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How to thank a potential supervisor's email?
I have recently interviewed by a professor in US after sending him my CV. A few days after the interview he mailed me and told me to do the formal application process and mention him as the professor I want to work with.
Now, I want to thank him for considering me as a choice of his future PhD student. What should I write?

Thank you? You’ve written thank you notes before, right?

Do not overthink this (and do not write a very long text). Just write

Dear Prof. NAME,
Thank you very much for considering me as a PhD student.
Best, NAME

Do you think when he has told me to apply. It means he has accepted me as his student?

I got the impression from your question that he did - what do you mean by "considering me as a choice of his future PhD student"? Are you his choice?

You can can add "I am looking forward to working in your lab" (or "working with you" if it is not experimental domain).

@Alireza it sounds like you're not quite accepted yet. While the professor sounds willing to supervise you, you have been told to make a formal application, which could still be rejected (especially if the department cannot find funding for you). Having a prof on your side certainly helps, though :) Also, don't know why this answer was downvoted, it's good advice imo.

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How to ask a professor to introduce other professors to me when he mentions that he has no funding?
When asking for an opportunity to do a PhD with a professor at a US university, he replied:

Excellent background. Unfortunately, I do not have funding to support
  new students. Good luck!

Now I want to tell him:

Thank you for your time and consideration. Please keep me in mind if a funded position opens up in the future.

and I want to add that if there is any other professors that he can introduce to me in order to ask them for a PhD position.
What should I say?

Don't ask the professor for contacts to other professors where you could apply - there's a risk that he will perceive it as annoying, and in principle it is work that you could easily do on your own.
Instead, you could add something like the following to your response:

Please feel free to forward my documents to any colleagues who could be interested in working with me.

This will put the professor more in a mindset of helping some colleagues to find a (hopefully) good student, which he might be more willing to consider instead of helping a random applicant to find another job opportunity.

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How can I protect my unpublished work that I've sent to others?
I am a masters student from India applying for a PhD in the US.
I emailed a potential adviser at Harvard University an unpublished paper I have been working on for some time.
The application in the end did not work out but the adviser was enthusiastic about the paper and said I wasn't admitted due to funding issues.
Now I am a bit worried he may publish part of my work without mentioning me, since the paper is not published.
How likely is this? What actions I can take to protect my work?

I know it is a continual worry of people that others will steal your ideas. Yet it rarely if ever actually happens. Ideas are a dime a dozen.

@Jon Custer Actually it's an entire paper that one can modify a bit and publish as is

Why would they do that? Really, this is not a concern at all.

I would expect good ethical practice from Harvard faculty. Perhaps, though, you have an opportunity for collaboration, or at least feedback.

This question is just opinion-based. At the bottom line: It just depends on you and the professor that you are sending your work to him/her. Everything has a bit risk. If you prefer to be 100% sure, do nothing and don't send anything to any other people, but if you think it just makes your PhD application better, OK, do it. I don't think a professor from Harvard University will steal someone else's work, but you may never know. I can't say the chance is absolute zero but it's really low. Again it depends on you to decide.

How likely is this? Have you ever heard a Professor of this caliber doing something like that?

This depends on the field -- in some fields people are more worried about being "scooped". It could be anywhere from "unlikely but possible" to "extremely unlikely". Overall it is not a serious concern that you should worry about, but it is a remote possibility that you could consider taking steps to prevent.
In response to some comments, let me add that blatant plagiarism (where they publish your writing as it is) is much less likely because that is academic misconduct that could get a professor in real trouble when you present the proof.
On the other hand, scooping is where you get the idea from the paper, and do it yourself. It is still academic misconduct, but more difficult to prove and it may go unpunished.

What actions I can take to protect my work, assuming I need about 6
  months to have it ready for publication?

The best solution is to publish the draft online. This is common in many fields and becoming common in others. If you publish online, everyone will see that this is your work and you did it first; you have documented proof on the internet.
It could also help to document it in other ways: send the draft to others, and put together some proof that you wrote it, just in case.

I think this is a misrepresentation. Much closer to the truth would be to say that there is absolutely no chance the person at Harvard would use any of your ideas without providing appropriate credit. The worry is just not realistic.

@AndrésE.Caicedo It is unlikely but possible. I have heard for example from friends in chemistry that even established professors hold onto ideas and are careful to share for fear of being scooped. The worry for a student (who has no status yet) should be greater.

My point is that "unlikely but possible" is really a bad representation of reality. It just has no basis in fact. Suggesting it has the potential to distort and damage potential interactions between the student and future colleagues.

@AndrésE.Caicedo OK, I clarified.

@Morgan That a tenured professor at an R1 university in the States has taken a paper from an unknown author and plagiarized it and gotten away with it? I am not "trying to claim" it has never happened. I am saying it hasn't.

@Morgan I would appreciate hearing of examples. It would be sobering.

That professor won’t “scoop” you as there is already a paper trail.
Also, he has his own reputation to consider, in fact he might be useful support to you getting your paper published.
I suggest you should not be worried about that professor but getting your paper published asap just in case someone else has a similar paper “ready to go”...

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Would doing machine learning during my PhD disqualify me from becoming a professor at a statistics department?
I would like to call myself as a statistician; I have been in statistics programs for seven years now (four year undergrad, two year master’s, one year PhD). I always thought that if I become a professor after my PhD, I would be hired in a statistics department.
But lately I started to doubt the above statement. My PhD research field is machine learning, more specifically I am trying to improve performance of the existing neural network model called “Transformer”, which is commonly used in natural-language processing (NLP) in data science. I don’t know how math-intensive my PhD dissertation will be, but I think my research is going in a direction that I won’t be publishing a lot of (math-intensive) papers in journals like JASA or other strictly statistically oriented journals, but instead I will be publishing in some of the deep-learning journals and attend a few machine-learning and/or computer-science conferences to present my work. My research involves a heavy Python programming, and I see my research as more of data science than traditional statistics.
If I keep on pursuing the current research road that I am on, would this eventually disqualify me from getting employed at statistics departments, since my research does not involve a heavy (traditional and math-intensive) statistical theory? Will I have a better chance, for example, to get hired at an engineering or computer-science department than a regular statistics department with this kind of research background? Would it be possible for data Scientist like myself to be hired at a statistics department? The thought of not being able to get hired at a statistics department amazes me since statistics is the discipline that I studied throughout my entire academic career.

I will be publishing in some of the deep-learning journals and [at] computer-science conferences...My research involves...Python programming, and I see my research as more of data science than traditional statistics...

You seem to be leaning towards a career in computer science, rather than mathematics.

If I keep on pursuing the current research road that I am on, would this eventually disqualify me from getting employed at statistics departments, since my research does not involve a heavy (traditional and math-intensive) statistical theory? Will I have a better chance, for example, to get hired at an engineering or computer-science department than a regular statistics department with this kind of research background? Would it be possible for data Scientist like myself to be hired at a statistics department?

You are surely making youreself more desirable for hire to computer science departments, rather than mathematics departments.

The thought of not being able to get hired at a statistics department
  amazes me since statistics is the discipline that I studied throughout
  my entire academic career.

If you're satisfied with the path you're on, why not embrace a change?
Perhaps you can find a computer science department that's like a mathematics department, or vice-versa.

Also, while traditionally CS and Statistics were clearly separate fields, machine learning is creating much more overlap between them. So universities also need to re-evaluate how they set up their faculties. Therefore, what disqualifies you at one university may not be a problem at another one.

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How to design research questions for a literature review?
I have to conduct a literature review for research topic. The plan is to add this as the first chapter of my doctoral dissertation, get the scoping and state of the art about topic, and preferably get it published to a journal (ACM Computing Survey, for example).
I have no experience writing review papers. So far, I learned that the review process starts with specifying the research questions. Well, this is paradox for me. I want to conduct the review to get the scoping of a research topic that I'm not familiar with (publication is a bonus). So, how can I even write research questions when I'm not familiar with the field.
Context: I am a beginner phd student

Your question is not sufficiently clear. In particular, when you say "I have to conduct a literature review for research topic", what is the context for which you have to conduct a literature review? Is this for your doctoral dissertation literature review chapter? Is this for a class assignment? The more details you give about why you need to do a review, the more people can help you. Please edit your question for clarity; do not give clarifications in the comments.

@Tripartio, I have revised the questing with the details.

What you are saying you want to do is impossible. To start the literature review you will have to enter terms into database searches such as Google Scholar. You get those terms by figuring out what your questions are. Of course, in the process of doing the lit review, you may find that your questions have already been answered, but academic papers almost always end with a small section on "further research needed".
Even as a beginning PhD student you should have some idea of what you want to research. Why did you apply for a PhD in this subject? What did you learn or read as an undergrad that fascinated you? Or, if you have a professor who you plan to work with, what does their research focus on?

