text:
Applying for postdoc after being assistant professor
I recently obtained my PhD in mathematics (about 6 months ago). I started a nice project in my PhD, but did not push to its limits (due to personal problems that occurred during my PhD that diverted my attention), as a result I have few publications and I think I have almost zero chance of getting a postdoc at the moment.
I might be able to get a low paying assistant professor or lecturer position in a university located in a low paying country. I am thinking about doing that to take some time (2-3 years) to work on my publications and then reapply for postdoc.
If I follow that plan, will postdoc admission committees give me a lower priority just because I held different an assistant professor position somewhere in the world? I noticed lots of postdocs positions have a rule that the PhD should be obtained within 5 years. Is this the rule in general?

The title of this post is misleading--can the OP say something like "If I Were an Assistant Professor, Could I Apply for a Postdoc?"

Since you mention moving to another country and did not specify where you are, I just wanted to add that in Germany postdocs are paid well and the job market is not very crowded, so if you manage to find an open position there, your chances may not be too low.

"Few publications" is usually more than enough to get a postdoc in mathematics.

@QuantumBrick What about few submitted papers, and 1-2 publications ?

@lostanonymous If the papers make extensive use of modern techniques in order to prove a new result, publishing 2 such papers during your phD can be a phenomenal achievement. For more applied fields without abstract proofs, e.g. some nice upper bound estimate of convergence of a particular numerical method (hard analysis), 2 papers might be less impressive to some (but not to me!). It would be easier if I knew your field.

This doesn't seem to me like an optimal career move, unless you would be happy in that assistant professor slot and wish to get tenured there. You are correct that postdocs are intended for people fresh out of doctoral programs and are also intended to help people get positions like the one you are applying from. Some people would worry that you have failed as an assistant professor by applying for a postdoc - not a good look and you would need to address that possibility.
But, your post sounds like everything is hypothetical. I'd apply both for postdocs and for regular positions and see what develops. But I'd try to avoid, if possible, any position in which you wouldn't be happy. It is hard, mentally, to succeed in such a position.
If you can maintain contacts with people so that you aren't working alone in such a potentially "weak" institution, then you might be able to extend your CV, but you will be busy there and, if you are working alone, even in math, it is hard to be productive. You would need to find a way to have frequent conversations with colleagues. Not every institution will provide that.

Tenure probably does not exist in the "low paying country."

"postdocs are intended for people fresh out of doctoral programs"  That's widely claimed, but the true purpose is to hire people more credentialed than PhD students who can be paid less than faculty.  If there is a requirement to hire a PhD to teach a course, a postdoc could be the cheapest way to do it.

What is the optimal career move then in the OP scenario , if S/he can't get a postdoc ? Stay jobless until S/he has more publications ?

@Amr, I mean leaving an assistant professor job for a postdoc. Or, more precisely, planning to do so. Try to work your career forward from where you are, not backward. Done well, you can produce publications from an assistant professor position, hopefully maintaining stability. Then, move forward or up.

@Buffy you mean the right move is to work on publications, then apply for an assistant professor at a higher institution?

@Amr, yes of course, but you do what you can.

Depending on your country, you should check the postdoc funding available and the post-PhD eligibility criteria. 2-3 years would exclude you from some opportunities in my region (EU) and field (not mathematics).
I do not know exactly what you mean by a "low paying country" but am guessing perhaps institutions in the so-called Global South, poorer EU countries in Eastern and Central Europe, or maybe declining Western economies such as the UK. In those cases, you should also carefully look at the teaching load. The priority of many institutions with a small budget is not research, but teaching. Depending on the country, you may also be evaluated on your research output but given very little time to accomplish this. You also need to make sure you are happy and enjoying your life, otherwise your professional progress could be hampered.
Here is what comes to mind for me. The best case scenario, if your PhD was promising, could be that you spin out a number of high-quality publications with relative ease in a short space of time. The worst case scenario is that you spend all of your time teaching and have very little time or energy for research. You could get stuck in a rut. It is hard to assess the risk within those bounds without knowing more about your field and your specific case.
In the short term, you could ask senior colleagues and mentors for feedback on your CV and application materials. They may be able to suggest field-specific funding opportunities. If you have a lot of material that could be publishable soon, a shorter postdoc might form a good bridge to future opportunities. Winning one postdoc funding will attract further funding, a bonus for future postdoc and professor applications.

Your approach may be a high risk one. I have noticed many new assistant professors being swamped with teaching duties and getting on top of teaching for the first few years. This can easily result in much less time for research than you hope for, and hence less productive publication building.

So what would you suggest in my case ?


text:
Are there any (automated) solutions for filling out application forms?
How do people usually handle so many application forms when applying? I find I need to fill out similar information for every single program I'm applying to, and each takes me almost one hour. Does anyone have a better solution?
(I'm applying for postgraduate)

You may be applying to too many programs.

An hour per application filling out a form doesn't sound onerous to me. You will need to spend more than that much time tailoring your statement of purpose and cover letter for each institution. @BryanKrause may have the right answer.

thanks! I'm also spending the most time on the state of purpose and cover letters, and actually, that's why I'm wondering if there's any better way to fill that repetitive information...

Personally I wouldn't fully trust any automated system, as each application system seems to have its own idiosyncrasies. Built-in auto-fill functionality in web browsers is helpful for names and addresses, but does mess up every now and then, and those fields are a lot more standardized than the ways to list your degrees and experience. For job and visa applications I instead find it helpful to have a text document with full versions of all the standard responses. Keep it open in a window next to the application form and copy/paste information as needed, massaging the way it's expressed when appropriate. This tends to speed up filling out the mind-numbing parts of applications (mostly because you won't waste time repeatedly looking things up) and helps avoid mistakes, leaving more time for tailoring application documents.

source: Stack Exchange

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

sort: votes


text:
While contacting professors should we mention if we have contacted some other faculty in same department?
If a student is contacting faculty member and finds that there are two professors that are of his interest. So, he decides to contact both of them.
While contacting should the student mention that he has also contacted another professor in the same department?

I'm assuming this is regarding admission to graduate school. I don't see any harm in mentioning this as a courtesy. The odds are high that if the two professors work in related areas they will discover this themselves. If you haven't mentioned this to them, it will seem as if you're flooding the department with applications.
It also helps personalize the letter, which is the number one thing you have to do if you expect to get any kind of response.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
Can we mention our own idea of a project in the letter to a professor during grad applications?
I am applying to 6 universities for MS and I have short-listed 2 professors from each university whose field of interest is nearly the same to that of mine.
Along with mentioning my interest in their work, can I also mention about a topic/project that I have been working on or 'am planning to work in future?
Please suggest!
PS: The topic/project will be similar to the research interests of the professor.

Sure, that shows proactiveness, interest, creativity and many good things.
I'd suggest to publish it somewhere before, even if it's just a blog, arxiv.org, safecreative.org or your favorite option.
Otherwise it will be their idea, at least for some professors. Some of those may actually have had that idea (years) before you suggested it, so it may really be their idea. By publishing it you are able to prove that at least you got to the same idea/conclusion on your own, even if it was years after them. In case that matters to you.
Make sure to emphasize the research aspects of that project.

Thanks for the suggestions. I will try those services you mentioned. After publishing it, should I also give its link in the letter I write?

@AnimeshPandey The best part is that you can publish an "extended version" somewhere and add a summary with a link in the letter. This makes the letter less intimidating and provides additional information iff they want it.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
Borrowing figures from the literature
In my dissertation, I have felt the need to illustrate some ideas with the help of figures and illustrations which I have found available in existing literature. I have borrowed a number of them and I give proper citations and everything. My question is:
Will it be considered a negative point to have multiple borrowed figures from existing publications?
Also, in two cases, I found it hard to rephrase the captions for the images and I just quoted the captions(the proper way).
Does that look like I am being lazy?

