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Learning as an adult: After the end of your formal education and before you get a job?
I'm a recent CS graduate. I realize the value of going to college and getting a degree now. It'd be absolutely impossible to learn everything taught in college on my own looking at my current situation.
I'm studying to get a job currently as well as to pass licensing exam for engineering graduates in  my country. But main focus is job.
I'm also studying subjects like DBMS, Operating System, Data Structures and Algorithms because they too are somewhat related to web development/programming and studying just 1 subject per day is very bad thing if you get stuck. My goal is to rotate between 3 things per day, Web development, DBMS and DSA/OS. I've to say that I'm re-learning these subjects. I've already studied them in college but I didn't studied them well at that time as they were taught when I was freshman in college.
Companies here (It's Nepal) Don't like training new grads so generally you're all on your own. I need to upskill myself to a point where I can get guidance but don't need that guidance.
Here are the problems I'm facing atm.

I"m not sure what topics should I learn? For eg: If I had to learn DSA in college, I'd just learn the syllabus/contents that the college gave to us. Do I still do the same?

I'm not sure what should I practice. What exercises. A book has 100s of exercises in 1 chapter and it's obvious, nobody can afford to solve each of them. In uni, I'd either solve "assignments" or "previous year question papers" and learn a lot from them. For each chapter(eg: memory mgmt,process mgmt are 2 chapters of OS), I'd be doing 20 long+short questions. What do I do now?

I've no natural/real deadline. No pressure of exams. That is really harmful as I won't be finishing anything in time like this. I'm always in a hurry. I'm scared of wasting more time. I am impatient because there's nobody to fix deadlines for me. There's nobody to tell me how much time something will require to me. I've never took an year loss in my entire life.

I'm facing failures after failures  in learning when starting to learn from a gap(I took around 2 weeks gap).

Staying at home all day is mentally tough and draining. I'm always unfocused. Mind is wandering here and there. I'm not sure the science behind that, but it's really creating cluttered and useless mind. "Empty mind, devil's home". There are no "IT Training Institutes" that are worth the money here in my state even though it's the state with capital city.

No public libraries that allow "work space with laptop and books" has been a huge issue. Recently, I've heard ihub allows it so I'm optimistic.
Luckily, I'm not really sad about being away from uni and amn't demotivated by it. I need guidance to move forward more than anything else. This is a huge change of scenario for me. It has been around 1 month of it and I'm still like this. It's true that I've not have to study for whole 1 month because I'd other things to do, so I was in a break from studying. I'm seeking for non-medical guidance here.
Some suggestions given to me by my friends is to "learn bare minimum and get a job", but that's  a catch-22. Learning bare minimum is what I'm trying to do. Make project, learn dsa for interviews. That's all. Learning a lot isn't a problem for me atm(ofc it is), but learning anything(even just 1 thing) is a problem.
Thank you.

You have too many questions. Please, ask 1 question for each post. Also, your questions are out of the scope of the community.

If you are really stuck, the world is full of options and you do not know which one you have to pick and you do not know what the different companies are really doing , look for an internship.
You will get a bit of life inside a company and you will be able to focus on what you want to do, what you can do and more importantly what they need.
Working for a company is not related to what you want. A company is simply buying your work to sell it for a profit ... so your task is now to find a reasonable match between what you can deliver and what a certain company is needing.

Here are my advises that could help:

You should spend some time for searching what you want exactly, and since your goal is to get a job, then it is necessary to check the job offers and know their requirements in order to learn them.
Make a roadmap for learning the required skills, and set a duration for each step, set goals and follow a rewarding system (if you learn/accomplish something, reward yourself).
Focus on one thing per time, learning many modules can make you distracted.
Create a group of serious friends to learn together and share knowledge.
Github is a treasure, you can check others' source codes and learn from them, as well as you can share your programs and get back comments. In general, working within a team can improve your skills.

Good luck


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Are there any disadvantages of pre-publishing figures for a paper separatly using a CC-BY license?
I recently came across a blog post, where it was suggested to pre-publish figures you intend to use in an academic paper somewhere using a CC-BY license. I find this idea really nice (as it allows easy re-use of my figures, without checking the journal's copyright policy), and never really thought about it for my papers but am considering to do it for my next paper. However, I have realized that nobody from my community is doing this (or even heard of it before), so I have the impression that this very uncommon. Am I missing something, apart from the extra work to publish the figures (i.e. uploading them to some repository), are there any further disadvantages?
I also found a second example where somebody is doing this, but that's not my field (and in general, this procedure seems to be very rare in academic research)

Related answer: https://academia.stackexchange.com/a/123912/17254

How many times do you think you will actually reuse the exact same figure? Why complicate things?

@JonCuster to clarify: these figures are illustrating the general mechanism of a diagnostics, so I have the naive idea of them being of some value (realistically to only a small number of people though...)

This depends on the field, and, more specifically, on publishers in that field. Some publishers won't publish anything for which they won't hold copyright as it can reduce the value of the publication to them. A problem with figures is that they can convey a lot of information and, thus, be considered to have a lot of value.
In math that would probably not be a problem, but in some other fields, with some other publishers, it might be.
I suggest you look at the pre-publication policies of a few reputable journals in your field and act accordingly.
The trend seems to be toward the more permissive in such things, but it isn't yet entirely open. Look before you jump.

Will some publishers seriously not allow to include CC-BY material in their papers...? Wow, I wasn't aware of that (I'm in physics)...

@Alf It's common to see guidelines such as "Reproduction of previously published figures, tables, and text should be kept to a minimum and must be properly referenced and comply with the copyright or licensing requirements of the paper’s publisher.". How the "previously published" and "minimum" are interpreted in practice is not clearly stated and left to the publisher's discretion. But, in general, such policies may limit how far you can take your approach.

@Anyon thanks for showing that example, and that is indeed a very vague expression...

@Alf The entire issue only arises because some publishers seriously do not allow reusing parts of "their" papers, as you know. That they don’t allow obvious workarounds shouldn’t be all that surprising.

source: Stack Exchange

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

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How to convince professors for undergrad research when you don't have enough credits?
I am a BSc physics student who wants to be a mathematician. I would like to do an undergraduate research project in mathematics. I can't take any pure math courses apart from real analysis at my university, but I have self-learned group theory, abstract linear algebra, real analysis and basic point set topology. (I have solved most exercises in popular textbooks in these topics.)
How do I convince professors to take me in, when I don't have math credits to prove my knowledge and passion? Will online courses (that have offline exams) work?

Given what you have learned so far, you are several years away from being able to do any meaningful mathematical research. If you had taken some combinatorics classes and the professor were working in the combinatorics area, then it would have made a difference.

"(I have solved most exercises in popular textbooks in these topics)." How do you know your so0lutions/proofs are all correct ? Suggestion for you, post some of your solutions/proofs on Math.SE and ask experts on that site to check them.

@Nobody, I cross check and learn from solution manuals. But I get your point

@Moishe Kohan, I have taken a basic combinatorics class. Also, do you think graph theory is accessible to me?

I have just edited your post to remove the first question. Questions should focus on only one issue  and we don’t cover research content here. If you feel I went too far you can always [edit] the question back in again.

Yes, graph theory requires very little math background. But you need an advisor who specializes in this subject. And, as others suggested, you should talk to this professor in person. It is far from clear they would take you even if you have the required background.

Can you clarify what the problem is exactly? Why are you talking about convincing professors with additional math credits? Why this approach is the only option you consider? Did you talk to the professors and they mandated you to convince them by taking additional math courses? Have you talked to the professors and your undergrad advisor at all? What exactly did they say? How did you approach these discussions? How did these discussions go? Do you know how to talk to people? Do you have experience solving any problem by just talking to people?

In your another question, you mentioned "I can only take introductory group theory and real anaysis from the math dept.". If you got A from both courses, you should not have too much  problem to convince the profs for you to join a research project.