It is misleading to think that just because the literature review chapter of a thesis is the second chapter, it is conducted to [near] completion before the actual study begins. I find it more helpful to completely separate the process of conducting the research (including the review) from the presentation of the final document.
When I teach research methodology (including literature review methodology), I like to give students two distinct lists of structure. The first is the ordered list of steps to take to conduct the research or review; the second is how the finished work should be arranged in the final document.
From this perspective, let's put aside the mistaken notion that you need to complete most of the literature review before your proceed with your research. More pragmatically, in your situation, I suggest that you think of the literature review as two major steps in your research process: an initial literature review and a final literature review. Here's how it could work:

Initial literature review. At this point, you do not have a clear idea about your research question. You have a general topic of interest but that's about it. So, the initial literature review is very useful for exploring your topic and helping you focus until you find a clear, meaningful research question. This initial literature review is very exploratory. You should read the articles you initially find interesting and only skim over those of secondary interest. For truly interesting articles, carefully examine their citation lists and read key cited articles. Also for these truly interesting articles, skim through the articles that have cited these articles (you can use Google Scholar following the "Cited articles" links) and then find more articles to skim and read in depth. Continue doing this with discussion and feedback from your advisor until you find a research opportunity and concrete questions that you can focus on for your doctoral research.

Do the doctoral research. This is the real work.

Final literature review. At this point, you have completed your research and have your findings. Based on the initial literature review you did (perhaps a couple of years previously by now), you have a good idea of the novelty of your findings. For a literature review chapter, you will not present your new findings as knowledge in the literature, but you should have a better idea now of the related research that you can search for and discuss that bears on the research that you will present in subsequent chapters. From this standpoint, it should be much clearer how to frame and arrange your literature review to set up the reader of your dissertation to appreciate the novelty and value of the research study in subsequent chapters.

By the time you do the final literature review, you should have more experience with publishing norms and you can work closely with your supervisor to ensure that the final literature review is in a form that would be suitable for ACM Computing Surveys or a similar journal.
The challenge I suspect you are facing now is that you are trying to clearly envision the final product whereas you are at the beginning of the process. I do not think that it is necessary or productive to do that. If you can accept the two-step process I suggest, I think you would have a more practical way forward.


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How to request other researchers to read one's paper for suggestions?
Suppose a researcher uses the application of another researcher's idea in his domain. Given that original researcher knows basics of his idea better, he may help correct any mistakes and give valuable suggestions. In this way, the quality of research paper will be increased. But at the same time, giving away one's complete unpublished paper to unknown person is a matter of a bit worry. In your opinion, should he ask for suggestion or not? If yes, what is a proper way?

It is perfectly acceptable to email your paper to another researcher, and ask if they have any comments or suggestions.
It would also be perfectly acceptable for him to not reply. If he does, the reply might be something short like "Thanks for sending, looks like a nice piece of work!"
If you do write, I'd recommend you do the following:

Keep your email brief and to the point.
Do not ask him to check your paper for mistakes. That's your job. If you feel that you can't do this on your own, then I'd suggest that you offer to make your paper a collaboration with him.
Don't try to be indirect, or hope that he reads between the lines. If you would like to ask him to do something, then it's good manners to do so plainly and directly.

You might also search for and read the many "Why isn't so-and-so responding to my emails" questions which (with good answers) can be found on this site.
Good luck!

Please note that if you do this, you eliminate that author as a reviewer for your paper when you submit to peer review.

@HEITZ please would you like to explain What are pros and cons of this? It seems good that I eliminate a tough person (who is the founder of idea) from peer review process. Just guessing

Depends on the reviewer. If he/she would find your work favorable, you might want that person as a reviewer and you can suggest as such at submission, in which case don’t ask for pre-submission reviews. If not, you’ll get some great critical feedback to deal with upfront while eliminating a potential detractor (and be able to put their name in the acknowledgments).


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Math Ph.D. does not know what to do with life?
Background: I am a Math Ph.D. student in the U.S. (originally from a developing nation) in partial differential equations (PDEs) but on the theoretical side of PDEs (no simulation, no numerical). I am starting my 7th year, and my advisor is expecting me to graduate this year. I am on the job market now for a postdoc. I have 5 publications so far, 2 arxiv preprints, and 3 peer-reviewed in okay-ish journals (not high impact). I am an international student as well.
Summarize the problem Academic jobs are hard to find and I want to stay in the U.S. After a while of looking into the industry without any results, I am now losing both motivation and hope for academia as well as an industry job.
6 months ago when talking about jobs (we all know how hard it is for jobs in academia), my advisor has been very pessimistic. I am advised to apply to all countries, around the world, for any postdoc listing I find. Through the conversation, I did not feel I can make it, therefore I started to lose my motivation and hope. I want to stay in the U.S., for the following reasons:

I could go back to be a lecturer in my home country with very low pay and a high teaching load. However, if it is the case, I think getting a postdoc, having more experience and connections for later collaborations when I am back is much better. I mentioned this to my advisor but I did not feel being supported.
I can make more money going to the industry here (if I am lucky to find a job), at least for a couple of years. My family is dirt poor and as a Ph.D., I was not able to support them at all for the last 10 years (undergrad + Ph.D. salary).

What I have tried:
So I started to look into the industry, as it is a natural thing to do. I first did a Bootcamp in Data Science and I bombed it hard, the pace was too fast and I fairly lost. I believe I can learn them, but not quickly enough in 3 weeks (the span of the Bootcamp).
I then tried Software Developer, taught myself using online courses and open sources projects. I have been trying to apply to some internships but have not been successful. I found myself panic every time looking at the job posting and see how under-qualified I am.
Back to Academia: I recently sort of having a verbal offer for a postdoc. However, after a couple of months of losing motivation in research and academia, I cannot seem to pick myself up again imaging I can be good at a postdoc. At the moment I just want to be out, but I am not sure if it is a good idea or I am just hate everything due to burnt out. I am extremely scared of making a big mistake and regret it later in life. I do not feel confident that I can land a TT position with this mindset and this level of motivation (assuming I can do 2 postdocs).
Somewhere inside me, I am still having fun doing some of the projects I have left unfinished, but I am not sure if it is just a comfort zone, doing something I am comfortable doing to avoid looking at real life. I want to comment that, I do not feel the work I do, while they are fun to me, are of interest or that helpful to many fellow mathematicians. I do not have a sense of fulfillment. However, I had a naive "dream" that given I have a permanent job, I can learn anything and make significant achievements in some related areas of Math. I realize this is a fantasy.
Resentments I hate being poor and lonely. I am approaching 30 without any relationship (even friendships). Throughout my life, I kept thinking about publishing and publishing, people will treat me better. I always have the sense of being worse than people, it really messes me up when trying to socialize and make friends. So, just like many other mathematicians I know, I followed them and isolate myself in the office, trying to write more and more papers, and thinking this is what defines me. I am sad.
Questions Do you have any advice for me to figure out what do I really want? Or just to lessen the tremendous stress I am having, which causes "analysis paralysis" to me?

Do these questions answer your question? https://academia.stackexchange.com/questions/109859/career-options-after-phd-in-math-international or https://academia.stackexchange.com/questions/125785/getting-a-job-with-a-phd-in-pure-mathematics or https://academia.stackexchange.com/questions/115930/career-prospects-for-a-math-phd-student-in-pure-math

Lots of comment answers here - please don't write answers in comments. It bypasses our quality measures by not having voting (both up and down) available on comments. You can write new answers and vote for ones that you find helpful.

You mention you miss the support of your PI. I am not sure what kind of support you expect. The academic job-market is hard for everyone, and academia can be a very depressing place. I am not sure how your supervisor could do better - his advice is realistic considering your situation.