The issue here is not "laziness"; the real issue with reusing figures from the literature is that, without appropriate permissions, you do not have the right to do so.
If you reuse a figure in the literature without the appropriate permission from the rights-holders, you are effectively stealing their work, which is not allowed. Therefore, you need to make sure that you have gotten the right to use the figures, and have the proof to back it up if challenged. Normally, for scholarly works such as theses, such rights are routinely granted and cost-free. However, you need to check with the publisher (or author of the paper, if she holds publication rights) before using the figure. Then, next to the figure you are reproducing, you'll need to have a statement such as "Figure reprinted by permission of X," where X is the person or institution authorized to grant reproduction rights.

But those stuff are in the "open" literature. Aren't they? Does that not mean that they are sharing the contents of their work? Like I said, I do acknowledge that the works are not mine and I give the credit.

Publishing a work is not the same thing as giving people unfettered access to do whatever they like with it. If I cite a figure used in a previous work that I wrote, I still have to include a reprint statement acknowledging the original publication. As for who holds the rights, that depends on where it's found. Rights for material in published journals can always be obtained through the publisher; rights for material in places like arXiv are usually through the authors themselves.

@aeismail: At least in the US, copyright law contains exceptions for "fair use": quoting short passages, making copies for academic use, etc. It could be argued that reproducing a figure would qualify, in which case you actually do have the legal right to use it. But I am not a lawyer.

Yes, I'm aware of fair use restrictions—that's where "appropriate permissions" come into play. If the publisher allows it, just follow their instructions. (I'm sure you could get away with it in a thesis, perhaps, but I think you'd be unlikely to get away with that in a journal article, fair use or no.)

The legal aspects are fuzzy and varies from country to
country. The American Fair Use doctrine may make borrowing
figures (with appropriate citations) permissible in American
copyright law. There may or may not be fair use equivalents in
other jurisdictions.
However, that is not what the question is about.
The question is whether it will be considered "negative" or not. And
the answer is a resounding no. Few authors would mind you borrowing
their figures, if you appropriately cite them. Even fewer thesis
readers would care wheter you drew the figures or someone else did
(again, if you appropriately cite the authors).
IANAL, this is not legal advice, just my experience with academics.

Be aware that "fair use" with respect to images is complicated by the fact that an image can carry a lot of information. Much more than a few sentences from  a paper. Just as copying a paragraph or so (with citation) might be problematic, so might copying (or reproducing) an image without explicit permission. The accepted answer has it right, here. And an examination committee reading the thesis might care a great deal if you are sloppy about proper academic conduct.

American copyright law doesn't care about a work's information content, only about its creativity and originality. But this is about how people would react, not the legality. My experience is that nobody cares. If you have different experience (i.e. know of a thesis committee raising a fuss over appropriately cited borrowed images) then you can write an interesting answer about that.

As the other answers indicate, permission for re-use is of paramount importance.
So much so that my university's graduate college (separate from the academic department where I did my research) had strict established procedures AND TIMELINES relative to graduation dates for demonstrating compliance.  They were somewhat involved.  Without that documentation, the dissertation would simply not be accepted.  The committee had no discretion.
I will note that "fair use" was not an adequate defense at my particular university.  Truly open licenses such as Creative Commons were, but still required documentation (although the burden was much lower.)
I strongly urge you to find out if similar guidelines and procedures exist at your institution.  If they do, they will tell exactly what you need to do.
I realize this is not your primary question, but it is important.
As to your primary question:  Dissertations necessarily build on the work that came before it.  We cite papers regularly, and there is no shame or laziness in using some well-designed figures from other sources, provided you have permission.  Likewise captions.

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


text:
Acknowledgements in an industry-sponsored dissertation
I am a doing a dissertation funded by a company and my dissertation is basically a report of my progress on the problem they have given me. I have an academic supervisor, an industry contact who has given me occasional guidance and basically the company itself who sponsored it, to acknowledge.

Should I acknowledge the industrial sponsorship the same way one would acknowledge a government grant?
Also, Since this is a mathematics dissertation, It is written in First person plural: "We do this we do that". For the acknowledgements section, should I use 3rd person to keep it formal: "The author would like to..." or first person singular: "I would like to thank"
Finally, I think the order should be sponsorship, academic adviser, and lastly the industry contact. Is that the right order?

I would say generally there are no perfect settings for acknowledgements. It all depends to your university dissertation rules. If the thesis/dissertation booklet does not cover the way acknowledgement should be stated then its up to you.

Well yeah the lack of standard rules was the reason I came here for opinions... :)

@Shb this site is not a place for soliciting opinions. Questions must be of the form that can receive expert answers.

@EnergyNumbers yes, but expert answers can actually be well-informed opinions… maybe there are no standard rules in university guidelines, but there are customs, expectations, etc. all of which form an important part of academic life


text:
Is it plagiarism using an AI to do the bulk of my LaTeX?
I am a graduate student in math. I am coming up on the end of my masters, and multiple classes require LaTeX submissions. These classes are all very difficult by default, and spending multiple hours doing LaTeX only to submit an incomplete homework assignment feels non-constructive to me. I am getting better at LaTeX efficiency, however, I have found options like https://mathpix.com/ which will let me upload PDFs of my handwritten work, and then their AI will output LaTeX code which I can copy to overleaf and tweak for accuracy and formatting. Is this act that I have described plagiarism, or some other (commonly) punishable academic offense?

Could this be the most brilliant guerrilla marketing campaign ever? ;)

Just a lowly student swimming in a sea of Tex.

Does this tool work for handwritten text? I would assume that they usually take typed text in pdf format and convert back to LaTeX.

I would say no. Eventually, your ideas are put to paper. Cite where appropriate and you will be fine. Reducing the tedium of TeXing is ok.

You tagged this with [tag:generative-ai], but AFAICT, the tool this is about is not generative AI, which is also crucial with respect to plagiarism issues.

@Wrzlprmft I don't know in this specific case, but I think generative AI could reasonably be used in such a tool. It's not just about being able to match squiggly lines to LaTeX commands, the software would work much better if it incorporated a LLM trained on math formulas. For example some symbols might be impossible to read correctly unless you can guess which field the formula is from and being able to predict likely following symbols giving a prefix of a formula would also be immensely useful.

@Wrzlprmft I.e. the software would be solving the same problem, whether it tries to guess what you intended to write, or if it corrects small mistakes. At graduate level I think this should be fine and not cheating, but might still be against the rules.

@Nobody: I think generative AI could reasonably be used in such a tool – Sure, but it can also lead to huge ethical, legal, or quality problems. The designers of the tool may even have explicitly avoided generative AI on accounts of questions like these. Anyway, my main point is that this is a crucial question to clarify.

But Latex is just a formatting tool. It does not generate ideas. How is it plagarism?

If you are struggling to write quickly in LaTeX, maybe you should try out Typst. I felt a noticeable jump in my productivity when I switched to Typst. It also has a free local compiler available here.

Why are these classes requiring you to use LaTeX?  Just so you can submit pdfs, or so that you learn LaTeX?

@Nobody: That wouldn't be a generative AI though.  It would use a lot of the same large language model technology underpinning generative AI, but in the end it's doing maximum-likelihood decoding of the input.

Seems like I didn't have a great grasp of what "plagiarism" really meant. It still felt like an ethical gray-area, thank you all for clearing up some of my misconceptions.

Is it plagiarism using a Fortran (or C, etc) compiler to translate your Fortran programs to machine code?

@BenVoigt I agree, but for plagiarism/cheating purposes it might still be a problem.

This website is way too obsessed with "AI".

Overall, no. The tool you use to write something hasn't got the same status as another author. I think it definitely would be treated differently if it was "found out".
One thing, be careful that any text generated isn't accidentally lifted from another document (I think this is unlikely), that can be plagiarism. So just use AI to help generate it, then edit it, check it, and its fine. I think on the whole that's a fair way to look at this issue.

I only intend to take generate Tex from my own handwritten work, so that shouldn't be an issue.