If you want to convince someone of something, you have to sit down with them. It is nearly impossible to do it remotely or by mail.
Find a professor in a field you'd like to explore and go visit them. Express your need, and tell them you'd be happy to try to demonstrate your knowledge, perhaps by taking an oral (or written) exam for one of the core courses. If you have written anything meaningful in the field, offer to let them see it.
I doubt that online courses, with some rare exceptions, will help you much as it can be difficult to trust them or their credentials (Open University UK is an exception).
I also wonder why switching majors, or even universities, isn't one of your best options. It will take time to switch, but maybe less time than switching after completing a physics degree. And note that pure and applied math are vastly different. You could explore that with a math professor in a sit down also.
And, if it is applied math that appeals, the right physics professor could probably get you started without the need to switch.

Academia differs highly between countries, and between individual universities. So not all of my advice might apply -- but I'll answer from my perspective as a mathematics professor in the United States.
If you asked me to take you on as a research student, I would ask -- why are you studying physics, if your goal is to become a mathematician? And why is it you can't take any pure math courses other than real analysis? At my university, you would be able to (1) switch your major to mathematics, (2) double major in physics and math, or (3) keep your physics major but take as many math courses as you would like. If you wanted to do research with me, I would ask you to do one of the above -- and in particular to get more formal training in math.
If real analysis is the only pure math course offered, and there is no math major available... then that is a possible sign of a weak mathematics department, and I'm not sure if this university is a good place to realize your ambitions.
If you can't add a mathematics major, or take other math courses, because of administrative roadblocks... then I'm not sure.
But if the obstacles are something you can resolve, I'd encourage you to try and do so.
In general, I don't encourage students to "work around the system", because the system is (while not perfect) designed to help students and works fairly well. And I would probably be reluctant to mentor a research student, if I did not have more infrastructure around me (e.g. a strong department that offered multiple pure math courses) to help.
So my thought -- and again, this is not knowing you or what your circumstances are, so take it with a grain of salt -- is, if possible, to consider improving your circumstances to line up better with your goals.

Due to the rigid system, 1,2 and 3 is not possible. It is outrageous, I know. I am not happy with it.

@Boay Yes, it is possible. I do know an Indian who was in a similar situation. He had to retake the college entrance exam and then got into the department of his preference. Of course, he graduated late. I remember his words to me was "I passed out later than my high school batchmates." something to that effect.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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How serious is it for an artist-scholar with a professor role to misrepresent their achievements?
There is a senior figure (a professor and director of a research centre) at my institution who it seems has misrepresented their achievements and level of expertise in what seems to me to be quite a serious way.
This person is a fiction writer and scholar, however their experience as a fiction writer is quite minimal.  They've published some short stories in very minor journals and anthologies, and won some extremely minor awards - legitimate but very minor, of the level it's not uncommon to see students win.  They have worked in the publishing industry, but again in not very significant positions.  Their PhD project is in an unrelated field (education), and from what I can see they have no credible academic publications (journal articles, chapters etc).  From what I've been able to verify, they have one or two modest achievements of a level that you wouldn't expect to see from a student, but well below the level of national and international success you'd expect to see on the CV of a professor who is primarily a practitioner.
On a document which they've sent out to students, they claim that they won a significant international level award for short fiction, however I've looked into their claim and it doesn't hold up.  It seems they won a very minor award from a small organization and have misrepresented that award to make it appear of an elite international scale (I won't give the real organization but let's say they won an award from a small regional arts organization and have presented it as part of the Sunday Times Short Story Awards - it's comparable to that).
Their university staff page repeats that claim (with slightly more moderate language), and makes other fictional claims.  Again, I'll use comparable non-exact examples that exemplify their claims: let's say they claim to have had stories selected for the Pushcart Prize anthology and for the O.Henry Prize anthology - and that those claims are fictional.  It's comparable to that.
This person also won a substantial research grant recently, and it seems a realistic concern that these untruthful claims may have been repeated in their application.  At the very least the funder may have viewed their staff profile and been influenced.
It should also be said that on the same staff page they advertise their availability to supervise doctoral candidates - so doctoral researchers could conceivably spend their life savings to move to our city and pay their tuition to work with someone with these impressive accolades, only to find out they're fictional.
I think this is very serious, with the potential to bring my institution into disrepute. It's clear that any professor who fabricates, say, a journal article would be guilty of gross misconduct, so if a professor in an arts practice discipline fabricates a major award are they too guilty of gross misconduct, and if so how should someone who discovers gross misconduct of a senior colleague proceed?

It is, obviously, not acceptable to invent things on one's CV. It is a matter of debate whether the award from a small regional arts organization can be considered major or minor -- that's a judgment call every reader of a CV will have to make for themselves. Most people will simply list the award on their CV and leave the judging to the reader; most readers will consider it petty if the person whose CV we are talking about oversells the award as anything bigger than it is.
The question is whether you should do anything about it. You don't say what your relationship to the person in question is. Between the lines, I can guess that you're a colleague, and then the right course of action might be an informal conversation with the department head. You bring up your concerns, and whether anyone does anything about it is then in the hands of the authorities (the department head).
I will add, however, that people don't get hired on a whim. Your post suggests that you equate the embellishment of the CV with a lack of skills as a professor. That seems like a tenuous connection to me, for which you don't present any evidence. In practice, department hires -- at least in the countries I have worked in -- are highly scrutinized by many people, and those who do get hired are typically highly skilled in their area. I would therefore invite you to consider whether your attitude is basically a disagreement in value for this or that prize, or whether you can objectively back up your claim that that person is not actually skilled.

obviously if someone is fabricating awards to make themselves look more expert than they are then they are grossly incompetent for a professorial post and directorship of a research centre, posts for which maintaining institutional standards of ethics and integrity are core job requirements. In addition, this person's CV is full of misleading info, of course I haven't given evidence which would violate their privacy. Please read the question carefully, particularly if you're going to pick holes - the issues I highlighted are in a student-facing doc & staff profile, not CV.

Additionally, regarding professorial ability and your feeling that I was making a tenuous link between dishonesty and job skill, I will add, as I mentioned in another reply, that the reason I started looking into this person's credentials was because I had numerous complaints from students about their teaching and their conduct. Why they were hired is unknowable and irrelevant - many incompetent and disreputable people acquire positions of power.

Then, if you think that they are incompetent regarding the duties of the job, going to the department head (or perhaps an ombudsperson at your university, if you'd like to keep it lower profile) would be the logical next step.

@AnonymousAcademic444 Beware, it sounds like this person has a considerable position. Attempting to bring these concerns to light might cause significant backlash on you. This would, of course be unethical, but it might still happen, and you could find yourself in the moral right but unemployed.

Yes I agree, that's why I'm anonymously seeking guidance

More so than mere misrepresentation and breach of code of conduct that is to be understood primarily, it depends otherwise upon what the said achievements were, and are the said skillsets that would have been required for achieving said pedestals, have been attained by the professor in question already or not, upon which the integrity of the said achievements must have played certain role in the social capital of the person, is that all there was to their approval upon qualification? if not, then it is a qualitative analysis from thereon really, secondarily speaking.


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Paraphrase or Quote Safety Guidelines in a Paper
I am currently writing a research paper that involves whether various sources involved in giving safety advice accurately list guidelines set out by governments/large organizations. I have created a table that includes all of the missed guidelines set out by the governing body from all of the sources that I have reviewed. Since these guidelines are quite simple (e.g. have someone else drive if you are feeling ill) and I explicitly list the source of these guidelines in the header row of the table (e.g. Header title: Missed guidelines from x), should I paraphrase the guidelines or list them as is?

I’ve removed the trailing question whether you need to quote something you copy verbatim, since it seemed like a technicality that detracts from the otherwise well focused question. Yes, if you copy something verbatim that is a quote and you must indicate this via formatting, commonly quotation marks.

What would the motivation be for paraphrasing them? It feels like there is probably some sort of misconception about plagiarism behind this question.