I'm a current software engineer in the bay area, and have a similar background (without the phd) as you. I've wanted to do physics since I was 8, but after graduating with my bachelors I felt there isn't much future and definitely no money in academia. My friend's internship pay as an undergrad software engineer for 12 weeks is higher than my expected annual income fresh out of PhD. I then spent a few years working in different academic research labs while doing a masters in CS and preparing for and interviewing for jobs, before landing one.
First, I will not depend on what your professor says or recommends. The way I see it, the kind of person who will become a professor is not the kind who thinks about money, or a profitable career. Many academics are also dismissive towards money and folks earning a high salary. The fact that your prof allows you to do a 7 year phd program without a career plan suggests to me they don't give a shit about your career, or about what you want, since you raising this question suggests you don't want an academic career by this stage.
Second, you mis-interpret what a bootcamp is nowadays. A bootcamp is not only time for learning, 8 weeks don't make an app developer. A bootcamp, for the reputable ones, is an assessment centre, for someone who have spent 1-2+ years polishing their skills to have someone assess them so they can use that qualification to sell themselves, their ideas, and apply for jobs. The less reputable ones are not helpful, not because they don't teach you anything, but because the value of the bootcamp comes from their prestige and connections with potential employers. Hone your skills before spending your time and money going in, otherwise it's a waste of the latter and a stressful use of the former.
Third, as people have said, definitely finish your phd.
Fourth, in my opinion, there are 2 goals you can aim for. First, a generic software engineering ("swe") position. Your selling point will be your quantitative skills. I would keep this as a backup option. If you have only a bachelors in maths, sure, phd you can probably aim for something more relevant, especially since yours is pretty applied and relevant. But I have seen it work. Second, data or research scientist positions. Brush up on your software engineering skills, tech companies generally still want these roles to have decent coding skills, though the bar is definitely lower than for pure software engineering. Get a job similar to software engineering and then gradually transition there in your daily work if that's your inclination. I've seen maths or engin post-docs reach pretty high positions at a similar pace to what a computer science software engineer would have, so it is viable. I would advertise myself as a data scientist with very solid background in quantitative skills and problem solving and capable-if-untested engineering skills. Another path is to leverage more on the PDE work and apply to hedge funds as a "quant" (quantitative analyst), those will work out too and pay a lot better, if you can get it. It's definitely more competitive however, reach out to headhunters on linkedin or through career centre or friends, I would cold email and message and be aggressive, but it is do-able.
Next, to provide some context on salaries and career progression. To aid discussion, I'm going to use google's L3 (junior swe) to L5 (senior swe) levelling scale. It typically takes 2-3 years to go from L3 -> L4, and 3-5 years to go for L4 -> L5. As a post-doc, you'll join as L4+, meaning it should take 1/2 the amount of time from a L4->L5 jump for you to hit L5. So as compared to someone starting with a bachelors in CS, you have a lead of around 4 years. For pay, you're looking at (again google, check levels.fyi) ~300-350k starting, to hit around 400k in 2 years. So you'll be fine.
For the quant path, the variance is much higher, but I would expect 200-300k (base+bonus) for your first year, and you should expect to hit 500k in 3-5 years, and 1m+ if you manage to survive that long in 8-10+years. Look at some of the quant forums to see the salaries people are posting. Downgrade their values by a bit since only successful  examples will post their inflated values there.
For your isolation. I felt exactly the same when I was grinding to get my current job too, and although my team back then is great, I hate the work since I don't feel it impacts anything, or pays well. I realize in retrospect that this has knock-on effects on my social life. Essentially, because I feel my current position in life is shit, I don't feel like going out that much or being socially active. I don't feel I deserve to be spending time out there, and that I should be grinding and doing something with my life instead. I'm not saying that life gets better when you get a high paying job. But that assuredness with my career and my life made me feel more confident going out and spending time trying to make new friends. That disposable income helps in subtle ways too, I can go out and spend without feeling guilty or indeed caring much for it, and that made me appear more outgoing and sociable. Maybe. So I will not think too much about the isolation part and focus on getting a decent job offer first.
Next, on what I would do if I were you now. First, I would create some application that leverages and advertises my strengths. Based on your bootcamp experience, I might do something like build a aws-hosted server that retrieves nyse stock data once every day automatically, derive some basic trading metrics, and post them on some website with some good-enough plots and graphics. Clean up the project, add a nice readme and some snapshots, and post on your github.
Second, interview prep. Leetcode, CTCI, elements of programming interviews, do all of them. Get good enough to confidently solve LC-medium questions you have never seen before, around 70% of the time. This should take around 3-6 months fulltime, but you can apply while preparing, since you only need to be ready come interview and not application time.
Third, get that interview. Clean up your resume, reach out to friends or folks currently in swe roles to ask them to review, get multiple data points since some opinions may be inaccurate. Reach out to career centre, I would take their resources and connections, but usually ignore their advice. Cold email and linkedin message amazon recruiters, apply to google/whatever's phd internships, for the last point you need to finish the internship before you graduate so do it early. Ask for referrals on teamblind or friend-of-friends or whoever you can find. Be aggressive and shameless in your search.
Finally, your situation is more common than what you might expect, so do reach out to other folks in potentially similar situations, for advice perhaps but more to have people to rant and talk to. It's a marathon, but like a marathon so long as you keep moving, you should be fine. Mentors are invaluable, have a few so you can diversify the rant load and get more considered opinions.
Caveat emptor.

This has a lot of jargon in it that most math phd students will not follow.

While I agree with most of the advice, I do not agree with the sentiment on academia. It is a supervisors job to help in your career in academia, but not necessarily outside. At 30, if you are waiting for your math professor to tell you how to be a software engineer, a consultant or whatever-not-even-remotely mathematics, you are delusional.

I agree, I allowed my own bitterness with the academic path to taint this rant quite a bit. I apologise for that. Have retained the problematic paragraph for reference.

I'd like to see some supporting references on (a) the current purpose of bootcamps, and (b) software salaries. I'm skeptical of those claims as-is.

While I do appreciate that the question is a fairly soft one, this is a very opinionated answer about a lot of things. Your take on bootcamps, quant jobs, SWE jobs, salaries, career progression, interview prep, isolation, and everything else would probably all benefit from at least a few links and/or refs at a minimum. Caveat emptor indeed.

OP seems to be at a relatively early stage of developing their SWE skills -- expecting them to get (the equivalent of) a mid-level SWE position at Google (!) seems very optimistic. Perhaps a more realistic statement is that their initial salary should be equivalent/better than that of a post-doc, and that will probably double within 5-10 years (assuming good performance).

Yup, it's hard to address all, but I'll give the easy ones a shot. Yoe (years of experience) vs levels vs salary range comparisons for SWEs are available here: https://www.levels.fyi/company/Google/salaries/Software-Engineer/. Quant is harder, I can't find the links I used previously when I applied for such roles, it was years back. Note that BB (bulge bracket) pay significantly less, the numbers are for funds (citadel++). Interview prep, BC, answers from teamblind/quora should give similar stories. The rest are subjective, some more than others. (continued)

I personally find opinionated pieces with idiosyncrasies and subjective anecdotes more useful than generic answers that one can just google for, hence me printing that wall of text up there. But I'll not use subjectivity as a catch-all shield, feel free to point out errors and suggestions.

These are imo useful, I'll dump here as I encounter them. There's the obvious issue of me cherry-picking stuff that align with my beliefs, but :shrug:

first answer in https://www.reddit.com/r/cscareerquestions/comments/gecvj1/quant_finance_vs_top_tech_company_salaries/

RE salary link: yeah, but that's at Google -- the best company in the most expensive city. If we look at entry-level software engineering roles in, say, Pittsburgh, we see salaries of $95K. And keep in mind that averages go both ways -- an international applicant with rudimentary software skills may make significantly less than this (though if they find a position using their PDE background, they could make more).

Let me just comment on what you say towards the end, wich I believe is the root of your predicament.

I hate being poor and lonely. I am approaching 30 without any relationship (even friendships). Throughout my life, I kept thinking about publishing and publishing, people will treat me better. ... [I kept] thinking this is what defines me. I am sad.

People can thrive without a great job, but they wither in isolation. You're revealing an important insight here, which is: No amount of publication and hardwork has brought you closer to positive and nourishing relations (people who "treat you better"). Now is a good time to reconsider your actions and future "life decisions" in view of this insight. Your academic accolades (or perceived lack thereof) are not what defines you. Relationships are much more important in this regard for most people.
It can be hard to get a broader perspective on what matters for you from within the thicket of everyday academic bustle. When was the last time you got on a bike or swam in a river? When was the last time you talked the night away with someone who doesn't speak math? If these examples strike a chord with you, I encourage you to take care of these human needs first, because it sounds like you haven't in a while. Perhaps this is incompatible with your larger career plans and you may decide to put them aside for a while. But maybe not. The happier I am with my life, the more curious I get about my work. YMMV.

Talk to a professional (mental health) counsellor. Many universities have an office that will provide such a service. I've known of one case in which people in the psych (or ed) department did this as a service - very effectively. You can't influence the external factors much, but you can gain control over the internal ones.

The advice from @Buffy is really to the point.  The OP sounds clinically depressed (very common) and might benefit greatly from straight-forward councelling.  This is what happens when people get the work-life balance wrong.  And most people do at some point in their lives.