@SBJ I think the concern here was that the AI might have been trained on other people's work, so even if you only show it your work, it might introduce traces of other people's works in its output. As an extreme example, imagine you write an equation that is somewhat similar with an equation in someone else's work that the AI was trained on; it's conceivable that the AI might put that other equation, instead of yours, in its output. But you have to check the output for mistakes anyway, so everything should be fine.

@SBJ As another extreme example, imagine you write a complicated handwritten equation; there is a straightforward-but-complicated way to write this equation in latex, and a very-creative way. If the AI has been trained on someone else's work, the AI might use the very-creative way, and that could be considered plagiarism even if the resulting equation is the same (but the resulting latex code is not the same). But that's a somewhat extreme example, and writing latex code is not an extremely creative endeavour, so it's fine.

@Stef Assuming the work is being graded on the mathematics as conveyed in the PDF and not on the LaTeX coding itself, I don't think even that situation would count as plagiarism.  (I certainly wouldn't count it as plagiarism in my classes.)  What you're suggesting feels to me like it's getting close to saying the authors of every piece of software you use should be credited as coauthors of your work.

(Which by the way I acknowledge is not always a cut-and-dry question, as evidenced by other questions on this site.)

@MarkMeckes My point is not about the software, it's about the training data used while training large machine learning models. Imagine if I ask an LLM to translate a sentence from another language into English, and the English sentence outputted by the LLM turns out to be a sentence taken straight from a Harry Potter book. Not only is this plagiarism if I claim that I wrote it, but it's also copyright infringement regardless of my claims. These things do happen regularly to people who use large language models or image-generation models.

@MarkMeckes And the issue is not just for literature and drawing; this has happened repeatedly to programmers who used code-generation models that were trained using code from github and other code repositories. Of course it's harder to recognise programming code than to recognise Harry Potter prose, and it's harder to recognise short LaTeX code than long programming code, and writing LaTeX is a lot less creative endeavour than writing novels, so it's less of an issue for LaTeX than for literature, but still the issue does exist.

@Stef Yes, I get your point.  The difference here is that (I assume) the student isn't turning in the LaTeX code, just the compiled PDF.  If they are turning in the LaTeX code itself, and especially if they're being graded on the LaTeX coding, then I agree with you completely.

Another issue is that part of the goal of these assignments may be to is to build proficiency in LaTeX.  So--check with instructors.

A very interesting issue! Although I do pay a bit of attention to various tech advances, I was not aware that there was any mechanism/app/device that could convert handwritten to TeX.
If any of my math grad students told me that they were using such a thing, I'd probably congratulate them for being ahead of the curve. :) But/and also advise them to double-check! :)
But, yes, many situations would declare that this was not ok... So, you have to ask in advance. I don't think it's "plagiarism" per se, but just maybe "against the rules".

Also, be sure to acknowledge "spell-check" in your bibliography. :)

As we all should!

Would they? This is just OCR but outputting TeX instead of Unicode. As long as the output matches the input and isn't "corrected" along the way, I see no difference between this and OCR, which I'd be surprised if it were considered bad.

MathPix is new to me, but Maple has a cell phone app that can read my handwriting and convert it to nice looking math---I was introduced to that at the JMMs a few years back.  Though this MathPix thing looks like a major improvement, as it seems to be intended to handle things at a more document level.

many situations would declare that this was not ok - I'm curious about your point. OP is writing their own equations, only that instead of a keyboard, they are using paper, pencil, camera and a bunch of processors to eventually put their own thoughts into Latex. Why would this be problematic? Mathpix is practically an advanced OCR, not a generative language model building on millions of previous thoughts. The only things it knows are reading formulas and writing TeX. Unlike LLMs, the output contains exactly the same info as it's input, only in a different format.

@Neinstein If this uses an LLM for the recognition that it needed a lot of other peoples thoughts to learn that this elongated S squiggle in your handwriting should be transformed into \int but I agree that this should be ok and that there shouldn't be any plagiarism here with any sensible definition of plagiarism.

Not to nitpick but that would be just plain old AI image recognition, not LLM. The problem with LLMs is that they spit out other's thoughts, curated and tailored, and by using those thoughts you may plagiarise the sources the LLM used. I don't see this happening with an IR model, since the only information it spits out is that "many other people write "S" similarly to this squiggle character you drew, so it's probably an "S"." This info is unrelated to the content going into the paper. That's why I don't get the point, neither in the question nor in the answer.

@Neinstein Classifying one squiggly handwritten symbol as being one latex symbol is just image recognition, but converting a complicated handwritten equation into complicated latex code is more involved than that. Compare "looking up one french word in a French-English dictionary" and "converting a French sentence into an English sentence". I agree that writing latex code is a lot less creative than writing full English sentences, but still, I think MathPix is doing much more than just converting each symbol, and it's not obvious where to draw the line between "creative" and "not creative".

@Stef As long it is only typesetting and typesetting is not part of the learning outcomes of the course, it really does not matter. I frankly would rather not have to worry about the positioning of the kerning, whether to use \stackrel or \substack or \overbox, how to make my commutative diagram look good with annotated morphisms or make sure that the 3D lines of the Hamming cubes properly shadow the lines behind them in the visual cone. This is work that might have been outsourced to some assistant in the past and adds nothing to the math.

@CaptainEmacs, oh, so you don't care about kerning? :) :)

@paulgarrett I am sure I do when I read, and I am sure I care that the TeX package does, but I do not wish to become a typesetting expert, at least not forcedly so ;-)

@Neinstein, sorry to respond so belatedly: people (in control) do often make unreasonable rules, and do not allow negotiation! Who knew? :) :)  In the 1960's, there were questions about whether slide rules were allowed... because kids who knew how to use them would have an ... unfair?!? ... advantage. :)

@quarague "If this uses an LLM for the recognition [then] it needed a lot of other peoples thoughts to learn that..." That's how all OCR (and machine translation, and speech recognition, and...) works. This is just OCR followed by translation to LaTeX.

Copying the output of a Large Language Model might be cheating, depending on the rules of the game you're playing, but unless the LLM itself is reproducing the work of a human author, then copying the output of the LLM cannot be plagiarism by any usual definition of the word (see final note, below). Plagiarism requires a human on both branches of the plagiariser/plagiarised fork.
If you are being tested or examined on your ability to write LaTeX, then having a machine produce the LaTeX for you would be considered cheating in the same way that the use of a calculator would be looked upon as cheating if you were being tested on your ability with mental arithmetic. It doesn't sound as if that is an issue in your case.
I have experimented quite a lot with using an LLM to produce LaTeX code, either from my handwriting or from a scanned (printed) document that has been poorly typeset. Here are two examples from handwritten material. The "mathematics" is of course complete junk but the results are impressively useful even if not completely correct.
Example 1
In this first example, I am interested in whether the LLM can get the basic structure of the equations correct.

This is the LaTeX code that the LLM produced.
\[ \int_{-\infty}^{\omega} N(\eta) \, d\eta - \int_{-z}^{p} e^{-i3\zeta} \, d\zeta \]
which is set as

Example 2
In the second example I was interested in whether the LLM could correctly align the equations and also how much of the details (e.g., the bar over one of the digits) would be correctly produced.

This was the LaTeX code ...
 \begin{align*} \sin x &= \sqrt{1 - \cos^2 x} \\ &= 27 \times \Omega \\ &= 2.6 \end{align*}
which is set as

As you can see, the results aren't perfect but they are nonetheless very useful.
My advice? Check the rules of the game. Are you being tested on your ability to do mathematics, or on your ability to typeset mathematics? If it is the former, and not the latter, then go ahead and use the LLM. It will potentially save you an immense amount of time (initially) and you will very quickly become familiar with the idiom of LaTeX so that:

You no longer need to rely on the LLM to the same degree but will be able to type your LaTeX directly, and
You will be able to give more nuanced instructions to your LLM so that it can set the mathematics in exactly the way that you want.