I assume you don't want to put quotation marks around every table entry, and I agree with that --- it would look ugly. But I still think you can use quotations rather than paraphrases provided you make it absolutely clear that these are quotations from the sources ion the headers. In my opnion, it would be sufficient to state that in the table's caption and also in the main text where the table is first mentioned.

What benefit to the reader will come from you paraphrasing the guidelines? Based on your description, I’d say the answer is “none”. Therefore in this situation, quoting seems like the best solution.
Paraphrasing makes sense in certain situations, for example when you are writing text in narrative form and feel like the flow of the text may be interrupted by the insertion of a quote, or if you genuinely believe your way of saying something is better than the way it was said in the reference you are citing, while retaining the original meaning. I can’t say for sure, but it does not sound like these considerations apply to the current case.

This is for your judgement since you see the text, but it would depend on whether you are able to paraphrase them completely accurately without quoting. That might be difficult for a variety of reasons, including the relative length of the advice in the various papers.
If you paraphrase to shorten them, then you might give the wrong impression.
An alternate solution is to include a paraphrase in the table for the longer ones, with the full text in foot/end notes as needed. Accuracy is essential.


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Is there any Marie Curie post doctoral call right now?
This webpage says that the MSCA (Marie Skłodowska-Curie) postdoctoral call for 2025 ended on 11 September, 2024. Moreover, the next call will be open in April 2025. My field is mathematics.
I am curious to know if this is the only option to apply for Marie Curie postdoctoral fellowship. Does it consider proposals for other types of positions throughout the year?

I'm confused. Your title says "Is there a post-doctoral call right now," but you explain there isn't, and then ask about "other types of positions." What is your actual question?

@AzorAhai-him-, I guess EU funds Marie Curie postdoctoral positions. My question was if there are other projects of EU under the banner of Marie Curie that accepts research proposal from some research labs (located in Europe) throughout the year.

No, the only option to apply for a Marie Curie postdoctoral fellowship is to wait until a call for Marie Curie postdoctoral fellowships is opened on the official website for Marie Curie postdoctoral fellowships and then to follow the instructions in that call.

The call for this action is closed.
The next call will open on 9 April 2025.


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Thoughts on graduate school application consultant?
I plan to apply to graduate programs to get a master's degree. My undergraduate GPA isn't impressive (3.067, can I round that to 3.1 on my résumé?). I completed a certificate program in geographic information systems at a community college, and my GPA there was much better (3.84).
My low undergraduate GPA makes me anxious about my chances of being admitted. Is it worth working with application consultants to shore up my application package? (examples)
fwiw, my friends who went on to grad programs say my work experience is an advantage despite my low GPA. And my GPA over my final 60 credits, which is a criteria I see listed on some program pages, is 3.37.

Are you still a university student or a very recent graduate?

Although not a duplicate, this questions tackle a similar issue and may yield usefull answers as well: https://academia.stackexchange.com/questions/38237/how-are-ph-d-applications-evaluated-in-the-us-particularly-for-weak-or-borderl

@Buffy - in May 2022 it will have been four years since I graduated. I had a few different jobs, but have been in my current engineering position for a year-and-a-half.

@Sursula-they- wow! thanks for that link. I did search for related questions prior to posting, but focused on looking for questions including "consultant" or "advisor." What you shared is a helpful reference to have.

Assuming you have a bachelors in engineering and want to get a master in engineering to increase your pay, I would suggest your best course of action is to gain work experience that will help you get into a high quality masters program.  Skip the paid consultant.

These consultants help you navigate graduate school applications, which is otherwise a complicated process. In return for your money, you save time researching the application processes at different schools, get help choosing which schools to apply to, advice on choosing recommenders, help with managing any exams you must take (like the GRE), and a lot of other little stuff.
That's not to say you can't compensate for their work by putting in more time yourself, but you can't compensate for their experience.
If you can afford it, if you are working full-time and have less time to spend on applications, or if you are keen on getting a position this year, then I'd say it's worth it. If the cost is a real barrier, if you are currently unemployed or have lots of free time to do the research yourself, or if you have a good plan B if you are rejected everywhere this year (i.e. if you are OK failing this year and trying again next year), then you can consider saving the money and going it alone.


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Is it ethical to give paper authorship in exchange for financially supporting a research project?
Would it be unethical to earn money by putting people's name in my papers? In a sense, these people would be sponsoring the paper so I believe it is fair to have their names on it.
Edit 1: In case these people do not join as author but are acknowledge in the paper, would they benefit from it? My intention with this question is just to know how a researcher could earn money as "freelancer", that is, without depending from funding agencies, etc or without being formally employed in industry.
Edit 2: How could a researcher approach an individual or a company to demonstrate their research can benefit them even they are "only" acknowledged in the paper?
Edit 3: Most answers here state that it is unethical since these people would not have contributed to the paper. So, say people pay me to join a research project idealized by me. These people could give their contributions just as a supervisor or colleagues do, correct? Would it still be unethical to have their names published in the paper in exchange for financially supporting the project? Besides, I could even ask these people to sign a statement ensuring they did not just paid to have their names published.

Freelancers get paid to do work for you, they don't pay you.

He means he is the freelancer.

What if your paper is rejected? Are you going to return the money? Lots of politicians got their degrees that way. So while it is not ethical, it is very practical.

I doubt that any "approach" will be successful. Unless you have a rich uncle.

@Buffy Well, that is unfortunate. In such case, researchers are unlikely to have an active role in their careers. Instead, they are doomed to always be waiting for an "external" aid whether from government, whether from companies.

Do not add more questions in edits, please. In particular, your first two edits introduce a completely different question: companies rarely care about publications/authorship, but they do care about R&D in other ways (basically formal employment, but it can be project-based as opposed to 9-to-5 in the office, which is pretty close to what you describe as the desired result). And the third edit is bordering on nonsense, sorry.

I've thought quite a bit about your problem of 'how could I get paid as a freelance researcher' before. Maybe you could ask that question directly; I haven't come up with a solution myself and while I appreciate your creative thinking unfortunately I think taking pay for authorship raises a number of ethical problems

@Lodinn why is Edit 3 nonsense? Say I am a experienced PostDoc researcher. I could ask Master students to join a research project idealized by me. After all, they would pay for my expertise in the area but they would still be part of the creative process, giving suggestions and contributions to the paper. What is wrong with it?

Maybe it would be possible to do a Kickstarter? All the supporters would be listed in the paper. Hell, for a special tier you could even include them AT THE VERY BEGINNING of the paper (although mentioned as golden sponsors, not as authors, of course).

On the motivating question: I know one or two people who work as freelancer researchers. They contribute to funded proposals either by being co-applicants (this will work for some funding agencies and not for others), or by being paid consultants for this research projects (again will be allowed by some funding agencies but not others). However, it's quite tough I think to make a reliable leaving this way.  The individual I am aware of is very well networked with long-standing cooperations with scientists with institutional affiliations and is well known in the field and has unique expertise.

(continuation of previous comments). Furthermore, their life partner has a stable job with good income, so they can cover patches without funding without major issues.
So it's something that will be the right career choice only under very specific narrow conditions

@AmbakeFletcher If you make intellectual contributions (a postdoc supervising a bunch of students), you are an author. Simple as that. I was more specifically talking about the last sentence, and the only statement that works that way is the one authors make when submitting a paper. And that requires contribution beyond just funding. So absolutely, approaching someone pitching a collaboration where they get to work with you and also funding comes from their side is completely fine, but outright selling authorship is not.

@frederik FWIW, I'm in a somewhat similar position for a couple of years now (a bit of hard money and filling in as a consultant for grants/R&D), and it only seems sustainable either at the beginning of the career or nearing/after the retirement. Great ratio of money/time spent and little administrative work though, but at the end of the day, not much different from doing selfsame grant applications sitting in the office.

@Lodinn Yes, that is what I meant with Edit 3. I do not see nothing wrong with getting paid to supervise students and having them authoring a paper with me.