A lot of years ago I worked with man-in-the-loop and hardware-in-the-loop simulators as a real-time computer vendor helping customers make use of the platform and tools. Two hard problems which were unsolved at the time - flight near the ground (take off and landing, generally altitude below the wing-span of the aircraft) and pot-holes (specifically simulating anti-lock breaking systems). These both involve numerical heuristics derived from PDE because of a lot of features that are not solvable analytically. The arena of simulation has not contracted, just the computers and tools are no longer "special" and I've moved on to other modalities.
To my mind, having a theoretical understanding of PDEs might provide insights into providing better numerical estimates for simulations. Certainly there is a way to find a field of simulation that needs improved modelling. Anything involving turbulence in fluids comes to mind.
Most programming is aimed at the bottom of the math capabilities, but there are computing environments that work at a higher level, such as Mathematica. Don't do programming from the bottom-up, but from the top-down, where your experience and skills are more appropriate.

Maybe you could consider to look for a job that combines both math and social interaction, something like school teacher? you could stay some time there and go back to academia in the future, or switch to the industry later.

Consider applying for academic positions in your home country.
Generally, there's a rule of thumb that academics tend to work at institutions less prestigious than the institutions that they went to school at. As a result, you may want to consider applying for academic jobs in your home country, since you say that you're from a developing country. While there may be exceptions for specific institutions in specific fields, generally a university in a developing nation will have less prestige than one in a developed country.
Additionally, since it's your home country, you would presumably be a citizen, and not need to deal with visa issues, and your cultural familiarity may help you with the feelings of social anxiety and alienation you mention. While I expect that such a job would likely pay less than one in a developed nation, it's also likely that the cost of living would also be significantly lower; depending on the ratio of pay to cost of living, it might even be possible that you'd be relatively wealthier working in your home country, compared to getting an academic job in America.

You write:

I want to comment that, I do not feel the work I do, while they are fun to me, are of interest or that helpful to many fellow mathematicians. I do not have a sense of fulfillment.

When considering what you can contribute to mathematics and what others may value, try reading Terence Tao's article What is good mathematics?.
I can't do his article justice by merely summarizing it, but note that he lists problem-solving, technique, theory, insight, discovery, application, exposition, pedagogy, vision, taste, public relations, meta-mathematics, rigor, beauty, elegance, creativity, usefulness, strength, depth, intuition, definitiveness, etc. You may be able to contribute in at least one of the above areas and perhaps you have been focusing on just a few of them, not realizing that the others also have merit.

Not sure if it helps, but where I live (Europe) just being able to do, and not being afraid of, high school math is already a selling point for software developers. So it's not like you have nothing special to offer, even if your field of specialization may have little overlap with the field a company works in.


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How do I handle a "fake" co-author?
I recently started my first postdoc, after completing my phd in a different field. I managed to come up with some results that I hope to publish at a reputable conference.  All the work, including the creative/theoretical part, as well as the programming part was done by me. My plan was to have me and my advisor as the authors of the paper. However my advisor insists that a colleague from a different university, who contributed nothing to the work and does not even work in the exact same field should be added as a third author, with the task of writing the introduction and related work section. I have no idea what my advisor's motivation for this is.
While I feel adding a random person as an author unfairly dilutes my contributions (especially since my advisor is already essentially a courtesy co-author) I could live with being pragmatic about the situation and submit the paper with a third author, even though I feel that writing opening sections to a paper without being involved in the actual scientific process does not justify authorship.
The issue is that person is completely incapable of grasping my work. They understand neither my theoretical arguments nor what my experiments do (and more importantly do not) show. This is at least partially due to the fact they lack a working knowledge of things like probability theory (on a very basic level, e.g. what is a random variable?) that I use in my work.
Worst of all they are not capable of writing somewhat precise English which means that nothing they write is actually usable. I frankly have no idea how they managed to obtain a phd.
I believe that to have a realistic chance to have my work accepted I need to write the sections that were assigned to the third author myself (which I don't mind doing). But how do I handle this situation socially? I feel like now that this person is officially on the author list I cannot simply delete and rewrite what they wrote before submitting, i.e. even though I consider them a "fake" co-author they are now a co-author that needs to clear the final version of the paper.

If you did the work, why is your advisor going to be on the paper? That was your first mistake, perhaps.

I presume your advisor secured funding for this work by writing some sort of research proposal? Which presumably contains important problems and novel ideas how to solve them? If this is true, can you clarify whether you used any of these pre-existing ideas, or indeed did all the work, including formulation of the problem and choice of methodology?

Can you clarify if the “advisor” refers to your PhD advisor (more correctly now thought of as your former advisor), or to your supervisor in your current postdoc position?

How does the word "fake" apply here? Fake would mean the person doesn't exist.

I disagree with your interpretation of "fake" @Coder. We don't call "fake news" as such because it doesn't exist, but rather because it fails to meet the criteria of good/real news. The same thinking could be applied in this case.

Semantically, fake author could referred as ghost author, or perhaps sleeping co-author, those who doesn't contribute anything but their name included in paper.

Why not just ask the adviser about the situation? You probably want to have the kind of relationship with them anyway where they mentor you through exactly these kinds of issues!

It is saddening how often situations like this come up in academia in general. I wonder when we stopped caring about science to put our heads so far up into political games...

Question is: sometimes STEM-trained academics look down on academics from humanities, whose way of expressing themselves appears less formal, but one should not underestimate it: sometimes, they have something to say that is not immediately visible to more formally trained academics. Is the colleague from a different faculty?

@T.Sar-ReinstateMonica  I have a guess. And my guess is, diversity. To the OP: Is this other author "diverse?"

@puppetsock What do you base that guess on?

@puppetsock I'm not sure of diversity is the main reason. The cases I stumbled upon were more often than not because there was money involved in some manner.

@Buffy That, at least, is fairly standard in some fields (chemistry, for example). The PI does the grant-writing and contributes to the initial design and later development of the project, while the PhD student or postdoc does the lab work, the (bulk of the?) analysis, and also contributes to the development of the project.

@owjburnham, but the OP described it as "courtesy" co-authorship, which isn't really the same thing.

" I have no idea what my advisor's motivation for this is.". Have you asked your advisor?

@Zenon Imo, the interpretation of fake news is not that the "news" (the act of reporting) doesn't exist, but that the events reported don't. You could make a case that fake applies in this case, as you did, but if fake has connotations of the author not existing, and this has to be explained to a significant portion of people, the choice of word is arguably poor and could be improved.

Hmmm. Socially:
If you have already agreed to it then you should just go along, graciously. In particular, don't take any action that makes vindictive people (who have power) want to sabotage your future. It is only one paper. There will be others. A paper is a good thing, even under such circumstances. If the advisor has some standing, that might actually be good for you.
Ethically:
Try to work to disassociate yourself from these people (leeches?) going forward. They are acting in their own interest, not yours. Advisors shouldn't play such a game. Find more honest and ethical collaborators.

About the ethics: how are you sure that "these people" are not going to return the favour one day?  If this is an issue of "publish or perish", it is natural that people try to squeeze as many coauthors as possible on every publication to help their colleagues.

@Alexey, yes, and I think that the practice of padding author lists is frowned on and the people who do it are not respected for it. However, in some fields, a lot of authors is common because those people do contribute. Papers from CERN, come to mind.

The pressure to publish is also frowned upon, and administration that imposes it is not respected for it...

@Alexey In my experience, favors from unethical people can be more harm than good...

I agree with the other answers, just adding my answer to this part of the question:

I believe that to have a realistic chance to have my work accepted I need to write the sections that were assigned to the third author myself (which I don't mind doing). But how do I handle this situation socially? I feel like now that this person is officially on the author list I cannot simply delete and rewrite what they wrote before submitting, i.e. even though I consider them a "fake" co-author they are now a co-author that needs to clear the final version of the paper.

I think you're right: given that you accepted this person as a co-author in order not to offend anybody, it would be counter-productive to risk offending them by unilaterally deleting their part.
However since it's your advisor who insisted on having this co-author (and you've already been kind enough to accept), maybe you could go through them: you could tell them that this person's part is "improvable" (if you use this word try to convey that it's an understatement!), that you're worried that this could harm the chances of getting the paper accepted (this is an important argument), and that you don't mind doing this part yourself and keeping the person as co-author... And tell your advisor that you're not comfortable saying this to the third author yourself as you don't know them personally (hinting that it's the advisor's mess, not yours), that's why you ask them (the advisor) to deal with this diplomatically since they have a closer relationship with the co-author.
This way you don't offend anyone, and hopefully your advisor will realize that it's the least they can do in this situation.

Without knowing what your advisor's motivation is, this question is difficult - not to mention dangerous - to answer. For all your know, you could ignore your advisor's advice, write the paper yourself, get it accepted, and then end up with an academic misconduct case leveled against you because you used something that the other person did in some obscure but vital way. For example, maybe your advisor gave you some results to start you off, and those results were obtained by the other person.
If after acquiring the facts you determine that your advisor is asking you to add an author unethically, then you can do something about it, but it's not a good idea to act without the facts. Determine the facts first, then worry about what to do next.