Note: ... from the Cambridge Dictionary of English. "plagiarism: the process or practice of using another person's ideas or work and pretending that it is your own"

Minor technical point: mathpix.com does not appear to use an LLM, but a different AI/ML technique that does image/handwriting recognition.

LLM, like pretty much all machine learning techniques, rely on training data. In most cases, this training data was created by humans, so it can very much be plagiarism if you try to pass the LLM's output as your own, and the LLM's output has recognisable traces of someone else's work.

I'm sorry but your point about plagiarism is just wrong, and not supported by various other dictionaries and sources (1, 2, 3,4). Plagiarizing is the act of presenting work you did not do, work that you had no hand in creating, as though it were yours. Arguing that you cannot plagiarize a machine is missing the entire point of why plagiarism is wrong.

The links I gave were the result of just a few seconds search. Just because the author of one dictionary used the unfortunate term "person" doesn't mean that you require the author to be a human being. All it takes to plagiarize is to pretend you produced work that was produced by someone other than you.

Agree with @terdon, the definition of plagiarism here seems too narrow. Suppose you copy an essay off the internet and submit it as your own work. I have a hard time accepting that it is impossible to tell whether that wholesale copying of text and false representation of it as your own is plagiarism or not, unless we also know for certain whether the original text came from a person or LLM. In an age where LLMs can pass the Turing Test, it's not even possible to tell whether something was written by a person or machine, meaning "I copied an LLM, not a person" is always an available defense.

@NuclearHoagie: Normal LLMs are trained on the writings of real humans, so you're still indirectly copying humans.  The legalities are the subject of various court cases.  This is all beside the point, of course: as terdon says, what matters is presenting something as your own creative work when it's not.  e.g. if I claimed to have written some assembly-language code but actually copied the output of an optimizing compiler, like GCC, Clang, or MSVC. Or a more obscure one so experienced humans might not recognize its tendencies... Current compilers are not AI at all, just human-built machinery

When you say "experimented quite a lot", were your illustrated experiments produced using https://mathpix.com/ like the op, or were you using some other LLMs/tools/whatever? If not mathpix, could you elaborate what tools you used to go from scanned pdfs of handwritten pages to LaTeX source? Thanks.

@terdon ... "I'm sorry but your point about plagiarism is just wrong". You shouldn't feel you have to apologize for expressing a contrary view; it's OK.

@eigengrau I have experimented a lot with ChatGPT and it was to ChatGPT that I uploaded the specific illustrations I used in my answer. I have also uploaded pages from several old printed works that were so dense and badly typeset that I found them impossible to read. By having ChatGPT scan them and produce the LaTeX code, I have been able to get the math double-space instead of compressed-single space ... and finally read the papers. I've jotted long notes in a notebook, and then uploaded those handwritten notes, and had them set beautifully. I have to write a bit more neatly than usual!

@CrimsonDark Thanks a lot for the detailed info. I have lots of handwritten notes, with lots of math, that I've already scanned as pdf pages ("one small step for a man"...). The further possibility of having them automatically LaTeX'ed hadn't even occurred to me (..."one giant leap for mankind"). I'd of thought I'd get to walk on the Moon first. Can't wait to give it a try. Thanks, again, Crimson.

@eigengrau I've found this instruction to ChatGPT to be a good starter (it sometimes doesn't start at the beginning, nor end at the end! ...
"The attached image shows a mathematics text.  The text begins with the words "Let $x$ be an element" and ends with the words "integrate over the". Please show me the LaTeX code to typeset the document correctly. Ensure that you begin at the beginning and end at the end.   DO NOT start your LaTeX code with \documentclass; just start with  \begin{document}"
... and I repeat that instruction with every page! If it goes wrong, I start a new chat.

@eigengrau ... one page at a time. I usually upload images not PDFs. With old works, I extract the images (on a Linux machine) with pdfimages. JPEGs, not PNGs. PNGs blow ChatGPTs mind.

The “Cambridge Dictionary” definition just didn’t realise that “work” might be created by someone or something not a person. If an “AI” had a high degree of real intelligence to create a work on its own, that could lead to plagiarism.

@CrimsonDark Thanks, again. I tried using my free chatgpt-3 account (uploading an image to the web, and pointing chatgpt to it), but it failed miserably. It typeset just a few text words, and none of the $math$, and none of the drawings. I tried both with a gif (first using convert .pdf --> .gif) and with the scanned pdf. Then I pointed it to your answer here https://academia.stackexchange.com/questions/206563#206569 and asked if chatgpt-4 is required. It said it didn't know. Are you using chatgpt-4? I didn't want to pay for it until I'm reasonably sure it will work on my more elaborate stuff.

@eigengrau Yes, I am using ChatGPT-4. Try for a month, no harm ... no guarantees. It's taken a while to get the hang of it. And ChatGPT3 ... completely useless, for almost everything. (no, I am not working for OpenAI :) !

As many answers have already pointed out, this would not be plagiarism. However, you should be aware that by using an AI, you turn over your data to them- that is, future users might plagiarise you. Using the example provider that you linked, here is their privacy FAQ (emphasis mine):

New and different images allow Mathpix to improve current recognition features and add new recognition features. If you allow Mathpix to use your images, anonymized versions of your images may be chosen for algorithm training purposes by our QA team. Regardless of if an image is selected by QA or not, all images in the QA database are permanently deleted after 60 days.

So while your use might not constitute plagiarism, others might plagiarise using the future trained model of this AI. If it's just homework it is probably okay, but a Master's thesis could already be something worth pursuing in a PhD.
In this case, the provider suggests that you can opt out. This would be something to always check when you use an AI provider, and proceed with caution.

Here is a good rule of thumb to understand what constitutes plagiarism.
Plagiarism is - in spirit - about claiming intellectual credit for yourself that you did not do, but copied from someone (or had someone do for you).
[That's why self-plagiarism is called "plagiarism", although it's a bit controversial naming. The use of that latter term focuses not so much on the aspect of stealing credit from others (which regular plagiarism also implies), but on claiming credit that you don't deserve (because you already received it earlier).]
Back to your question: Under above interpretation, as long as the AI does not carry out any intellectual work that you are supposed to do, you should be fine.
For instance, if the course involves actually learning to use LaTeX, it would be plagiarism. If the course only involves somehow typesetting the material in whatever way is suitable, you could ask the tutor if it is legitimate to use an AI helper for that purpose and to cite it if relevant.

@DanielHatton Indeed. Though, nobody will put quotes around all words they looked up in the dictionary or which was fixed by Grammarly. With the increasing power of tools, the boundaries where external work needs to be acknowledged will become increasingly blurry. Had your human assistant typeset your math, you would probably acknowledge and thank them for typesetting, but not cite them, or mention them as co-author.

Self-plagiarism isn't called "plagiarism", it's called "self-plagiarism". That doesn't mean it's plagiarism any more than calling something a "sweet potato" means it's a potato. Of course, I'm not disputing that both of the former are misconduct, or that both of the latter are vegetables.

@EspeciallyLime I used also to fall for that trap, but then I understood where it comes from. The word plagiarism has two aspects and they are linked, but not equivalent: 1. "taking undeserved credit from others", 2. "claiming undeserved credit for oneself". Self-plagiarism gets the "-plagiarism" epithet not because of 1., but because of 2. Of course, that implies that credit is a quantity to be "counted", but in a publication-beancounting society, that's pretty much is given.

@CaptainEmacs does that second definition come from an actual dictionary? I couldn't find anything similar.

@EspeciallyLime Not that I know of, but I kept wondering why the term self-plagiarism took hold and is so persistently used. That's the explanation that I came up with to explain it to myself. Feel free to disagree, to me that made it finally make sense.

@DanielHatton There are different issues here. One is multiple use of the same data set. If disguised, it's as bad as data manipulation/faking.  The other one is having multiple publications from the same author which copy each other or are very similar. I must say that I find the latter only a hard problem for hiring committees who count papers. There are authors who tend to repeat the same point over and over, in different words, and nobody considers that self-plagiarism. Maybe they have only one thought. Maybe there are all these different facets of the one thought.

