty lax about admission if they aren't funding you.

My sympathies. When on-line course instructors say "try every other resource before emailing them", you are being short-changed... The economics of purely-on-line "campuses" and so on coerces this, sadly, and short-changes students who want to go to grad school. The quality of on-line instruction is NOT My necessarily that barren... but the pre-Covid model was very stingy.

@FourierFlux I am at ASU for my undergrad actually but I really want to do an in-person MS program.

Hmm, Im not sure. You could ask your professors about in person MS programs that they have experience with. ASU is pretty well known so your degree isn't a disadvantage.


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Do my publications help my department/university?
I am currently a mathematics lecturer at a state university in the US. I still do research and put a lot of effort into publications, although it is not required for my position. My question is: Will my publications (in good journals) be seen as a positive by the math department and/or university overall? Do they gain any benefits from my research? Is there some baseline for number of publications that they need to meet for funding, etc?

The publications of faculty add to the reputation of a university, more specifically, to a department. But there is no direct effect. In funding for a particular project it will help if they can show productive activity in that area and your papers might be cited. Likewise having research seminars in a topic is helpful. But there aren't cutoffs or similar.
Regular faculty are in a good position for getting salary increases and/or reduced teaching loads, but this is probably less available to a lecturer. But it might give you an edge in a number of ways. It might not be possible to bypass regular procedures to hire you for a TT position, but people will look favorably upon an application. Likewise, if you work collaboratively with the tenured faculty you will be in a good position to get good letters when it is time to move on.
So, benefits: yes. Formulas: no.

One positive side-effect of your publications pertain to world university rankings.
All such higher education rankings I know of take into account the number of scholarly publications (and citations to these publications). They do so in two ways:
First, as inclusion criteria for institutes to be listed in a ranking (e.g. the THE World University Ranking demands more than 150 publications in a single year [p. 6]; or the CWTS Leiden Ranking ranks universities only if they have at least 800 publications in 2015-8 [see here]).
And secondly, publications (and citations) serve as as core performance indicators. For instance, publications weigh 20% of a journal's score in the Shanghai Ranking (according to their Ranking Methodology).
And these university rankings, in turn, have their real-life impact - as many studies show.

Getting your university from rank 1201 to 1198 does not buy you even one coffee, and helping to get into the lower fifth of such a ranking is equally worthless.


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How to make a bachelor thesis out of optimizing /updating an application?
I work for a company and want to write my bachelor thesis there. This company has a Quality Assurance Application written in Python, that is very unstructured and follows no design pattern.
My job would be to restructure the Application into a layered architecture, and possibly get rid of the GUI and completely automate it.
My question now is how do I make a bachelor thesis out of this?

Write about software design/architecture and use this as proof of concept?
Write about improved speed and improved future maintenance (kind of hard to measure)?

This is country specific

The usual, and normally a good, way is to get an advisor at the university if you don't already have one and discuss this with them. It could save you a lot of grief later and their advice would be more valid in your circumstances than mine.
You may also need to discuss this with the company in case any trade secrets are involved in the application.
But, in general, reimplementing a legacy application using modern design patterns and/or improving performance and/or providing better UI is not a bad idea.


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Dealing with a huge number of textbooks
As an undergraduate in the field of biology/Chemistry, I've seen plenty of professors recommending at least two textbooks for a mere credit hour of two, each of which comprised of more than 1000 pages. I'm somehow confused by this huge amount of text and it came to my mind to only rely on my class notes instead of the books from now on. Plus some of these books, despite being said to target undergrads' needs, are so hard, complicated, and extensive that even many master's candidates wouldn't take a look at according to my conversations with other people in the field. How should an undergraduate focus on the subjects with this bombardment of information, specifically how should an undergrad prioritize among textbooks, class notes, papers to be read(if any)? and roughly how many textbooks should one read for the whole four years to obtain proficiency in the field? (Is it a good idea to count them in the first place?)

Your question is very justified. One might argue that your professors apply a questionable pedagogical practice by giving you the full textbooks without proving any guidance of how to work with them. If they don't point out specific things to read in these textbooks, it's likely that they're not important anyways.