Have you asked your supervisor? Instead of asking us, talk to him. He might have good reason. Even if not, then you know some reasons.
Regarding his incapability to write the assigned section, also talk to your adviser how to proceed. You might write it and let the fake author still remain as an author. It might not feel right, but removing an author usually burns bridges (unless suggested by the removed author himself).

Your advisor being a co-author is completely normal. He goes as last author. Everyone knows what that means. After all it was he that wrote the grant proposal etc.
Your advisor is probably trying to get the citation count of a friend of his increased nefariously. I'm going to go against the grain and say unless your advisor volunteers a sensible answer, talk to a department chair, as it's not a good situation to be in. This may blow up in your face, but if it does it's exceedingly unlikely that you wouldn't have been looking for a new job anyway sooner rather than later.
Id also take this as a bad indication of your advisor and quietly look for another job whatever happens.

What you say in the first paragraph is very field dependent. In some it would be unheard of, not completely normal. Pure Math is an example.

@Buffy Doesn't that rather depend on the work?  If the student came up with the idea completely on their own and didn't need any input from an advisor, then sure.  But many students take projects which extend previous work by their advisor and his previous students on that subject, so their advisor's input is deserving of a co-author credit.  I don't believe Pure Maths is different in this regard, is it?

@Graham, we generally use acknowledgements for that, not co-authorship. Especially in the case of an extension. My dissertation included my advisor's proof of one of the theorems, but no one would think that anyone was the author but myself. It was long ago, of course.

Would anyone commenting here care to state their countries ?  I was thinking from a USA applied science perspective where my 1st statement is true. The norms in the field are important here.

We can take the first paragraph to be the OPs perspective, based on what they have witnessed in their field and working culture (and country, if they so insist). But largely, conventions differ too much even within the same country across different sub-branches of the same discipline, that it is hard to expect that someone exposed to another culture, would dismiss the first paragraph as normal. Hence, the upvotes on Buffy's comment. That isn't so much of an opposition, but rather an affirmation, that we need to take a broader perspective. Cheers :)

What would happen if you just kept sending their parts back for revision until it was at least middling acceptable?  Keep a paper trail of all correspondence should something blow up.  But in this case all you're doing is requiring rigor.  The injustice is something you may have to get used to until you are running completely independent (whatever that means!).  And I'm not saying to accept overt academic dishonesty, just to be clear.
Try to put all the questions of "should this person even be here"--they clearly should not--aside and say "if this was a student of mine what would I require of them on this paper" and just enforce academic rigor.
This approach could have the advantage of discouraging future fake collaboration, and you have the defense from a social perspective that you are "only requesting that the writing be rigorously correct".  This will probably work better if you try to pull your emotions out of it as completely as possible and pretend you are a third party evaluating the work (otherwise your animosity is going to show through in how you word requests for revision, is what I'm saying here). "This sentence is unclear" "This actually implies the opposite of our conclusion, can you fix this part" "I'm concerned with the phrasing here".  As neutral as possible.  It will be much more painful than doing it yourself and it still won't be as good as what you would have done.  But it will be better, and if the pain feedback loop works, your advisor will know what your standards are next time and maybe pick a better "collaborator" or at least be prepared for a lot of revision requests.

It looks like a situation in which one has to cry that the king is naked, but everyone might just as well not do it. And there's an element of conflict to manage, of course. My two cents.
You could also submit 'as is', and then see what the reviewers say. After the first round, your co-authors will probably have a lot of ideas about how you will have to fix the shortcomings in their parts. Then, perhaps, you will be able to plant your heels on the ground. And this may help you keep your potential overconfidence in check.
On another tack, in general, I think that a statement in the acknowledgement such as Author X has done x, Author Y has done y, Author Z has done z is perfectly acceptable. For example, I found a forum post in the Elsevier environment https://www.elsevier.com/connect/clarifying-attribution-in-a-digital-world: the keyword there is clarifying attribution. It can even help readers interested in x, y, or z seek contact with the right person for questions tangential to the article (for which the corresponding author is the contact person).
If the statement has to boil down to Author Z has written the introduction, this might stimulate a moment of self-reflection and the retraction of the idea (out of restraint and shame, if present). There should be a form to fill when an author withdraws after submission, which has to be signed by all initial co-authors to avoid ostracism; don't know whether your co-author would admit such a retreat. Else, the statement will be left to the scrutiny of the the editor/reviewers, assumed they cast their eyeballs on it.
And, as a corresponding author, it is your role to make sure that the manuscript has been approved by all co-authors. That is to say: editors and reviewers do not want to be bothered by what happens behind the scenes, nor should they. On the bright side, Author Z should not bother the editors and reviewers if he does not like the stand of Author X. The dirty linen have to be washed in the family first.
Socially, you will not be the pliable postdoc that they would have wanted to have. They will be clearly disappointed by having chosen the wrong person.

Ethically, serious editorial policies oppose guest and ghost authors, that is false positives and false negatives for the test question Who is the originator of this content? An interesting reading is the Vancouver recommendations http://www.icmje.org/icmje-recommendations.pdf of the International Committee of Medical Journal Editors --- it may provide ammunitions to your short- and long-term positioning.

In fact, some journals now ask for author contributions as part of the submission process. This might be one way to obliquely raise the issue.
(That said, I think the older Vancouver recommendations are fairly bad; the 2019 revision finally gives the actual experimental work the emphasis it deserves.)

It sounds as though you work in the field of statistics. Typically, in this field we start with real world problems and try build statistical models that will answer this question.
One aspect of statistical research that was not evident to me in grad school but is quite evident now is that a good deal of the work is actually finding interesting real world problems and turning those in questions that can be answered by our new, awesome statistical model. Often times, an advisor will do a lot of work setting up a real world problem as a statistics problem and then pass the rest to a grad student or postdoc.
Note that in this process, outside researchers play a very important role; they provide us with real world problems! The field of statistics in a vacuum is quite boring, but interesting models are created from outside researchers coming to statisticians and saying "The standard methods that I'm aware don't work well for this type of data, what can you do?". A lot of back and forth happens between the outside research and the statistician and sometime later, a paper is produced.
My point of all this: there is an innocent explanation for your advisor's behavior. It is possible that they've had long discussions with this outside researcher which ultimately motivated the work you did. In such a case, including them as a co-author is very reasonable. Of course, there's also the not-so-great explanation that they are just trying to help a buddy before their tenure review too.

Good grief.  Academia is absolutely among the worst in having people completely overstep their authority.
This is going to be hard, because it goes counter to what you've been taught.  But simply establish it this way:

You cannot allow a 3rd party in there that has done no other work.
You are the final arbitrator of who becomes added to your own paper.  I'm sorry, but your advisor simply doesn't count.

You'll discover (hopefully not the hard way) that

There is no other way that won't leave you feeling like you've been had.
There is no other way, period.

I wish you well.  But how to stand up to others who wish to steal both your thunder and self-respect is going to be part of what you gain in life as a tool.  A tool no less important than anything else you learned in school.

I would never go along with this. It is obviously unfair to you. Ultimately, your job as a post-doc is to publish well and signal to potential employers that you are a highly capable job candidate. Your advisor is asking you to do something that runs counter to that goal.
Not only would I not do this, I would seriously question my advisor’s motives and consider whether or not my advisor makes decisions with my best interests in mind.


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When are authors on publications in Google Scholar clickable
Whenever one searches for publications on Google Scholar, some of the authors of some publications are clickable (underlined / hyperlinked), but others aren't.
What determines this behavior? Is there a way to manage this as an author?
I have a few publications that are in my profile, but I am not clickable as an author in some of them when searching for the publication.

Have you checked if you have set your profile to public? (The gist of Brian Borcher's answer)

@lighthousekeeper Yes, it's marked as public

OK, I can confirm that your profile is public, while your name is not clickable. For long has your profile been public?

@lighthousekeeper It has been from the start (half a year ago)

After such a long time, I would call that a bug. One idea is to set your profile to non-public, then to public again and see what happens.

In order to get a clickable link in an author's name in Google Scholar results, three main conditions must be met:

The author must have created a public profile in Google Scholar.
The profile must be verified with an academic email account.
The profile must be up to date (only documents that have been added to the profile will appear with a link to the author profile in a Google Scholar page of results).

If these conditions are met and still the link does not appear, the cause might be that Google Scholar is not able to match the name of the author in the profile, to one name in the list of authors of the documents (the names might be just different enough). But I don't remember seeing cases of this.
Hope this helps

Some authors have published their Google Scholar profiles and other authors have not.  If you click on an author's name and the author has a profile, then you'll see that author's profile information.
You might think that Google Scholar would show you the list of all publications by authors with that same name, but there are so many name duplications that this isn't done.
If you have a public author profile, then it should be possible for anyone who accesses one of your publications to click on your name and get to that public profile.