@DanielHatton Apart from that, I did not criticise the word self-plagiarism, but I saw many people criticize the choice of word. As a consequence, I wondered, as I said, why people used it. And this was the explanation I came up with for myself.

self-plagiarism is an oxymoron as plagiarism is the practice of taking someone else's work or ideas and passing them off as one's own.

@deep64blue This is precisely what I was wondering about. If you interpret plagiarism as having two different aspects to its meaning, 1. taking credit away from someone else vs. 2. claiming undeserved credit, however, under interpretation 2, the name self-plagiarism makes sense again. It is clear that originally meaning 1 was the dominant one, but words exhibit semantic creep, so, without being a language expert, I can imagine that something like that may have taken place. Maybe someone with scientific linguistic expertise can clarify.

Even sense 2 doesn't fit as you're not claiming undeserved credit when it's your own work!

@deep64blue If you read my comments again, you will notice that I refer to committees counting papers. Having two papers saying the same thing, in US-style evaluation scenarios, is essentially claiming duplicate credit. I personally do not agree with this style of evaluation, but this is the norm in many locations. This is why CVs have separate Journal sections, because they split out similar earlier conference papers. I tried to understand the origin of the term 'self-plagiarism' and why it's frowned upon. If you have a better idea why it's considered harmful, let me know.

Ask the person teaching the course
Only they know whether the (secondary) goal of the course is to teach you LaTeX skills or not. If it is, using an unapproved tool might circumvent that didactic goal. If it isn't, it's still up to the teacher to decide which tools are ok to use for their course and which aren't.
And don't ask about plagiarism. That's not the issue here. Ask whether you are allowed to use that tool for your coursework.
Since these AI tools are fairly new, there is no "established consensus" on this issue, so be prepared for answers ranging from "Absolutely not!" to "Sure, why would you even ask?" to "Uh, no idea, I need some time to think about that"¹.

¹ Next week on academa.SE: "Should I allow my student to use an AI tool for LaTeX markup?"

Oh shoot, I wish I would have seen your comment sooner. I asked specifically about plagiarism this morning. All of them seemed to echo "that's not an issue here".

I'm going to go against the consensus here and argue that what you are doing is self-defeating, whether or not it is technically plagiarism.
I'm sure your lecturers aren't asking for submissions in LaTeX in order to torture you. It's possible they are doing it for their own convenience (because well-written LaTeX is much easier to read than handwriting); but it seems much more likely that training you to use LaTeX is part of the course goals – LaTeX is, like it or not, the "industry standard" for typesetting mathematical documents and so being able to write in LaTeX is a necessary skill for a mathematician. If so, then using a fancy OCR program to generate TeX from handwritten math is cheating.
It's really not that hard to pick up; with a little practice, you can get fluent enough that you can even take notes in lectures directly into LaTeX in real time ("live-TeXing"). Unless you have a disability which prevents you from using a normal keyboard (or something of that sort), then I suspect that in the time it's taken you to find this handwriting-recognition website, learn to use it, then fret about whether it's allowed or not, you could have sharpened your LaTeX skills to the point where you don't need to cheat any more.

I agree with your main point (+1), but actually from the examples in this thread the LaTeX it generates is better than a lot of the code I see from human authors. So playing around with this tool and looking at the code it produces might be an efficient way to learn LaTeX.

LaTeX is, like it or not, the "industry standard" for typesetting math.  Well that depends what industry you work in. If you’re an academic whose business is writing papers in math or physics or comp sci, then I’d agree. If you’re writing mathematical documents in industry, or you’re a high school math teacher, or you’re an academic in engineering or economics, then (like it or not) MS Word and Google Docs are more widely used.

Regarding "being able to write in LaTeX is a necessary skill for a mathematician", that may be true currently, but it's unlikely to be the case for long given that there are already tools that do a really good job of generating the LaTeX. I would argue there's nothing self-defeating about not learning a soon to be redundant skill.

If you are a whiz in LaTeX, probably you will keep honing this skill. However, if you want to write math instead of worrying how to move characters into the right position, then such a tool is for you. Personally, I enjoy coding a lot, but dedicated and clever LaTeX manipulation to get the typesetting right, not so much.

Thanks for your consideration. Yes, I agree with your main point. However, I have done LaTeX for multiple years and 100+ hours, and it still does take me multiple hours to code up an in-depth assignment. Consider me behind the curve or whatever you want, but it took me about 15 minutes to figure out the website, and another 24 hours to really realize how useful of a learning tool this could be for me, and the colleagues of mine who struggle with LaTeX more than I do. I talked to my professors also, and none of them considered this "cheating", as the point of each class isn't learning LaTeX.

@cigien “I would argue there's nothing self-defeating about not learning a soon to be redundant skill” – when I first learned LaTeX people were already dismissing it as outdated and predicting its imminent demise. That was in 1998. Yet here we are a quarter of a century later discussing this question.

Ah, so you think that knowing that \int is the latex code for integral or \pm for plus or minus, has a scientific value to the human knowledge?

@NotaChoice No, I did not claim that.

This question, like most questions of the kind "Is X plagiarism" can easily be answered by going back to the fundamental reason(s) why plagiarism is considered such a grave offense against academic integrity in the first place.
Traceability of ideas
The primary and most important reason why plagiarism is a Bad Thing™, is the importance of traceability of ideas in academia, science, research, culture, art, music, …, and really, society in general. But specifically in academia.
Imagine, you find a flaw in someone's argument. Or, since you are a mathematician, imagine, you find a flaw in someone's proof. It's a subtle flaw that took a while to spot, so, there have already been new papers written by other authors, relying on the theorem.
Traceability guarantees that it is possible to find every paper relying on the theorem and see if the flaw affects them or not. If the author of the original paper got the idea for the proof from somewhere else, then traceability guarantees that you can find the root cause of the flaw, and find other papers that might have picked the flawed idea up from the original source.
Plagiarism is a problem because it breaks the chain of ideas, so an idea can no longer be traced backwards to its original source or forwards to all the other ideas that build on it. This means that any flaw discovered in the idea cannot be fixed: it cannot be fixed at the root, because you don't know where the root is. It often cannot be fixed by the plagiator, because, well, they "stole" the idea and there is a chance they don't actually understand how it works!
Even if there isn't a flaw in the idea, there is still a problem: say, you want to build your idea on top of someone else's idea, but there is some detail you don't quite understand. So, you contact the author and ask them about it. If that author plagiarized the idea, there is now a possibility that they don't understand the idea enough to be able to answer your question. In the unrealistic best case, they will admit to plagiarism and point you to the original source. The probably more realistic case is, they just ghost you. The worst case is, they make up something, and it is convincing enough that you don't notice right away and go off and start building your idea on top of this made up answer, potentially wasting a lot of time, resources, money, and effort, until you notice there is something wrong.
Traceability is also one of the reasons why self-plagiarism is a thing: it still "breaks the chain". If you use the same idea in two different papers without properly referencing and citing it and someone looks at one of the two papers and finds a flaw, they have no way of knowing that there is a whole other paper out there with the same flaw. Other authors may have cited only one of the two papers, so there may be whole separate chain of papers all built on the flawed idea that nobody knows about.
Recognizing contributions
The reason that is often cited as the most important or even only reason, but is actually secondary in my opinion, is that contributing good ideas should be recognized. An author, group, or organization which advances the field should get credit for this advancement. In other words, the giants whose shoulders you stand on, should be rewarded for carrying the load.
This is another, although admittedly much weaker, argument for why self-plagiarism is a thing: you get twice the recognition for one idea. However, I find this a pretty weak argument, and I can see how people don't get why self-plagiarism is a problem if the idea of plagiarism is merely presented as "stealing someone's credit". That is why, in my opinion, focusing on the traceability aspect is important.
Conclusion
I think it should be obvious when applying the two criteria above that what you are doing is not plagiarism.
However, as pointed out in other answers and comments as well, it might still be academic misconduct in other ways. In particular, if demonstrating proficiency in LaTeX is part of the course goal, then it might be considered cheating. Or, it might be considered clever use of available tools.