Yes, they may be "in" the paper.
If someone provides support (monetary or not), it is common practice to mention them in a "thanks" paragraph. Some granting agencies may require acknowledgement.  We often see thanks to parents, spouses, co-workers, librarians, editors, and so on.  I have even seen thanks given for the author's favorite snack food.
What should be avoided is adding this person as an author, if they have not done any of the work for the paper.

+1 for the distinction between authors and acknowledgements. However OP talks about "earning" money and "people's names", so I interpret this as being very unethical.

The last paragraph is misleading. Adding a person who gave money as a coauthor not only “should be avoided”, it is unethical. You’re not helping anybody by being so understated.

Yes - it is absolutely unethical to sell authorship spots.
Consider reviewing abundantly available resources on what qualifies as authorship (e.g. https://www.icmje.org/recommendations/browse/roles-and-responsibilities/defining-the-role-of-authors-and-contributors.html)
Here, it says authorship is defined as:

substantial contributions to design / analysis / interpretation, AND
drafting/revising of work, AND
final approval of published work, AND
agreement to be accountable FOR ALL ASPECTS of the work and its integrity

Consider putting the names of those who sponsored/funded the paper in the Acknowledgements section.

Thanks for being clear-cut. Observe that the asker has accepted the currently only answer that does not say that it is unethical (it says merely that adding as an author "should be avoided"). Want to guess why?

@user21820 I understood that it "should be avoided" is an incorrect term. I got that. I accepted that answer as correct because he made a clear distinction between acknowledgement and authors. Anyway, I upvoted all other answers because all of them are clarifying. I will not go out there selling authorship just because I accepted as correct the answer that says "should be avoided". I am just raising an issue that probably might have bothered other researchers. Besides, look at the Edits. I raised other issues other than just selling authorship.

@AmbakeFletcher: Same distinction was made in this answer, posted within the same minute of the other answer. Anyway, it's good that you state that you know "should be avoided" is incorrect. But your other edits don't demonstrate that you are firm on the issue that authorship must never be based even partly on money. You even said "I could even ask these people to sign a statement ensuring they did not just pa[y] to have their names published.". Firstly, "did not just pay" is wrong". Secondly, signing such a statement means nothing if you still get paid to include their names!

This is not how it works.
Although supervisors are sometimes added to a paper because they "only obtained the grant money", the research proposal they had to write to obtain the grant is their intellectual contribution: coming up with a feasible and well thought-out subject for research is not easy: it may in fact be the most difficult part in the entire process from idea to execution and publication.
Paying or receiving money to add a name to a paper is unethical.

This sounds right, but is there anything to back up "This is not how it works"? Do journals say this? Do universities have this coded in some written document? The question asks about "financially supporting a research project" which seems different than "receiving money" which sounds rather personal (e.g. stuffing it in one's pocket) Am I misunderstanding your answer?

@uhoh Funding agencies do not really get authorship, do they? An argument could be made that this is precisely how it sometimes works in the modern publish or perish environment, but it does not make this arrangement any more ethical. And yes, publishers and universities do have it in writing - see littleraspberry's answer for an example.

@Lodinn Oh I haven't asked about ethics nor how it should work; of course I do agree that it would be unethical. Referencing (at)littleraspberry's answer works nicely in this case as it supports that "(t)his is not how it works". Thanks.

You bring up the role of a supervisor. Is it very different if, instead of a supervisor, the person formulating the research proposal works for a corporation and, using their connections to the R&D department, gets substantial funding for the project? Not saying that it would be "nice", but rather a grey area. For the record, I have not seen this ever happen, but I have heard rumors to such an effect. The basic scenario is similar to what you outline, but this time the "supervisor" is employed on the client side rather than in the academia.

Paying to add a name as author is unethical. It's perfectly fine to pay to add your name as a sponsor.

Is it ethical to give paper authorship in exchange for financially supporting a research project?

No, it isn't. The authors should be the people who participated significantly in the production of the scientific content of the paper.

Would it be unethical to earn money by putting people's name in my papers?

For most interpretations of that sentence, yes. But this is vague phrasing.

In a sense, these people would be sponsoring the paper so I believe it is fair to have their names on it.

You believe wrong. You can acknowledge sponsorship, and that is actually rather common in footnotes for author names, saying something like:

The N'th author was supported by grant no. 123 of the National Endowment for blah blah blah. The M'th author's work was partly supported by BigCorp inc.

You could even go as far as writing an acknowledgement in the body of the paper, extolling your funders.

In case these people do not join as author but are acknowledge in the paper, would they benefit from it?

I'd ask that as a different question. They would certainly not be able to present it as one of the papers they are authors of.

My intention with this question is just to know how a researcher could earn money as "freelancer", that is, without depending from funding agencies,

A freelancer does depend on others who fund him/her, just not the same funder all the time: The free lancer offers his lance for hire. That is as opposed to being bound to some specific lord, permanently (to continue the medieval knightly analogy) - or just being a brigand or revolting peasant.

In most academic fields adding non-participants as "authors" is considered unethical. Authors are those who contribute ideas, intellectual content, not money. The people added commit a sort of plagiarism, actually.
But there are fields in which the opposite is true. Many popular books are "authored" by some famous person but written for hire by a "ghost" writer. The latter isn't always known. Works for hire are a special category of copyright for example.
In some fields the overall supervisor of a scientific lab is added to the list of authors. The rationale is that they have made the research possible through both funding and setting the goals of the lab as well as providing overall advice and direction. But they give more than money to support the research.
In academia you can acknowledge financial support in a paragraph or so of the paper as is usually done when acknowledging grants.
To respond to the edit about "benefit" of acknowledgement to a sponsor, there are several possibilities. Some companies, and maybe individuals, really want to see the results of some research but don't have the staff or other resources to carry it out. So "contracting with" an independent researcher might be an option for them. Some patronage is done because the sponsor wants to seem to be associated with a researcher or a line of research.
For the first option, a colleague and I once had some expertise that a large multinational needed and wanted a quick startup. We were given grants (not actual money) for participation, though it wasn't research as such, other than that it gave the company some feedback on the compatibility of our approach with that of the company. The grants provided funds for travel, equipment, and such.


text:
Asking PhD advisor if I can be the sole author
First of all, I am a second-year PhD student in pure maths in Italy, in case some of this information is relevant.
My situation: around a month ago, my PhD advisor posed me a question (related to my previous research, I also had this question in mind) and told me we could work together since he had some ideas. Two weeks ago I found a full solution to the problem, quite interesting also and I told my advisor. He told me he also is thinking on some ideas for the problem but I think they won't be needed.
Question: Would it be OK to ask him if he can withdraw from the project since I think I can finish it by myself with my ideas? In case it's OK, any advice on how to tackle such a complicated discussion?
Extra info: I'm very happy with my advisor. He does not demand authorship for all papers, many papers of his former PhD students have been solo. My solution to the problem does not use any of his current ideas. I have the feeling that he is quite interested in the problem though.

Does posing the question represent an intellectual contribution? Was the question just a curiosity, or did it actually require years of experience in the field to come up with this question and with the belief that it can be answered? If so, posing the question is an intellectual contribution and requires co-authorship.

@WolfgangBangerth well, the question is a natural follow-up to my previous problem so I don't think that is the case.

You'll just have to discuss it with them in person and see what they say is the short answer.

Maybe you could see if his approaches would lead to some novel areas, and would be enough for a second paper. Then after a few weeks of collaborating on his ideas, you could propose making it into 2 papers, 1 where you are the solo author, and the second paper where you are collaborating?

What is your goal here? Perhaps it depends on field, but to me, a paper on your CV with yourself as first author and your advisor as co-author would have equal weight as a sole author paper.

If this was originally a topic your advisor was very fond and passionate about, it may be that pushing him out of it will hurt his feelings, and negatively affect your relationship. It is maybe okay to exclude him if he turns out to offer no substantial contribution, but actually asking him to back off of the project that he himself came up with (and thus preventing him from even starting to help in the first place) will probably be very, very bad.