This answer contradicts the question.  Is the question wrong?  Is Scholar buggy?

I've described how Google Scholar works in my experience and how it is supposed to work.  I've never seen any situation in which it doesn't work as described.  Therefore, I  assume that the OP either doesn't have a public profile or is confused.      There's really no way to confirm this report without detailed information (i.e. the name of the OP.)  If the OP would send me a message directly, I'd be happy to check what's happening.

At least at the moment, only one of the two papers in Xander's profile links to the profile.  The other paper is in the profile, but there's no link from the paper to the profile.

My colleague also has the same problem.  His profile can only be reached via mine, but it will never appear on Google search result, and if his papers appear, his name is not clickable.

The reason for this is there is a major bug with Google Scholar that just doesn't pick up some names; yes of course I am one such academic, but if you search you will find numerous examples.
So unclickable names may be because the authors profile is not set to public, or the simple bug described below.
Naturally other answers will all be about making it public etc etc, but in fact, after many hours of investigation, there seems to also be a simple bug that no one has a solution to.  Of course I have reported this to Google with out response.  It seems to be because whatever you do some names are not indexed; so the profile exists, but is just not linked.
Try mine for example; search for my name you find my papers, but no indexed (clickable) name and no profile. One can only find this with a direct link, which one can of course put on your website etc
RBJ profile.
Another example is here Another example, but there are many.
The reason for entering this as an answer, rather than a comment is that there are many academics, and authorities that judge academics by their Google metrics and simply do not understand that these unfixable bugs exist.  "S/he can't be a reputable academic because doesn't even have a Google Scholar Profile". Metrics are never a great way to assess one another anyway, but it is essential that everyone recognises Google Scholar is buggy and unreliable.
Please don't anyone respond with "click make it public".  Obviously we have all done this. I am astonished that people assume, despite evidence and people's experience to the contrary, that this is the one computer system that has been invented without bugs.
screen shot of the public tick


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What are the publication options for academic contributions that don't lend themselves to a journal article?
What are the publication options for academic contributions that don't lend themselves to the journal article format? In the case of datasets, there are some suggestions here, but I'm also wondering about other types of resources, such as

software packages for scientific computing, and
presentations of information that include interactive elements that are integral to the usefulness of the resource.

It seems to me that a common practice is for creators of such resources to publish an accompanying article, such that there is an avenue through which the resource can be 'cited'. But my impression is that often such articles do not add much value beyond that of the original resource. So a two part question:

Are there other options for 'publishing' such resources directly?
Are there pathways for having such resources peer-reviewed?

With regard to interactive resources, I'm thinking of a broad range, from this kind of interactive exposition to, say, a formal rubric-like taxonomy with more than two dimensions, such that some interactivity is required to toggle between which pair of dimensions are displayed (assuming only a 2D representation is used). To have such resources peer-reviewed, the closest option I know of is Distill, an web-only journal for machine-learning that facilitates interactive elements in the articles it publishes. But, for now at least, that option is limited to contributions in machine learning.

@artificial_moonlet I've recently completed a MSc in statistics/stochastic processes, and am currently drifting between a few different fields (stats, NLP, epistemology, media studies, ...). Thanks for your comment, a core part of my question is the bit about peer review pathways, I'll update it to make this more salient.

Good point, there are definitely other ways to accumulate credibility. I think that there are likely still situations in which peer review makes sense. The crowdsourcing approach (a la GitHub) fails if the research doesn't have a large, active audience, and simply posting work on your own website doesn't allow for any publicly verifiable review, especially if you aren't already known/trusted as a researcher.

It seems to me that a common practice is for creators of such resources to publish an accompanying article, such that there is an avenue through which the resource can be 'cited'. But my impression is that often such articles do not add much value beyond that of the original resource. Are there other options for 'publishing' such resources directly, or pathways for having them peer-reviewed?

I don't think you give articles enough credit. They have several upsides:

They hook into the "citation score" mechanics that help establish your academic credentials. That might sounds shallow and self-serving. But if you worked hard and made something good, there's nothing wrong in wanting get credit for it.

If someone uses your dataset for research, or uses your software package as a key tool, then they need to provide references. This allows readers of that research to see what it's based on and how it could be reproduced. So you are helping a lot if you make it easy for people using your work to provide a good reference to it. Now, you yourself say you're not sure how to publish it; the same goes for anyone wondering how to cite a dataset or package. But by tying it to an article, you make it a lot easier. Academics might not know how to cite a dataset or package, but citing an article is familiar to them. And finding an article is also more familiar than chasing down a dataset or package. So the article makes your work a lot more accessible.

You can hand anyone a PDF or print of an article and they can read it through, and decide if it's relevant for them. That's something you can do in the hallway at a conference. Telling people to download a dataset or install a package and play around with it? Takes longer, and you need to be behind your own desktop. So an article is a more portable preview of your work.

How good the article is, is really up to what you put into it as a writer.

So what should be in the article?
As I've already outlined, the article is sort of a preview of your work, helping people decide if they should download your work. It's also a map to help find your work.
For a dataset you could talk about:

Where to find it. What's the stable URL?
Explanation of what the data is, where it came from and how it was gathered. If there are ethical, confidentiality or privacy issues that someone using the data needs to know, also describe those.
Statistical analysis of the data, like what the distribution is of different items in the data.
What kind of outlier removal or data cleaning has been done.
What kind of data types are used, are any transformations like binning done? What is the range of different values?

For a piece of software you could talk about:

Where to get it.
How your software is licenced.
What kind of long-term maintenance users can expect.
High-level indication of hardware requirements and software dependencies. People reading your article should be able to identify whether this is something that will run on their desktop PC, smartphone, or that it requires a supercomputer, and what kind of OS and programming languages will work.
A high-level overview of the structure of the package.
Where to find the detailed documentation.
Discussion of any (scientifically) interesting design choices. For example, if you're implementing an algorithm but not all of the literature defines the algorithm in exactly the same way, make it clear which one you used.
Discussion, code fragments or pseudocode explaining the key/original algorithms.
If under the hood you use a different algorithm than what people would expect, you may want to include a theoretical proof showing they're equivalent.

Appreciate the thought that has gone into this answer. Apart from the accessibility of PDFs, I feel that many of their advantages could exist for other resources too. Eg. there's no a priori reason why datasets and software cannot be referenced and contribute to citation counts. Similarly, many of your suggestions of what to include in an accompanying article should also be included in the documentation for the dataset/software, so there's still duplication. But accessibility is a significant point, and I can see there may not be much incentive to break out of the paper-based system.

What are the publication options for...software packages for scientific computing,

The software can be made available on the Internet, e.g., via GitHub. (A personal website could be used too, but GitHub has many advantages.) A tutorial for the software could be published using traditional channels.

and  presentations of information that include interactive elements that are integral to the usefulness of the resource.

To include interactive elements you'll need a medium that can support such elements. Publishing a video on the Internet might suffice, e.g., on YouTube. (A personal website could also be used.)

My answer doesn't address the (new) peer-review aspect, which was added to the question after my answer was written.


text:
Taking a break from industry and becoming an unpaid research assistant (or atleast getting involved in reserach at a school)
I am planning to take a break from industry (software) and want to work under a professor/lab on a research project for 3-6 months, computer science/computing related. I was wondering if people could give me some advice on how to go about achieving this arrangement - success tips, what not to do and the feasibility of this whole endeavour.
I'm in my late 20s. Went to a good UK school and got a decent GPA. I got what is known as an undergraduate masters (MEng), which for all intents and purposes is a BSc + MSc. I regret never undertaking a summer UROP placement while doing my undergrad. I've often wondered about doing a PhD (I kinda always thought I would) and this would be one way to get some kind of feel of what it might be like. Who knows maybe I will change my career and move into research.
I have some potential projects (though still a little vague) that I would like to work on, but I am also looking for existing projects that sound interesting to contribute to. My current plan is to reach out to professors that seem like a good fit with my research interests (by scouring their academic pages and published work). I'm yet to reach out to anyone. Actually that's a good question - would I have more luck joining an existing research project or proposing my own?
This potential opportunity is unlikely to happen again - I currently do not have too many responsibilities e.g. kids, a mortgage, etc. That and the window for me doing something like this is shrinking all the time. I want to make the most of it by going to go to what is considered a competitive school (not that I'm applying for a programme per se).
I also want to sample US university life (I have a degree from the UK), go to a new city and meet some new people.
What I hope works in my favour is I have the money to entirely fund myself - I've been working in the tech indusry for the last half decade. Hopefully this means I don't have to work within the confines of the academic calendar nor compete for funding. I am concerned about the legality of working for free - I have seen Nonpaid, volunteering position in a lab.
I understand what I am trying to do may be a little unorthodox, but if I was a professor, and there was an enthusiastic individual who has a decent academics and willing to give up 6 figures for a chance to work on something interesting to us both, then I'd like to meet them. Of course I'm nothing special and I could be a hindrance, but hopefully my work experience, previous academics and genuine interest abate these concerns. To academics reading this, imagine if it was you I contacted asking for this opportunity, what would make you consider me?
Anyway, if people could give me some kind of assurance if what I want to do is not out of the question (or let me know it is), along with some pointers on how to be successful in finding a position.
Really appreciate it,
Thomas