I really like the traceability argument and generally your description of why plagiarism is a problem. However, in the specific case of OP, the thing you consider secondary, is actually the primary, namely getting credit. This is a class, and thus the original contribution of OP is at essence here. Also self-plagiarism - I agree with your take on it where it comes to taking credit from others; however, the problem specifically for a student is getting undeserved credit (whether through work of others or through cloning of one's own work).

In the professional realm, I agree that the argument against self-plagiarism is weaker. It's about not getting credit counted multiply for oneself, but it is only a problem because it's fashionable to count papers rather than value insights.

This isn't really an answer to your question but too long for a comment.  (Largely an elaboration on David Loeffler's answer.)
In my math graduate courses I require all of the homework to be typed.  I don't require the students to use any specific software, but I encourage them to start using LaTeX if they aren't already.  I would not consider the use of AI tools that you describe to be plagiarism, or any other kind of cheating in my classes.
However, there are three reasons I require the homework to be typed:

So that it is legible.

When students take their handwritten scratchwork and type it up, they go through another round of thinking about their arguments (in my experience, more thorough than when they just recopy by hand) and end up with better reasoned (and more likely to be correct) work.

They will all eventually need to be able to use LaTeX fluently, and it's better to start learning sooner rather than later.

Your system partially defeats the second and third reasons.  Only partially, since you're still typing up the text part yourself, plus reading and tweaking the AI's LaTeX output.  So I get, and don't fully disagree with, your choice to do things this way at this stage, when you are pressed for time and focusing on learning the math.  But although as I said I wouldn't consider what you're doing to be cheating, I see it as not really in the spirit of the requirement.

is an excellent reason. 3. is also great. Moreover, I always found that every tool to speed up things LaTeX-wise ends up wasting even more of my time. Frontends for bibliography cease to work at critical moments, or are incompatible with my collaborators; auto-completions end up messing up with the code, etc... In the end, it is better to just bite the bullet and type LaTeX directly. (I never used these AI tools, but I suspect they are still at this stage where they are more of a waste of time)

Regarding #3: I’d say it’s pretty unlikely that the average undergrad in the average math class will end up in a job where LaTeX fluency is required.

@bubba Agreed.  Which is part of why I don't have that same requirement in my undergrad classes.  For the PhD students, they'll at least need LaTeX fluency for writing their theses, regardless of their post-degree employment.

In my opinion there should be no issue in using such methods for mechanistic conversions (as opposed to generation of text, solutions, ideas, etc.), assuming you check the output for accuracy, of course. In spirit, it is the same as using OCR. Further, I am not aware of anyone having objections to use of Detexify, which also uses a machine learning method. I see no clear reason for why it would be OK to use machine learning methods to recognize one symbol at a time, but not entire equations or sections... That said, Mathpix's marketing leans heavily into the AI angle so it may be a likelier target of overly broad policies. Finally, the data security concern raised in this answer is worth taking into account.
As some answers have mentioned, courses and assignments where the goal is to learn using (La)TeX can be different in this regard from cases where (La)TeX is just used to typeset documents, and it's worth asking the instructor about both rules and advice. Jumping straight to automation tools like this may mean you overlook learning useful structures and how to effectively read TeX. However, at the same time, personally I tend to think that such courses should introduce useful tools like this (and, e.g., various editors, online table generators, and the TeX StackExchange!) that help overcoming the (often exaggerated) entry barriers to learning (La)TeX. Having to constantly flip through tables of symbols until you learn a sufficient number of commands for math symbols was frustrating, but hasn't been necessary for a while now, and courses ought to reflect this reality.

Heck, using Word’s spellchecker is using a fairly primitive LLM and I doubt, aside from elementary school spelling class, that anyone cares. And one does need to check the suggestions at times, particularly for technical terms.

If you entered a spelling competition it would be cheating. If there was a competition for “most beautiful latex output of complex formulas” it would be cheating. Since what you do is producing maths it’s not.

I saw handwriting input for equations years ago.  It was used with Word, but used a TeX-like format at least as an intermediate step.  That required using writing on a graphics tablet rather than scanning, but fundamentally it's the same concept (and akin to a cleverer version of automatically generating bounding boxes round characters and feeding them to detexify).
So this is an improved input tool.  It's not plagiarism.
That doesn't mean it's not cheating in a LaTeX course, where the goal is to learn to write your own code. But there are also click-and-place equation generators for TeX and I'd see those in the same light.

I think you should talk to the prof, as it's possible that learning LaTex is one of their educational objectives.
That said, IMO, if you use a tool to turn your handwritten notes into LaTex, and then prominently cite the tool and say in the submissions how LaTex was generated, then this is NOT an academic honesty problem (with the caveat that there may be language in the syllabus saying that it IS an academic honesty problem -- maybe "all turned in work must be your own" or some such -- in which case, it assuredly is).  This way, you haven't claimed, in any way, personal provenance over work that isn't yours.  You may certainly lose points for not doing it "right", but that doesn't make it an honesty issue.

What is the assignement about?
Is the evaluation based on the quality of LaTex code?
If yes, and learning LaTex is part of the course and therefore an essential part of the hand-in? -> don't use it!
If not, and it is about the content, and the format is simply required to be LaTex? -> No problem!
Why this is not a problem
(stated well in other answers)
Assumption: as stated, the tool does not do anything generative. Even if other sources were used to train it, so have other sources been used to train humans -> the tool should cite sources used, but this doesn't mean that there is content in there.
Plagiarism applies to ideas and content. You could cite the tools you use (in academia, that would surely be the right way), such as LaTex itself, maybe a compiler etc. But if you use handwritten text as a base, Word and a converter, whether you use a keyboard or voice promts to write: it's irrelevant.

plagiarism - no
other academic misconduct - no, unless one of the purposes of the course or the assignment is for you to learn LaTeX, in which case, you would be cheating.
If not certain, you can always ask your instructor.


text:
Where can I find professors online to judge my study tool?
I am doing my masters in education in an Arabic speaking country and I have created my own test instrument to use as a pre-test and post-test in an experiment.  However, I was told that I need 4 professors in the same major (English curriculum and teaching methods) to proofread and provide input about my test instrument ... in effect, to use them as "jury members(?)" to guarantee the quality of the content and the suitability of the test.
The problem I now face is that that there aren't any professors in my university with the relevant  major so I have to find professors online. To me it seems  rude to email professors to do such a service because it's normally a paid service, so I was wondering if there was a website specifically for that? In Arabic, this was called رأي الخبراء but I haven't found a similar term in English and I would appreciate any help.
Is there a website for services by professors to proofread a test study tool?
And what is this process of checking the study tool called in English?

Using Google Translate, the Arabic that the OP includes translates simply as: "opinion of experts".

In my experience, asking never hurts and more often than you might expect, people are willing and happy to help out. I don't think many professors find it rude to receive such a request, if they are too busy they will probably simply ignore it and go about their day. See https://academia.stackexchange.com/questions/90725/how-should-i-phrase-an-important-question-that-i-need-to-ask-a-professor for pointers on how such an email request could be phrased.

Do you have an opportunity to attend a conference in your field? That would be the place where experts in your area congregate.


text:
Switching Career from Theoretical Physics to Biomedical Engineering
I am doing my Ph.D. in theoretical physics but want to switch to biomedical engineering (BME), especially tissue engineering and regenerative medicine.
Do Master's programs accept students without any background in BME?
If I have to meet the course requirements for BME, what are the options?

In which country do you plan to study?

It’s a pretty big leap. Do you have any biology background, including labwork?

@Buffy I'm studying in the United States but I'm international student

@Aruralreader That is the problem. I have zero background on the field.

@user184967, it might be useful to explore your motivations for pursuing biomedical engineering in light of your past decision to pursue physics. Likely something has changed for you. An occasional bit of reflection can be helpful. It’s possible you can contribute to tissue engineering as a physicist. Best of luck whatever you do!