@thegreatemu It definitely depends on field, since in pure math (OP's field) there is no concept of "first author". Consequently a joint paper with one's advisor would tend to have less weight on a CV, since it could well be that the advisor has done most of the work.

How is this work being funded? In some fields (all?) the person who secured the funding has by default made a significant contribution to the work.

He told me he also is thinking on some ideas for the problem but I think they won't be needed.

You may be jumping the gun here a bit. Yes, perhaps you can finish the paper on your own and have a solo publication. It may also be that your advisor's ideas will result in a better paper or open avenues for further research that you might not notice on your own. It rarely happens that solving a problem is an open and shut case with no further avenues to build on the solution, or to look at it from different perspectives. Preemptively asking him if he can withdraw from the project without hearing out what his ideas on how to approach the problem are therefore seems premature to me.
Certainly if he has nothing crucial to add to your solution to the problem, it makes perfect sense to ask him whether you can turn your solution into a solo paper.
On the other hand, asking him to withdraw from the project so that a situation where he has something crucial to add to your solution doesn't have a chance to arise (and mess up your would-be solo publication) is a different story.
A solo publication would certainly be valuable, but also don't underestimate the value of a lively on-going collaboration with your advisor which can lead you to places that you might not foresee yourself. Especially if you're not in a hurry to amass as many solo publications as you can.
The way you phrase your question makes it sound like you want to say: let's not collaborate on this topic any further so that I can get a solo paper. I would consider thinking of it instead as: let's continue working on this topic together, and in the meantime I suggest that I write up and submit my solution as a solo paper.

@MathAuthor Well, you can tell him exactly that. It's not like you have to either ask him to stop this collaboration or commit to writing a paper with him. You can just say that you think this is a good opportunity for you to write a solo paper of your own and ask him whether he can agree to keep that option on the table as you continue discussing the topic. A transparent discussion about authorship should take place, but that doesn't mean that the authorship issue needs to be set in stone right here and now.

To further emphasize the first paragraph: the student doesn't need to worry about the authorship question at all until the paper is written. Maybe the advisor will be needed for help along the way, maybe not. But it's a question for the future when most of the paper is done. Start writing and forget all else for now.

Note that in mathematics it is quite common that an advisor will collaborate with their PhD student on some paper and the paper will still be published with the student as the sole author. So definitely continue collaborating with your advisor on the paper and then ask them whether they want to be an author. They may answer either way and I would recommend following their wishes.

In an ethical and humane world, yes, you can ask and he will say OK. But I don't know if that is your world. You have to make an analysis of what his reaction might be.
But if you approach it right it will help. "Dr. M, I'm confident that I can finish this on my own and get a sole author publication. It would do me a lot of good. What do you think?"
That is sort of a US approach, however, though normally US doctoral advisors in math don't assume authorship on their students dissertation work. From what you say about him, I'd guess he will go along.

I also wonder which one is my world, although my advisor has always shown to be both ethical and humane. I wouldn't like to strain our relationship though and I'm under the impression that in general it is not an OK thing to ask for.

@MathAuthor can you explain what gives you that impression?

@DanRomik My precise impression is that once you start collaborating you cannot back out and say I want to do it by myself. I don't have much experience though so I might be mistaken of course

@MathAuthor there’s nothing about the description in your question that suggests that you and your advisor have “started collaborating”. He is your advisor and posed you a research problem, then sent you off to work on it - that’s what advisors do, which normally does not imply a collaboration. Was there anything he said that implied that he meant that this would be a collaboration?

@DanRomik He told me that we could work together on it, meaning starting a collaboration (of that I'm 100% sure). He had some ideas but it is not clear these ideas work for this problem.

@MathAuthor okay, maybe there’s something to what you’re saying but it’s a bit too vague to be able to say anything definite about whether “there is a collaboration”. Most likely it’s one of those situations when there isn’t a well-defined binary answer to the question, just a set of vague unspoken assumptions. I honestly don’t see a reason not to simply discuss it with your advisor like the two adults that you are.

While neither @DanRomik nor myself are Italian, we both have friends and colleagues from around the world. Academics are a lot alike most everywhere.

So you advisor gave you an idea and you want to publish a solo article based on that idea?
Okay, I am not a mathematician and not Italian. Every research field is different, and every country is different. Maybe this is totally fine for mathematics in Italy. Maybe your professor will say, "Yeah, sure, go for it!"
But that would definitely not go in Japan, at least in most research fields. Everyone would be appalled by the fact that this came to your mind. A solo article is when you come up with an idea yourself, do all the work yourself, and write the manuscript yourself. And if you don't want to find yourself in the grey area of ethics, you shouldn't get any help or advice whatsoever in relation to your article. Ideally, you don't even let anyone know until the paper is published - otherwise people may give you advice and you won't be able to unhear it. And it's really not nice if you publish a solo article while being funded from a grant secured by someone else.
(Update: a comment below says that in mathematics, merely asking a question without contributing to its solution does not normally justify authorship, and obtaining funding doesn't either. Lucky you mathematicians. But read on. There's a totally different thing to consider.)
Another aspect is that even if you come up with an idea yourself, do all the work yourself, write the manuscript yourself, are being paid not from anyone's grant, and are thus perfectly positioned from the ethics standpoint to submit a solo article, you might later find yourself truly regretting publishing it. It happened to one of my colleagues. He wasn't experienced enough. He wishes he could unpublish it.
Look, you are a PhD student and don't have a lot of experience. Are you really sure you can write a paper you won't later regret publishing? Are you sure you won't overlook a serious issue?
There are a multitude of ways to screw up. If you make an error or a wrong statement in your paper, someone may publish a comment, and it will be a huge blow. If you write your paper poorly in terms of the language, structure, clarity, etc., this will seriously affect how others see you. If you publish your paper in a subpar journal, others will think it's what you and your work is worth. Your first papers set the expectations of others - it's called the anchoring effect. if you submit your paper to a high-profile journal and the referees say that your work falls very short of meeting the acceptance criteria, the editor may well have prejudice against you next time - that is, when you submit another paper to that journal. Remember, the editor chooses the referees, so you don't want the editor to have prejudice against you. And this might make it almost impossible for you to publish anything in that journal later. Also, if you publish an article and no one cites it, it won't look good to anyone looking at the citation stats of your papers - and that's what many referees do.
If you have your professor as a co-author, he'll ensure your paper won't have any serious issues. It's about his or her reputation. And having your professor as a co-author is likely to have a positive effect on the recognition of the paper by the referees and readers as well as on its citations.
My advice is: think twice whether you really want to proceed with this on your own and publish a solo paper. That's the very first thing to decide on. Make sure to take a well-thought decision. If you do decide to talk with your professor, do your best and utmost to ensure he or she won't feel bad about you. One of the key factors is whether you are a paid a salary or a stipend from a grant secured by your professor. If that's the case, he might feel as if you were trying to steal his money. Remember, you depend on your professor. The relationship is extremely important. Focus on that.
Consider this:

Hey boss, I've noticed some of your PhD students published solo
papers. Is there any chance I can do the same and you'll be fine with
it? If so, how?

That's a good start, and his reaction will show whether it's a good idea to talk about that particular paper.

This does not really apply to mathematics, where merely asking a question without contributing to its solution does not normally justify authorship (and obtaining funding certainly doesn't either).

@EspeciallyLime Lucky you mathematicians. The OP still has to consider risks of doing something wrong in the paper and/or alienating his advisor.

@EspeciallyLime I've added an update in the middle of my post to mention your comment

Thanks for you answer! I have the feeling that the culture in mathematics (or Italy) is different from what you describe. Though I worry a bit about him feeling bad about me

Maybe I'm wrong, but seeing the OP's responses to various questions, I get the sense that (s)he had more or less made up their mind about going ahead with solo publishing, and was hoping to have that validated by posting here. Unfortunately, the answers don't bear that out ;-).