In my field (though different from yours), 3-6 months is not nearly enough time for a novice to approach a research project.
Student volunteers (undergraduates, who may also get credit for the work so not entirely "volunteer") may take on projects of this duration, but there is little expectation that they accomplish anything concrete - they take more time to train than their research output is worth.
That said, a university has a mission to educate students, and that trade-off is okay for students - it's a service to the next generation of researchers, to make sure students get exposure to what research is like. If you aren't a student, it's harder to make a case that the time should be spent with you rather than those interested, enrolled students. Yes, you may be interested in maybe switching to a research career, but you're not nearly as invested in that exploration as someone who is enrolled in a degree program.
Additionally, there are the legal issues with what defines an employee as in the answer you already linked.
There are more issues as well involving privacy, data security, intellectual property, etc: universities have policies and agreements in place to address these concerns for both students and staff; you can't really sneak a volunteer in without going through those same processes, so it isn't quite as simple as just "showing up".
Lastly, just a bit of a caution:

an enthusiastic individual who has a decent academics and willing to give up 6 figures

does not seem to me nearly as impressive as you make it sound, especially when you've made it clear you are secure enough financially to go unpaid for a bit. Any university is full of currently enrolled students who have financial and life difficulties and yet are working towards a degree already without the security that you've built for yourself. They are enrolled and earning meager salary despite having those responsibilities like children, sick parents, and family members in dangerous situations elsewhere in the world. It's fine to be proud of what you've done for yourself so far, but I'd be very cautious in thinking that it positions you above others in any way.

thanks for replying - really appreciate it. I've thought about what you said, and I think I will still apply to some professors, but set my expectations low. I'm not entirely convinced that what I want to do is illegal, though it does seem ambiguous and potentially risky, and probably another reason for some departments simply not to consider it. Apologies if I came off the wrong way, and I guess it's a good thing I asked here - I actually did spend not-a-small-amount-of-time reworking things in an attempt to get a fairly balance tone but I guess I was still off. Thanks again :)

@DoubtingThomas Best of luck. Hopefully some warning from a stranger on the internet will help you avoid saying something foolish in front of someone that can help you get where you want to be. :)

There are “pre-doc” research positions in many fields. If you are considering going back to get a PhD this would likely be an appropriate thing to apply for. Usually they are working on a pre-ordained project with a faculty member who has been successful in getting a grant. But they are typically a year minimum... it would probably not be worth it for a faculty member to try to train you up for just a 3 month gig.

aha predoctoral is an actual term. obvious in hindsight. thanks for replying. like i just wrote in the reply above, I think I will try approaching some professors, but with the expectation of being unsuccessful. thanks :)


text:
Send reference letters from mathjobs to other positions
I am currently applying to several postdoc positions. My referees have uploaded their reference letters to Mathjobs, but I'm also applying to some positions out of Mathjobs. In order to avoid disturbing my referees again and again:
Question: Is there a way to send a reference letter uploaded on Mathjobs to a position out of Mathjobs?

Why don't you contact Mathjobs directly?

@user4050: Done!

Short answer: no.
As suggested by user4050, I contacted Mathjobs directly and they answered the following:

Hello Sebastien,
Applicants do not have access to the letters uploaded into MathJobs.
  There is some import capability between MathJobs and
  AcademicJobsOnline, but you do not have the ability to export your
  letters otherwise.
If you need anything else, please let me know.
Regards,
Kim Kuda
  Senior Program Coordinator


text:
Is there a max number of authors for a paper of math?
I never saw a paper published in a journal of (pure) math with more than six authors. Is it a rule?
(see this one)

In the link you provided, in the Reference list, the #7 article has 7 authors if I count it correctly. (Same authors plus Hagge)

@scaaahu: yes but it is not a journal of pure math.

Who could possibly set or enforce such a rule?

No. But there is a min number of authors...

This blog post may be of interest. I'm not sure what's included in Scopus' Mathematics subject area, but during the 2010-2016 period the highest number of authors was nine, which was a clear outlier.

Not published yet, but we sure hope to publish it soon. It was very hard to collaborate on so many people though...

I remember a paper in pure math (On Invariant Random Subgroups)  cowritten by 7 authors who referred to themselves as "7 samurai".

Let's go one more beyond Denis Nardin's example: the "10-author paper" at https://arxiv.org/abs/1812.09999.

Also of interest: https://en.wikipedia.org/wiki/Polymath_Project

1 - is the spirit of this question actually 'what's the highest number of authors on a maths paper?' ? 2 - what's the highest number of authors on a maths paper?

https://academia.stackexchange.com/questions/16759/is-there-an-inflation-in-the-number-of-authors-per-paper?rq=1

The MMA monthly Problem Section occasionally has solutions by groups like "Podunk College Problem Solving Team."  That could be more than seven.

clearly the number of authors could not exceed the total number of people, so there is an upper bound on the number of authors

Yes. 3.1415926, by convention

I ran a quick check in Web of Science: for articles published in journals in the mathematics category for 2020, there were 277 articles with six authors, and 154 with more than six - out of a total of 37,379. 98.8% of them had less than six authors. So not impossible - but also quite plausible you'd not see many on a day-to-day basis.

@DanRomik But is that number 1?  Or 0?  If I wrote a Markov chain generator or some other kind of AI and trained it on every mathematical paper ever published, and set it to generate a new paper that was plausible enough to be published, am I the author?  Or is there no author at all?

@DanRomik: Some papers are imaginary and have imaginary authors. So there's no linear order to say "minimum" here.

@Andrew - nice finding, please consider copy-pasting into the answer box

Why on Earth should this be a rule?

@cag51 turns out someone did it much more comprehensively two weeks ago! have written that up with my own notes as well.

No: Authorship is governed by the number of contributing mathematicians, rather than some arbitrary limit.

When a math research group grows, so does the likelihood that many questions will be asked within it and sub groups will take them up individually. Six as an "effective" max seems about right, and hard to achieve. Perhaps some of the papers with long author lists also have some other acknowledged people, pointing to the larger group.

@Buffy The number of contributors is certainly limited by the degree to which contributors can effectively collaborate, but there's no rule. Physicists seem to organise in a manner that facilitates a greater degree of collaboration, publishing thirty three page articles that devote a whopping twenty-four pages to list all 5,154 authors and their affiliations (https://doi.org/10.1103/PhysRevLett.114.191803).

Yes, lab sciences in general have a larger number of authors due to the nature of experimentation. And high energy physics in particular. Several physics papers have longer author lists than the actual article.

1 - is the spirit of this question actually 'what's the highest number of authors on a maths paper?' ? 2 - what's the highest number of authors on a maths paper?

@user2768 However, those branches of science use completely different authorship creteria. All authors on the author list of the collaboration automatically become the authors even if they have never seen the manuscript and work on a completely different sub-project.

@BCLC I can't answer either.

@VladimirF Indeed, comments are off-topic.

It turns out that someone put out a bibliometric analysis of publication characteristics in mathematics papers this month, which is very convenient for answering the question!

Richard & Sun (2021). Bibliometric analysis on mathematics, 3 snapshots: 2005, 2010, 2015. arXiv:2102.06831

They found a general increase in the number of authors per paper over time, from 2.1 in 2005 to 2.4 in 2015. (Interestingly, this collaboration was both "internal" and "external" - the number of distinct institutions and distinct countries on a paper also increased steadily). The share of papers with five or more authors was 5.4% in 2015, so presumably slightly higher now. Papers with more authors, or from more places, tended to be more highly cited, which I believe is a common phenomenon across most fields.
They used the Web of Science "research area" classification, which as I understand it will group together a few different Web of Science "categories" (which in turn are inferred from the journal the paper was published in). It will probably thus include more interdisciplinary material than a narrowly defined field of "mathematics" might. They do not break down authorship by category, but it's possible to pull the data and do it yourself.
I ran the numbers for 2020 papers in "mathematics" and in "mathematics, applied", filtered to just "articles". Papers in "mathematics" had an average of 2.24 authors; those in "mathematics, applied" had an average of 2.56. 3.4% of papers in "mathematics" had 5+ authors, versus 5.7% of those in "mathematics, applied".
If we limit it to just those papers published in journals which were only classified as "mathematics" and not as eg "logic / mathematics" or "mathematics / mathematics, applied" (about a third of papers were in journals which were in multiple categories), then we get an average of 2.20 authors, and 3.3% with 5+ authors.
So whole we don't have an explicit classification for "pure mathematics", the non-applied group clearly skews towards a slightly smaller number of authors than applied, and the "just mathematics" group ditto. Papers with five or six authors are not unknown, but they are definitely uncommon - only a few percent of papers. (7 or more authors was around 0.4-0.5%, depending which group you looked at).