@user184967 Hello! Sharing link to a post that might help you: Bogdan Budnik on Analyzing Proteins to Develop Better Diagnostics and Therapeutics.

In the US you are very likely qualified for an entry into a doctoral program in a different field. But it would be a long, hard, journey from there. I'm guessing it would be another six or seven years to complete it.
But here in the US a bachelors graduate can enter a doctoral program in most fields with a very general background. Having no biology at all would be an issue. You might need a few undergraduate biology courses to make a serious case, however. But you wouldn't need the equivalent of a masters.
Your physics background wouldn't do you a lot of good other than to show you are capable of learning. The research process in the two fields is, I suspect, vastly different.
Also, complicating the case, is that your prior education (undergraduate...) may not look at all like a general US education which is very broad. If your entire journey to now has been physics based it would be harder than if you had a more general background. You will also be competing with people better prepared in field.
I wonder why you would want to make such a great leap, however. But if you want it bad enough and can spend the time doing it you can probably make it work. Others in the application process will also have that question, I think.
The only way to know for sure, however, is to make application. If you are situated to do so you might want to visit an interesting department and talk with them about what you might need to get accepted. Your case is unusual.

I know a surprising number of physicists (phds in physics) who are doing very well working on the computational side of biology.  If you have experience with programming and analysing large datasets or handling large mathematical models, then these are skills which are very much in need within the biological sciences at the moment.  If you have these skills, then sell yourself on those, and you will learn the biology you need as you work in the field.
Most of the people I know working in biology with a Physics background moved across after their PhD, so they got a postdoc in computational biology/bioinformatics, leaning on these skills and learning the new field as they went.  Perhaps as the field matures and there are more students with a computational biology / bioinformatics background this pathway might get harder to get a foot in the door, but my feeling at the moment is that there are still a lot of positions and not so many people with the skills to take them.  Lab biologists can generate enough data in a few weeks to keep a good data scientist busy for a year or more.
I would imagine getting a second PhD position would be harder - firstly, you will need to deal with any regulations that only first PhDs are funded (depends on funder). Secondly, if you're in the US then there will be coursework as well which will entail learning more biology than just the stuff that's necessary to do your job and competing in graded courses (especially if grading is on a curve) against people who have a lot more biology at undergraduate level.


text:
How do you answer questions about previous submissions?
I have always taken "Has this manuscript been submitted previously?" to mean that the journal wants to know whether you have submitted the manuscript previously to the same journal and it was rejected/withdrawn, or you were late in submitting your revision and hence need to submit as a new submission to the same journal. However, it just clicked that the question does not explicitly say so. Do we need to mention submissions to other journals in the past here?
Similarly, I read the following to mean I am being asked about RIGHT NOW not having submitted elsewhere, not in the past. Clearly it should not be published on in press anywhere.
"Confirm that the manuscript has been submitted solely to this journal and is not published, in press, or submitted elsewhere."
How do others answer these questions?

I've not encountered the first question before. Taken literally, it's asking if you have submitted the manuscript to this journal. However, any good editorial management system should flag resubmitted manuscripts, while whether the paper's been submitted to another journal ought to not be this journal's business. If you have encountered the question, just take the first interpretation.
The second question is much easier to parse. If your manuscript has been published somewhere else (or is in press), then you shouldn't submit it. Similarly if it is currently submitted somewhere else (and is under review), then it shouldn't be submitted. But some people will anyway, hence they're asking to make sure.

Taken literally, it is actually asking if the paper has been submitted before, ever, to anything at all. It is a nonsensical question, and I suspect the OP is expected to read between the lines and read that as "has it been submitted to us before" but that isn't what the question is asking. What an awful system!

Thank you for your help!

Yes, it actually meant what you said first and NOT the second. The journal wants to know whether you have submitted the manuscript previously to the same journal and it was rejected/withdrawn. Whether it was rejected/withdrawn is normally a follow up question, or they ask you what was the previous submission ID. Maybe the editors and reviewers would do a comparison to see what has improved. In every reputed journal, you normally attach a cover letter highlight your research and manuscript. There is no harm in being open with the editors as you can mention in the cover letter that what your research/manuscript is about and if you submitted it before, you could write what has improved.


text:
I want to submit an abstract to a conference. But the results are quite preliminary. What are the chances of acceptance?
I (3 months into a PhD) have been fortunate enough to receive some funding that I must use within the next few months to go to a conference. I found a conference I would like to attend that I realistically could submit an abstract for (deadline is within 3 weeks). The conference will be 3 months from now, so I would be 6 months into the PhD by then.
Whilst I do not have to specifically present anything, I would really like to so that I can get practice presenting research at conferences and come away with it saying that I got to make some sort of contribution to my field (whilst obviously quite minuscule for the time being)!
For context, this is for a clinical research conference and I am presenting some computational modelling results. Whilst the preliminary results that I would submit are not substantial at the moment, they do bring a couple of ideas from disciplines together into something that my supervisor has agreed is novel, and would form the theoretical basis for the rest of my PhD. An issue is that some of the results have been inconsistent with other computational papers in similar domains.
Despite this, I would love to discuss these results with others as I saw some giants within my field will be present/speaking. Is it reasonable to attend a conference with very minimal results? What is considered the minimum requirement for an abstract submitted to a (clinical) conference? My abstract is more computational modeling (ie. engineering) focused, but still very much relevant to the field.

When I did my first conference presentation I didn't really have results and the situation was maybe similar to yours (although somewhat better because it was a conference specifically for young researchers). I felt somewhat bad about others having much more elaborated material, but it was a good experience nonetheless. Acceptance criteria can strongly depend on the field and specific conference (some accept pretty much everything, some are very selective), so it's hard to tell what your chances are.

Congrats on the funding! I agree with you that it's a great opportunity to meet some folks in your new field. I hope you are aware that you can attend conferences without presenting research at them. If your funding allows this, that would probably be the best option, since you are just starting out.
If the funding only funds you if you present research, then you can submit an abstract. No one here can tell you your chances of being accepted because it depends on things we don't know like the size and quality of the conference, the quality of your results, where you're getting your PhD, who your advisor is, etc. But even if it's not accepted, it will be good practice for you to write a submission, and it can turn into a better piece of work later on.
A word of warning, though: first impressions matter. If any bigshots in your field attend your talk, and think the research is junk, this could harm you in the long term. If you do get accepted, then in your talk I recommend you emphasize that you are just starting out, these are all very preliminary results, and you would love to talk to experts and improve the research. The time to impress people with the quality of your results will be when you're on the job market. Right now, it's more important to be eager, curious, hard-working, and trying to learn.

Your chances of acceptance depend on the conference. I've been to some conferences that accept almost any paper and to other conferences that accept very few papers. This depends not only on the prestige of the conference but the organization: Some have a dozen (or more!) tracks running at once, others have only one.
A couple of suggestions: 1) Does the conference have a section for "student papers" or "first time presenters" or something like that?  These can be very useful, and some conferences offer assistance to first-timers. (And, at least sometimes, the audience may be more gentle on you).  2) Does the conference have posters?  Presenting a poster can be a good introduction to the world of conferences. They are usually less stressful than papers. 3) Since you are doing a PhD, I'm assuming you have a mentor. Ask them about the conference. They may know the organizers, or have presented there before, or have other advice.


text:
How can I overcome academic "researcher's block"?
I work as a senior academic in an important university in Europe. My name is in several publications in top journals in my field.
I have always published papers together with brilliant collaborators who really made the difference but they are not there any more.
I am working on a new paper as a solo author but I am suffering a mental blockage and serious problems of anxiety.
I have previously published some papers as a solo author but I need help with this new paper. The difference now is that I am not able to start writing the proof demonstrations and therefore I cannot attract collaborators. Blank page syndrome. When I try to work on it, I have panic attacks. It's not a lack of skills because I have previously performed at a high level, I am blocked because I am used to collaborative work and talk about work helps me develop my ideas. I am now in a vicious loop, without proofs to attract collaborators and without collaborators to develop proofs
I was invited to give a seminar on my previous paper in an American university. I could use that opportunity to talk with them about my new ideas. I also spoke with some of my department colleagues. They are waiting for me to develop a bit more the proofs to decide whether my idea is feasible and collaborate. They are busy and will not help me at the moment. Right now, I am alone with my unsolved proof and my panic attacks.
Two questions:

How can I overcome this mental block when working with theoretical mathematics?
My job is my life, I don't want to leave academia but this situation is killing me. Should I leave academia or stay regardless the consequences?