@xadu I don't think that's fair. The three most voted answers say otherwise

This is a well written answer, but to add to what @EspeciallyLime said, two other reasons why almost everything you said does not apply to mathematicians are: 1. In mathematics it is very common for graduate students to publish solo papers. They are perfectly capable of producing good papers written to the standards of the discipline (and usually receive detailed advice on the writing from their advisors, without the advisors expecting coauthorship in return). …

… 2. In mathematics, being paid by someone’s grant does not make the PI of the grant feel entitled to be a coauthor of your papers. Again, it is very common for students and postdocs to publish without their PI, even if they are paid from a grant.

This certainly gives some interesting insight into the academic culture in Japan (not sure in which discipline) but is very very different than what I am used to -- and I'm not really sure it goes well with my personal preferences either. I am most surprised that you think any sort of help or suggestion deserves authorship - it is not uncommon in my department to ask a colleague for a read and provide some feedback when submitting a high-stakes manuscript, where the expectation for what they get in return ranges from a coffee to an acknowledgement. (This is in a computer science department)

Would it be OK to ask him if he can withdraw from the project since I think I can finish it by myself with my ideas?

Yes, it’s okay to ask.

In case it's OK, any advice on how to tackle such a complicated discussion?

Your assumption that it’s a complicated discussion is part of the problem. It isn’t. Your advisor may be disappointed by your wish, and might even push back on it or outright say no — we cannot predict the outcome. But he is a grown-up and does not need you to tiptoe around his feelings. Your question is both reasonable and straightforward, so just go ahead and bring it up, and you’ll be fine. Good luck!

Thanks for your answer! I wonder whether the fact that I find it difficult and you don't might be due to some cultural difference. If that is the case, unfortunately my advisor is also italian.

@MathAuthor “unfortunately also Italian”? lol. The Italians I know are all super nice and reasonable people and make me think that it’s unfortunate that I am not Italian. (Admittedly, I have heard rumors that there are some non-nice Italians out there, but I have yet to meet such an exotic specimen.) Well, obviously only you know your advisor and your culture, so you’ll have to filter our answers through that knowledge. But, for what it’s worth, there isn’t anything about the description you’ve provided, or about my knowledge of Italian culture, that makes me reconsider my answer.

hahaha the "unfortunately" was conditional on there being cultural differences making the situation more thorny for italians.

My advice would be to ask not if you can publish this solo, but whether you should.
Assuming a reasonable supervisor open to solo papers from their students, you have two options here:

You carry on this project on your own and gain a single-author publication
You and your supervisor work together on this problem, developing a potentially richer and more interesting paper in the process

The difference between the two is your supervisor's contribution, and it's up to them to decide how much they are willing to commit. Therefore, you should ask them whether they wish to spend time and effort on the current work (option 2), or not (option 1). This doesn't rule out collaborating in the future on the same topic, of course.
Note that it's really the same question but with a subtle difference in focus - instead of "I'd like you to not contribute so I can have a single-author paper", it's "I'm happy to go ahead and publish this single-author unless you tell me you want to contribute". However, presenting it as two options is less confrontational, makes you look more collaborative, and if your supervisor isn't actually happy to let you publish this solo, by picking option 2 they have implicitly committed to doing active work on it (which honestly may be more useful for you at this stage than a solo paper).
Disclaimer: I'm from a field where solo papers are uncommon and typically reserved for reviews and minor work. My impression, but it's coloured by my field, is that the value of solo papers as proof of independence can be overestimated, especially by very early career researchers - I'd be more impressed by a collaborative paper that does not include your supervisor (for example, together with other PhD students).

Thanks for you answer @Ottie ! The only problem is that we are collaborating by default since this was raised before I obtained a full solution.

@MathAuthor that's exactly the point: by explicitly presenting the problem as a choice between options 1 and 2, both of which are a good outcome to you, you are trying to rule out the undesirable option 3 (you do all the work and still get your supervisor's name on the paper).

I refer you to lots of good answers here that advise whether or not you should do this, but if you are set on publishing solo, I just have one piece of advice: write a manuscript first, then have that discussion. If you put a fully written paper in front of someone, they are more likely to see that they have not contributed to it and might decline authorship on their own (if they are reasonable).
I did a similar thing. I sent my postdoc advisor a manuscript (though it was completely my own idea). She gave me useful feedback on the manuscript, then I asked her if she wanted to be a co-author. She said that she didn't think she had contributed enough, and I ended up publishing it solo, only mentioning her in the acknowledgment. That paper landed me an academic position. Don't underestimate the power of single-author papers (note: I'm not a mathematician, so this may not be as important in your field).

My advice would be to be generous.
In the long view of life, it doesn't really matter if your paper has 1 or 2 authors, particularly if that author is in a position to contribute to the work, either now, or at the time of manuscript revision, or both. So, by erring on the side of generosity, you have much to gain (including learning new things from your advisor).
On the other hand, if you chose to go solo, that's fine too, but this attitude can quickly become about "I/me/mine" rather than the far more sublime attitude of the service of math/science. There is also the very real possibility that over time people will be reluctant to discuss ideas freely with you, because there is the possibility of an impression that if you cross the "least publishable unit" boundary by yourself, they get cut out.

Thanks for you answer! It will not matter if my paper has 1 or 2 authors in the long view of life. But it will definitely matter for getting postdoc positions and similar, and that's what I should worry now I think.

@Trunk Why wouldn't I get a coauthorship if the idea is mine and I can carry it out by myself? Also, if I keep doing like this how I am going to get sole authored papers? Finally, if the result is good (hopefully) but the coauthor is a big name, then by default it will be assumed that it is mostly his contribution.

Thanks for your answers @Trunk! So the thing is that I don't want to force him to withdraw, but I'd like to raise the issue (in a delicate way, but I'm not sure how). If he says he is not OK with that, that's fine. But I will feel bad about myself if I "surrender" without trying.

@MathAuthor your question seems to be drawing a lot of advice from people who work on different disciplines or aren’t even from academia. Without implying anything bad about those people, who may be very smart and generally people who give sensible advice, this is something for you to be mindful of. Mathematics has a very different publishing culture than a lot of other disciplines, in ways that aren’t widely understood by non-mathematicians.

Reminds me of a paper I wrote in grad school, it was a term paper, and I did all the work upfront. All of the ideas were mine from start to end. I wrote the paper up. I made all of the work and effort. Turned it in, and was advised via a note at the top of the paper, that with a bit of polishing, it could be made publishable. I took the paper to my advisor with the notes and all. He agreed with the other professor's assessment and he helped me add some shine to the paper, but otherwise didn't contribute much to the substance of the ideas I put forward. We submitted it as coauthors.
Why?
Without his contributions to the actual writing to get it to an acceptable state for a journal, the damned thing wouldn't have been published, or at least if I did manage to get it published, it would have been published in a lower-tiered journal. I learned a lot about the publishing business in academia by allowing my advisor to help me and share credit along the way. Lessons that were invaluable later on.
I would suggest being generous on this one and learning from someone that has been in the trenches for some time on how to get the publishing done. You might actually learn something different than you think about the business of a career in academia that you wouldn't learn in any other way.

Might be useful to wait for review to see if their contribution is necessary in the opinion of refs/ed. If after review their contributions aren’t necessary then you have a solo paper, else you have helped your advisor hook into the topic.
If you accept their contribution and it makes publication that will be something they won’t forget. If the contribution is thought superfluous in review then you have a solo paper.
I don’t really know the advantages one way or the other, just consider your long term goals and know that you might find yourself on the other side of the symbiosis in the future.

In mathematics, as far as I know, the paper is sent as a single unit to review. The referee does not discriminate between authors.

On all my PhD papers I included my supervisors as authors, not because they contributed but because they stood behind me, guided me and I benefited from fruitful discussions with them.
If you are first author then everyone who reads your paper will know that you are the primary contributor and you will received due recognition.  Bear in mind you will awarded your PhD on the basis of the Supervisor acknowledging your contribution - not because you are sole author on a particular paper.  Take the time to read some papers by some of our great scientists and you will see that none of them were afraid to recognise the contribution of their supervisors.
Have confidence.  Asking to be a sole author will prove nothing and your risk being seen as churlish.