This is very interesting, but doesn't quite come on-topic until the last sentence. :-)

authors: Vladimir F Героям слава


text:
Information Regarding PhD Admissions
Are there universities that offer PhD in Mathematics without GRE or TOEFL in Europe?
I have completed my Masters in Applied Mathematics with a cgpa 8.0. I am keen to pursue research in Mathematics but I am not aware about the same. I would highly appreciate the comments in this regard.

You have to check with each institution ofering the PhD that you ate interested in - they have their own requirements / standards...

The GRE is generally not used at all in Europe for Master/PhD admissions.
Another thing is TOEFL, if you will be studying in English you usually have to prove that you are proficient with the language, and there are multiple ways to do it. You have to check with particular institutions to what they require, it could be the TOEFL or IELTS or any other test of english, or proof that you have already completed a degree in English, etc.

You need to write the GRE exam, is not a big deal and many funding opportunities in mathematics but you can research institutions in Germany ,Germany dnt need Gre

Welcome, Cryptobosslady! I know it's discouraging to get downvotes, especially if they don't say what's wrong. You have a partial answer here--that German institutions don't need GRE scores. But also the question was put on hold because it is a "shopping question," where it's especially hard to provide good answers that will still be helpful to other people, say who are searching a year later. Anyway, I hope you contribute on more questions, and many of us use the [edit] button extensively on our own answers, to improve them based on comments. :)


text:
Where do PhD scholars get data to test their thesis on?
For example PhD scholars working on ML/AI algorithms need a lot of data to train and test their research. Research on distributed systems might require terabytes of data to test.
Where do these scholars get so much data i.e. the scale which is only produced in big companies?

They create relationships with companies to be able access the data or they purchase (buy, pay for) it...

If you work in the biological sciences there are lots of databases: national center for biotechnology information, protein data bank, national institutes of standards and technology.

The question is very vague. For some fields such as linguistics/language there are huge open-access research corpuses available such as the British National Corpus, maintained by academic or charitable organisations. For some things, e.g. images, you can also use open, permissively-licenced sources like Wikimedia Commons, which offers a lot of APIs for searching and processing; the Internet Archive has a huge collection of video, texts, audio, etc. For some subjects it is possible to use internet searches or other archives. Many commercial entities will have large databases and research project are often done in conjunction with a commercial partner, as mentioned in a comment. You can also purchase data, but that will probably require a commercial partner to pay for it.

One of the things you should remember is that nothing in life is free, especially not data. I have seen instances of inexperienced students/postdocs reaching out to companies asking for their data (without informing their advisors). These requests go either ignored, or politely refused. The company needs to know that there is some real benefit in working with you, whether it is an improvement to their current processes or a monetary incentive. In either case, it often involves the university's lawyers making sure that the transaction is

Legal/ethical - the data you're getting doesn't require someone's consent and is indeed owned by the company. You may need to get IRB involved too.
Transparent for both sides - what are you going to do with your analysis? Will the data be published? Will it be anonymized? Can you patent the results? If so - what part of the patent is owned by the university/company/yourself?
Modes of compensation for the company, if any.

(this is a partial list, I'm not a lawyer)
This is even less fun when one works on data provided by a government agency. This is why often enough researchers either work on public datasets (e.g. those on Kaggle/Github), collect their own, run simulations, or just go on research visits to Amazon/Uber/Google/Facebook to get access to actual data, see that their models make sense, and get a nice paycheck while doing so.


text:
Is it possible to do PhD in pure mathematics after engineering
I have an MTech in Industrial Drives and Control (Electrical Eng). After that could not go for any work... After giving some tuition, I came to the conclusion that I am genuinely interested in mathematics... be it to study or to teach. Is it possible for me to do a PhD in mathematics? Or, are there any PhD options in Electrical Eng that are related to mathematics? I am even ready to take time and get a bachelors and masters in mathematics by distance education.

Sure, it is "possible".
I really question your stated rationale for it, though (couldn't get a job in engineering, thus staying in school and moving to a field that usually has harder time with job placement).  I think you would be better served beating the bushes and getting a job.

The only real difficulty with joining a doctoral program in CS or mathematics is getting admitted to a graduate program. If you can get admitted you are on your way. In the US admissions committees generally expect that you will have the knowledge in a "typical" undergraduate degree program. The Mathematics Association of America (MAA) has made curriculum recommendations to colleges. You can read those to see whether you have the knowledge background that people will be looking for.
Those recommendations are a guideline, however, and most colleges will deviate from them somewhat. On the other hand, most colleges will teach other, somewhat more advanced, topics to undergraduates. Those get little mention in the recommendations. But each undergraduate program seeks to give a broad look at mathematics.
But if you have the knowledge in most of the recommended areas and can demonstrate it somehow, it will be easier to make your case for admission. Many students move from a BA/BS program directly to doctoral studies but initially there is (in the US) a lot of coursework for such students prior to specializing in a research area. So there is opportunity to make up for topics you aren't familiar with.

Is it possible for me to do a PhD in mathematics?

Yes it is possible - there is no rule that says you have to stick to your undergraduate discipline and engineering is sufficiently quantitative that you probably meet the admissions requirements. However, because you do not come from a pure math background, you might find it challenging to begin with. I did a masters in mathematics after a chemical engineering undergraduate and I had to work quite hard to bridge the gap - for example in functional analysis, which I knew nothing about. I would actually recommend you consider a masters (but not another bachelors!), as it gives you a chance to see if you really would enjoy spending +4 years working in pure mathematics and will likely strength your application to PhD programs.

are there any PhD options in Electrical Eng that are related to mathematics?

Control theory is pretty mathsy.

If you are from India,All your questions will be answered here about going to mathematics after engineering
https://mathsafterengineering.blogspot.com/2020/03/how-to-do-msc-mathematics-after-btech.html


text:
Can a paper proposing an algorithm use pseudocode only (and not a high-level mathematical description)?
If it greatly simplifies the explanation, is it possible to present an algorithm in a paper without a high-level mathematical description but simply with pseudocode and very clear elaboration? Or should a high level mathematical description always be included?

That probably depends on the requirements of the journal you submit to. A referee may ask for a mathematical description.

What do you mean by "very clear elaboration"? Would that not include explaining what your algorithm does in detail, including whatever math is needed?

What is the point of writing a paper?  Who are your audience? The audience will ask different set of research questions.  What is the reason for using a math description?  Once you find the corresponding answer(s), then you'll know how to write it.

Make sure you have a reference implementation, of course. Whether you intend to publish it or not.

I would say that it strongly depends on the target conference/journal that you will be submitting to. For instance, if you plan to submit to e.g., Algorithmica I wouldn't say that this would be suggested. But if for instance, you plan to submit on a conference that is not algo-oriented, then a high-level mathematical representation might be replaced with a detailed pseudocode along with the appropriate explanation.
But, even if this is the case, there is still the matter of

Completeness
Converging

I do believe, that you would need at least some mathematical representations in order to convince the reviewers about those two points. And in many cases, those are not THAT hard to prove, but once again, this also depends on your algorithm and your application.
So to answer your question, it is possible that you will be asked during the peer-review at least for the completeness of your approach. So I would put a bit of effort in order to justify this point.

Generally speaking, the purpose of the mathematics is to clarify the algorithm and prove that it works (or at least set up the mathematical problem so that it is clear what you need to prove).  In some cases the pseudo-code might be sufficiently clear to describe the algorithm, but it will not set the problem up in a way that allows mathematical analysis.  This might be okay for some journals/referees, but others will want a mathematical description.
Some commentators have already noted that the answer here depends on the journal you submit to, and their expectations for the level of detail for an algorithm.  I would also add that it will probably also depend on the idiosyncrasies of the particular referee you get --- into that crystal ball none of us can peer.  If you have good reason to believe that your textual explanation and pseudo-code set out the algorithm clearly, and little is gained from adding a mathematical description, then you should feel free to submit on that basis and see what the referees come back with.