I am a chemist, and own quite a few of such books myself. From what I can tell, when getting something equivalent to a Master's degree, the contents of the lectures, seminars etc. will have covered most of the contents of the books, at least of the basic/standard ones. Be realistic - you are trying to get a university degree. You should not be scared by extensive, complicated information. After all, you are trying to become an expert in your field.

I went to college more than half a century ago. I accumulated and still have all (I think) of the books in math. But I never actually read any of those books front to back. They were used as a resource to make it possible to gain insight and to solve problems. Some of them were more useful on the insight part, of course.
But, to answer the question, one way to use the books is to let the lecture notes be your guide as to where you should focus within them. Use keywords from the lecture, along with the table of contents and the index to find the things you need to focus on.
Textbooks aren't novels. They provide the outline of a field and, hopefully, plenty of useful (hard) exercises to build skill. With enough hard work, insight may come.
Read textbooks in "snippets", stopping frequently to think about what you have read and find associated exercises to solidify the ideas.
This is especially true for the later chapters. It may be necessary to do more, such as re-reading, for the early parts, since you probably start out with very little skill. But the exercises may be more important than the text itself.

I think this issue with textbooks is also a bit field dependent. Most math textbooks at the undergraduate level seem to me to be at least reasonable for a student to master, even in those cases where the class might only cover the first half. However, undergraduate biology, biochemistry, and molecular biology texts (but typically not pure chemistry texts) seem to have more material than one would expect anyone to master, even in graduate school. My wife recently completed a BSN in nursing, and a couple of her books were nearly 1000 pages with dozens of chapters each written by a specialist.

"But I never actually read any of those books front to back." True most of time for most people, I guess. As a student I read exactly two books from the first to the last page, including all exercises. Those were really good books on hard topics, but after that, I really mastered the topics. So it may be worthwhile to make exceptions from time to time. And when you "read textbooks in 'snippets'" parallel to lectures etc., you will have worked your way through quite a few books almost completely when getting the degree.

@DaveLRenfro Yes, it's field dependent. Math syllabi at the undergraduate level, for good or bad, are relatively standardized and it's easy to find textbooks that cover the material. But consider for instance the class I teach, which is about measurements and measuring instruments and devices. There exists thousands and thousands of different measuring instruments, devices and sensors: each author and each instructor chooses a certain,very limited subset according to their personal preferences and treat them to a depth which fits their goal, with the result that there is no standard book.

For instance, I prefer to limit the variety of topics going more in depth, but there is no textbook that has the same approach. So, I usually suggest a few textbooks where to pick specific topics, with the result that the students complain that there is no course textbook.

Ignore the textbooks and concentrate on the lecture notes. If the lectures say "read pages X to Y of [textbook]" then do that, but otherwise look only at what the lecturer provides. After all, that material is what will actually show up in the exams.
Use the textbooks if:

There's something you don't understand well from the lecture notes (or you can ask the lecturer/TA about it).
You want to understand [topic] in more detail than in the lecture notes. Usually this will be out of interest or desire to truly master the material, not from the need to pass the exams.
To find exercises and examples.

-1, you do not study for the exams exclusively.


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What departments in a university could want a volunteer pure math alumni during the summer?
I am looking for academic opportunities in the summer. Tomorrow I am going in person to ask professors in the math department. An engineering PhD candidate told me that there may be other departments I could investigate. They stated engineering as an example, but didn't give me what kind of engineering I should be looking in. Something like that would be useful.
I wish to become a professor, so summer opportunities would provide great exposure as well as a boost to next years graduate school application.
I apologize if I did anything wrong when posting this (I don't know the website that well) and hope you have a good day :)

Your post implies, but doesn't state that you have a bachelor's in pure math, is that correct?

Did you apply to the various internships opportunities that all universities have?

If asking in a math department, I would not look for "volunteers" or "opportunities".
Instead, I'd identify something specific you'd like to accomplish, and ask for help with that. You might, if you're lucky, find someone willing to supervise a summer reading or research project. Identify a topic or two of interest, do a bit of background reading first, think about what you'd like to achieve, and only then approach faculty members.
If you have difficulty deciding on your goals in general, you might try to meet with student services-oriented staff members, who might be better equipped than individual faculty researchers. Nobody is going to tell you what department to approach, you have to decide for yourself what you find most interesting.
Good luck!