This answer does not apply to the OP's field, which is pure maths. Authors are ordered alphabetically in pure maths, so there is no concept of a "first author". Courtesy authorship for PhD advisors (as suggested in your first paragraph) is frowned upon in this field. Regarding your last paragraph: it's not about "proving something", it's about having a single authored paper. (For instance, some members of hiring committees tend to be more skeptical towards candidates with no or only very few single authored papers).

Thanks for picking me up on the "alphabetical listing" in mathematics.  I was not aware of that, but I don't accept that during your PhD work you do not benefit from your Supervisor, but I suppose "acknowledgements" may be a way out of the dilema.


text:
Does year gap create any problem before Computer science(nlp) PhD
I  completed masters in 2017. After then I did internship as a software engineer in one  company X for 6 month in 2018. And then did another company Y job in 2019 as a full stack developer. But during that time(2020-2021) my family was infected by COVID-19, so insistly I quit my job for look after my family.
Consequently my family 4 members including me was infected. And in that time I  lost my elder brother.I was mentally broken.During this time in rural areas humans didn't have no money to survive, during that time I was started to help the people and teach the all village students and parallelly I have been started study very intuitively my personal all the computer science 12 to 14 subjects and try to contribute stack overflow site(Mathematics,computer science,Networking exchange,computer graphics etc) and focused on masters thesis. And the year 2022 I have published my research paper and parallelly started preparing for GRE and TOEFL. I scored 315,108 on GRE and TOEFL respectively. I have 4 gpa for both undergraduate and masters.I also get informal PhD offer from my home university where I did masters.
My question is could I get PhD admission with full scholarship in USA or any other university in world with full scholarship? I need the help and suggestions. In this situation what should I do by which I could get PhD admission with full scholarship?

No, a gap year won't be an issue. It is actually fairly common.
However, "full scholarship" isn't a real concept for US doctoral education in most fields. Instead, most doctoral students serve as Teaching Assistants or (less common) Research Assistants for a stipend that includes tuition and is sufficient (barely) for a person with a small family.
But funding with no duties attached is rare in the US unless you happen to work in a field that is richly funded by grants held by your advisor.
I would guess that, from your description, that you could gain admission to a good US program with the gap year not a consideration. But make sure you have good letters of recommendation from your earlier studies. Funding may be more difficult and expect it to be modest and to come with some duties.
Lots of other places doctoral students are considered regular employees of the university. Again, there are duties attached.
Also see: How does the admissions process work for Ph.D. programs in Country X?

"Funding may be more difficult  "-- this statement not understand properly?

Funding is a more important issue for you than the gap year. You will need to work that out with any university. Note that most doctoral students in the US have such funding, but it may be a bit more difficult for international students. The grading scheme you describe seems like India. In such case I'd expect fewer problems as your English language skills wouldn't be an issue. So you would "fit" in a TA slot.

When My Indian grade marks converted into USA grade points, I got both undergraduate and masters have 4 gpa. Thank u for your mental help. But industry experience certificate didn't collect from my 2nd company, they could ask for submit?

That "certificate" probably won't matter at all. Good luck.

By one TA, could I survive 2 people if we don't have any luxurious life style.

Yes, but a "modest" lifestyle. Far from luxurious. You'll be too busy to spend much money anyway.

TA provide 12 months salary? If not, how could I survive in not giving month?

The gap year is not an issue. Especially since you tried to do something on your own (reasonable people in research knows that we all stand on the shoulders of giant, so being cut off from university&co no one expects from you some breakthrough coming from you on that period).
Depending on the country, PhD programs have no requirements at all with respect to age.
An issue you may have is about speaking and writing in correct English: I strongly suggest you to work on this aspect (English is not my mother tongue, I say this out of experience).
Other than that, the correct answer depends too much on the specific scolarship, so try to focus on some scolarship (get in touch with the relevant offices at the universities you aim to, they can be of tremendous help in navigating the bureaucracy).

One thing tell industry experience certificate could be verified by PhD committee?

No offence intended, but please, use commas when writing.

No offense, actually didn't not collect experience letter.

“Experience letter” is an Indian thing I guess. I’ve never gotten one in the ~40 years since my bachelor’s degree - they aren’t a thing in the US at all.

@JonCuster PhD committee can contact with my previous worked company as for checking I am responsible, brilliant person or not etc. ? Although I didn't lor from company.

Why would they bother trying to contact some random company somewhere else in the world?


text:
If a tenure-track position has been advertised at the Assistant Professor level, is it legal to hire someone in it at the Associate level?
I am interested in a position that is advertised at the Assistant level but I already have been promoted to Associate at the same university but in a different department. In theory, if I were chosen, is it legal for the University to hire me in the new position at my current Associate rank even though the position was listed at the Assistant level?

Possibly, but laws vary. Ask HR.

For various reasons, professors sometimes switch departments. Pretty much anything is possible if the administration approves.

Often I see wording in academic job postings that allows them to consider other, higher ranked, candidates should one come up.

What country is this?

The specific wording of the posting, combined with specific HR policies, are important. Perusing one US university's hiring page (name withheld since it is not important), I found a number of variations:

XXX invites applicants for an Assistant Professor position... Seasoned untenured professors will be considered.

OK, pretty clear that a tenured professor would not fit the posting.

XXX is seeking to fill a tenure-track faculty position... This is a tenure track position at a rank fitting with the candidate’s record of accomplishments.

Pretty much anything goes here.

These new positions are open-rank, long-term, full-time, on-campus, non-tenure-track positions that can be focused on teaching, research, or a combination of both.

Not tenure track, but you could apply if you wanted to.

XXX invites applications for tenured or tenure‐track faculty position in YYY...

Anything goes.

The tenure-track position will be hired at the rank of full professor...

Unlikely to hire a postdoc into a full professor position, but it does not rule out a current Associate professor from applying.
Some have breadth stated explicitly, some don't. However, one would perhaps have to dig deeper into the HR policies of the institution to see what, if anything, they allow to be done, including altering the posting in situ, reposting at a different job level for an attractive candidate, etc.

I'm going to focus on the US, I think other countries are likely to be rather different.  The US has relatively few rules around hiring and firing.  There's no law requiring positions to be advertised!  Universities can and do routinely hire people outside of the standard search process, and can and do routinely hire at levels or areas that do not match the advertisement. A key word here is "target of opportunity," and I have been offered a job as a target of opportunity and have been involved in trying to hire people as targets of opportunity.
Nonetheless, there's real constraints on this happening.  Legally the main constraint is that it can be difficult to get a work visa for someone who was not hired through a regular search, so if you are not a permanent resident there may be complications.  A secondary legal issue is that although you're not required to be fair in hiring, there are certain specific ways of being unfair which are banned ("protected categories" such as race, religion, or being over-40).
The main constraint isn't legal, but rather administrative.  Getting approval to hire for a position involves a dean and a provost, and hiring outside the approved position requires going back through the chain of command again.  This means there's a lot more veto points where people might not approve a hire outside of the search parameters.