Do you already have tenure?

Yes, I do have a permanent contract.

In that case, I wonder if you would like reading about the time that Feynman got burnt out on research, and he decided to just stop worrying about being productive in research and instead do whatever he thought was fun. He tells the story in Surely You're Joking, Mr. Feynman.

Thank you for your advice. Feynman is always very inspirational.

@littleO That's OK if you have a tenured permanent position, not OK if you are a PhD student or a postdoc.

@Tom That’s why I asked first if OP has tenure.

I am sort of reading the post as ''In the past, I got my name on papers where my collaborators did most of the work and had most of the ideas, but I'm not talented enough to do good work by myself now that they are gone''.  That's kind of how it reads, no offence.  Perhaps you should have published papers by yourself to develop ability to work independently?

I am an academic with tenure. I experienced difficulties with research at one point. I had been working on mathematics for about 30 years. I share below what helped to tackle it. I am back in a creative zone, happily producing results--in fact delivering some of my best results.
Others have given great advice, including finding new research partners to work with. Can you take on a grad student? I always found conversations with grad students very stimulating.
Panic attacks can be addressed via breathing techniques (very helpful and simple to apply). There could be other causes for stress or blank page syndrome too (e.g. conditions affecting sleep such as apnea etc), so perhaps check your health with a GP.
Others suggested engaging in sports. I find swimming energizing and super useful prior to a research session.
A creative activity (other than maths), such as sculpting or writing (or drumming or portrait drawing as Feynman did) will help to regain creativity elsewhere, which you can bring back to research in due time. It worked for me.
Gain distance. If one is too close to the work and attaches too much importance to it, then the work can suffer. I work with far more detachment now on a topic that I find more important than any other I worked on before. I keep perspective, humor and balance in the work. I found better pacing than when I was younger. If you change your life style and get more distance from your work by socializing, sports or creative undertakings, then the distance and added perspective this brings will help to overcome stress. I never stress in research at this stage. It is delightful (again and far more so than when I was a younger scientist).
Get a sabbatical to work with a mentor. Finding the right mentor to work with can make all the difference. I found a mentor who is very active, yet retired for quite a while. He is an inspiration and working with him and seeing him in action has changed my work practice.
All of the above helped me to move forward. Life always brings many challenges. A research block can be a sign that you require something different. So perhaps consider it as the opportunity that it is to regain what you are looking for...

Forgive me but I'm going to just wildly speculate here and hope that you find a bit of value in it. Perhaps you are just the sort of thinker that thrives on the synergy of working with others and getting ideas bounced around and reinforced (or shot down). That doesn't make you less of a mathematician, of course, but just represents one way of getting all of the pieces together.
It seems like you thought of yourself up to now as the 'junior' member of your circle and now the others have died or retired and so you are left 'alone'. In fact, IMO, you are left, now, as the senior member, but you don't need to continue to be the 'only' member.
Try to build up the circle again with new junior members with whom you can interact, building up their ideas as well as your own. It will give you that synergy again, if this is indeed the issue (like I said, speculative). A local circle is best, of course, but today's communication resources give additional options if learn to use them intensively.
And you have the opportunity to become the master that those younger scholars look up to and revere as they grow into the profession. Very cool.

One additional factor might be at play. When a person tries too hard for too long at intellectual activity, the brain sometimes rebels and shuts down. A break is called for, especially a break that gets the blood flowing, such as physical exercise. Physical exercise that also engages the brain but in a different way from the normal research mode can be helpful. I use Tai Chi for this as it is a mind-body fusion exercise, though not aerobic. When younger, I used cycling and x-c-skiing and such though they didn't have the same mental component. But an hour or so break for physical exercise can sometimes invigorate you.
And since the mind works subconsciously as well as when forced, sometimes insights magically appear during or immediately after a break. Even a sleep break.

Note: after the OP updates the question, I feel this answer doesn't answer it much. Nevertheless, it's still applicable in a general case I think.
The method to solve mental block is very easy: take a break. Everyone has it, even your brilliant collaborators, so there is no need to be anxious about it. (The more you are anxious, the more likely you have it).
My experience is that if you don't know what to write, read more books/papers. During the reading if you catch relevant idea, then it will invoke the idea that you are looking for, and then it will come as flood. If it still doesn't come, then perhaps ideas for other problems will come?
Other resources:

Writer's block
Occupational burnout (for a psychology approach on this)
Process theory of composition (for those who is interest in the field studying about writing: composition)

Here is an excerpt from 'Surely You're Joking Mr. Feynman!'. Copy from here

When I was at Princeton in the 1940s I could see what happened to those great minds at the Institute for Advanced Study, who had been specially selected for their tremendous brains and were now given this opportunity to sit in this lovely house by the woods there, with no classes to teach, with no obligations whatsoever. These poor bastards could now sit and think clearly all by themselves, OK? So they don't get any ideas for a while: They have every opportunity to do something, and they are not getting any ideas. I believe that in a situation like this a kind of guilt or depression worms inside of you, and you begin to worry about not getting any ideas. And nothing happens. Still no ideas come.
Nothing happens because there's not enough real activity and challenge: You're not in contact with the experimental guys. You don't have to think how to answer questions from the students. Nothing!
In any thinking process there are moments when everything is going good and you've got wonderful ideas. Teaching is an interruption, and so it's the greatest pain in the neck in the world. And then there are the longer period of time when not much is coming to you. You're not getting any ideas, and if you're doing nothing at all, it drives you nuts! You can't even say "I'm teaching my class."
If you're teaching a class, you can think about the elementary things that you know very well. These things are kind of fun and delightful. It doesn't do any harm to think them over again. Is there a better way to present them? The elementary things are easy to think about; if you can't think of a new thought, no harm done; what you thought about it before is good enough for the class. If you do think of something new, you're rather pleased that you have a new way of looking at it.
The questions of the students are often the source of new research. They often ask profound questions that I've thought about at times and then given up on, so to speak, for a while. It wouldn't do me any harm to think about them again and see if I can go any further now. The students may not be able to see the thing I want to answer, or the subtleties I want to think about, but they remind me of a problem by asking questions in the neighborhood of that problem. It's not so easy to remind yourself of these things.
So I find that teaching and the students keep life going, and I would never accept any position in which somebody has invented a happy situation for me where I don't have to teach. Never.

Maybe you could try out a method from another field ! (Computer Sciences.)
It does not help with the exact same problem, but you could try out the rubber duck method, usually used to find a problem in some code, but it works by explaining what [the code] does to somebody else [which happens to be a toy].
Maybe it could stimulate you to just talk to a rubber duck, as long as you haven't got anybody else to talk to.

There are those who do not do well with theoretical mathematics.  And they always consult a mathematician for that work when it comes up in their research.  This situation is OK.  (It is said that Einstein always had a mathematician handy to help him with his math.)  It may mean sometimes that the mathematician will be added as a co-author; and other times it may not.

off-topic, but who tended to be that mathematician? Minkowski?

@Ooker Here is a fun read (pdf): https://arxiv.org/pdf/1210.6929

When Einstein was at the Institute for Advanced Study, it seems he was allowed to hire a young mathematician as his "assistant".  Each one would stay for a few years, then continue with his career.   See a list here ... https://hsm.stackexchange.com/questions/1827/einsteins-assistants