This may be changing currently, at least at a policy level, since having a pre-selected candidate-of-choice has de-facto denied other people a chance to compete. Specifically, people who don't have adequate "connections", are put at a disadvantage in such scenarios, which leads to perpetuation of various unfairnesses... But, yeah, if it's just policy and not law, if the big shots approve, it'll probably "be fine", in some sense... :)

It is my impression that, in the U.S., whatever position is filled needs to have been advertised: to fill a position at a different level than advertised would have misled/deceived potential candidates.
But the enforcement mechanism is weak, so far as I can tell, so that if the administration has ok'd such a hire (for whatever reason) there's probably no other actor in the scene who can effectively object or complain.
One extreme case where no one would object, if you're already at level X in dept A, and change to level X in dept B in the same university, is if your line_item is transferred from dept A to dept B. But I'd suspect that dept A would not want to give up a line item in their budget.
The most up-and-up approach here would be to suggest/request of dept B that they modify their advertised position (with sufficient lead time to be fair). An obstacle might be that their Dean does not necessarily want to "give them" another already-tenured slot.


text:
Should I do a second PhD after a bad one?
I am expected to finish my Ph.D. by the end of the year and I am seriously considering going for a second one. After finishing my master's in Biomedical Engineering, I became interested in Machine Learning and self-taught myself until I eventually landed a Ph.D. project in healthcare. At the risk of sounding cliché, the further I explored the field of ML, the more I felt my competencies were shaky at best. Now, this is not your typical "the more I know, the more I know I don't know" dilemma, since I have never had a formal background in the field.
Sadly, I now realize this Ph.D. was a terrible career choice, as was my choice of Biomedical Engineering for a minor/major.
Biomedical Engineering was a very fun but very challenging major. Fun in the sense that I had exposure to nearly all science fields. Challenging because I had first-contact courses at the level of other Engineering programs that had pre-requisite courses, forcing me to learn an insane amount of material in a semester, only to forget everything afterward since there was no follow-up. Thus, I feel like a true impostor, and sometimes I wonder if I should do another more focused major.
Regarding the Ph.D., I am in a peculiar position since I am pretty much the only one doing ML research in my group and the university does not offer graduate ML courses. Furthermore, since the funding comes from a European project with a specific goal, I have a very narrow set of tasks. I tried to learn everything I could myself, but since I never had a project where I could apply my new knowledge, I ended up needing to learn things over and over.
I would not say I was unsuccessful at all. I have published a technical paper in a top-tier ML conference and a clinical one in a top-tier medical journal (and have two of each kind just about ready to submit before I graduate). However, when I am looking for my next steps, I still feel like I barely know anything and that I will feel like an incompetent forever.
I have a good relationship with my supervisor, but he has not published anything in the field for a very long time, so I am pretty much on my own all of the time. I like the freedom I have, but not having someone with field experience to discuss my ideas made me pursue a dead-end path for more than a year. Also, I am now struggling to incorporate the feedback I got when my last technical paper was rejected at a top-tier conference.
Thus, I would like some advice regarding my next move. I am confident I could take a few more practical data science courses to mitigate my blind spots (NLP, I am looking at you) and get hired for a standard Data Scientist job, but ideally, I would like to continue working in a science field. I am therefore wondering whether I should do another, proper Ph.D. since this one was a fraud. I am desperate to feel like I am knowledgeable about something for once in my life and that I am progressing towards a goal I am excited about.
Sorry for the long text. I appreciate your advice.

Right. I wonder if I will be able to transition to a new field like neuroscience as a PostDoc or industry employee with the current experience I have. Like, should I take a few months off to intensively work on new skills before applying to jobs or should I apply and try to get them on the job?

@astronat kind of. Although the general sentiment answers some of my concerns, I believe it does not directly apply because I feel like I got little value from this PhD

Doing a second PhD, unless you're radically changing fields, is telling the world (1) - you think your university made a mistake when they gave you the first one, and (2), by extension, you also don't think you can do research independently yet.

@Roland More specifically, it's a piece of paper that's supposed to certify that you are able to learn independently and conduct research on your own within a broad area. So it might make sense to get a second PhD in comparative literature after getting one in the sciences, but it probably doesn't to get a second PhD in a related science field.

You are dramatically overestimating how much people will look into the details of your PhD. Nobody will read your thesis and, after you land your first job, nobody will care what it was about.
If you decide to switch fields, you'd be surprised how quickly people stop caring what your major was. You will are a STEM PhD first and foremost, and people will only care about details that are directly relevant to your/their work.
Two years of work experience in your desired career will quickly wash away whatever you think was "bad" about your PhD.
For what it's worth, your experience is not uncommon. Despite the (also common) imposter syndrome, you've developed independent research skills and established academic credibility. You're finally wrapping up and want to move onto something new after graduation (and, you guessed it, that's common too).
Finish your PhD and find a job you like in the field you want. That will help you much more than a second PhD.

While this may work in some cognate fields, trying to do this with "work experience" in completely unrelated fields (say, statistics and medieval French lit - and yes, I know of someone who did this) would be pretty hard.

Short answer: no
Longer answer: Finishing your PhD does not mean that you are done learning and improving. Everybody needs to continue doing that, and they do so without doing an additional PhD. Most (gradually) migrate to new topics, and learn about those through self-study or the occasional course/workshop. Most need to learn new skills; Many are shocked to find out when they got their first professorship that they are now more managers than researchers and need to learn a whole new set of skills. All universities I have been part of offered courses for early career researchers to facilitate that. The list continues. So it is normal that you are not "done" even though you finished your PhD. That unfinished state will hopefully continue for the rest of your life (your life would become pretty boring otherwise...).

Thanks for the advice! To clarify, I am not suggesting I want to be in a position where I am done learning. I love learning new things and my primary motivator is creating new things. The problem is that I feel my creativity is limited by my lack in background knowledge. I am about to graduate as a PhD in a field where first year PhDs probably know more than I do.

A PhD is not about getting background knowledge, it is vocational training for researchers. The emphasis is no longer on learning facts, it is about learning how to find those facts. So starting a new PhD because you want to learn facts is a really bad idea.

Maybe you can start a bookclub with fellow postdocs, and delve in some topics together with others. Some like to study on their own. Others like MOOCS. There are options to filling in background knowledge.

You are right regarding the PhD and learning facts. I am just worried that by not having the initial year of graduate courses a typical PhD offers, I did not get a "boost" in my background knowledge which would have been quite useful for my research. Thus, I am questioning whether I should re-do the process the "right" way. Maybe a second PhD is not the answer though. Maybe a postdoc is. Maybe a job while I do a second master is. This is the general advice I am looking for.

What you are feeling is normal, but is not a reason to continue formal education (i.e. getting a second master or PhD). You can, and should, fix relevant gaps in your knowledge, but you can do so without entering school again. Notice the word relevant: most of the things PhD students learn in their first year proof to be not important to them later on.

I am now at the point where I will retire before I figure out what I want to do when I grow up. On that journey I've branched out, learned a bunch of stuff, and often come back to certain themes several times, but each time with a different approach. When I get feeling complacent and bored it is time to find a new challenge.

While I agree with the other responses, let me give you the perspective of someone who was part of a group where second PhDs were common. I think many of this will not apply in all countries (including the US), though.
Reasons to do a second PhD:

Funding. Sometimes it is just about how someone can be hired. Also, in some countries PhD researchers are rather well paid so it can be an economic decision. (Also, in the country where this happened considers the PhD years as work experience, so years spent on the PhD are not "lost".)

Changing fields. If the fields are too far apart, it could be a requirement to get a (faculty) job, publications in the field are not enough.

Wanting formal supervision in a specialised field. As other answers and comments suggested this is not really necessary and a postdoc could work nicely to achieve this.

Countries not recognising degree from certain institutions/countries. Sometimes degrees are not automatically recognised and naturalisation is complicated. This is less of an issue nowadays but it still could happen.

Moving abroad.

Practical reasons. For example, wanting to work with a particular advisor who needs to hire a PhD student.

+1 Fun.
This a compilation of reasons I have been told or have observed. Of course, this does not mean that doing a second PhD is advantageous from any other perspective. You will not necessarily get a better job or be more successful.

Even in the US, 2 and 3 can sometimes happen - I know of several examples, especially when the fields were separate enough.

And, honestly, it's pretty hard to completely switch fields without some minimal continuing income, and PhD programs may provide that ability to actually have the time to learn new field Y while not having to keep working 40-60 hours a week at X.

Thank you for the different perspective. I am in Europe so, for the most part, 1) applies (although I sometimes flirt with the idea of moving to the US because of the mind-blowing nature). 2 and 3 also apply so the question is whether I can get a postdoc in a different field having limited experience.

The difficulty in finding a postdoc in a different field is that you need to convince someone that they should choose you despite your different background. The positive part is that, if you find such a person, they tend to be open-minded and flexible.