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15 months ago, I improved the bounds for an open math problem which I think is worthy of publication. Later, 9 months ago, I came up with two further results that I also would like to publish. I have even confirmed with the authors whose work I have improved upon that my results are interesting and my techniques seem valid.

However, I have gotten myself hopeless lost in the editing process for my papers. With the pandemic, professors I know from college and REU have been too busy dealing with shifts in administration to take a look at my work. I’ve written drafts for two the results which I feel are “mostly there,” but I’ve been floundering when it comes to wrapping things up. I have some learning disabilities, and so on a number of occasions I’ve been stuck for an unreasonable amount of time on something basic such as clearly phrasing a particular definition. I have become frustrated with myself and the writing process because it doesn’t feel like I’m making progress anymore, which just drives me to write less.

Obviously, something has to change. To the best of my knowledge, my school does not have a writing center. I’m thinking I will have to pay a technical copy editor look at my work, and perhaps advice me on how clearly express some definitions. I was wondering if this would be looked down upon, and would devalue the worth of my papers. I am also interested to hear where I can find technical copy editors, and if there any other options I should consider.

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    Why don't you collaborate with the authors whose work you improved upon? Perhaps more improvements can be done and then you have a multi-author paper? Jan 31 at 14:34
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    I asked the author of one paper to collaborate, who declined. he is a professor with a bit of authority, and said that people would assume that he did most of the work if he was a coauthor (especially since I'm an undergrad). I guess I could ask the other group to collaborate, but I am nervous that I would come off as forward, since they are accomplished PhD students. perhaps I will make another post about inviting collaboration sometime... Jan 31 at 15:03
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    I'd strongly recommend to learn how to write well. If you plan on staying in academia (and probably also if not), it will be a big plus. And it will probably also help you to understand your ideas better (and thus make further progress), since a main part about presenting results well is having them clear and structured in your head.
    – user151413
    Jan 31 at 19:05
  • yes, it is my every intention to be a good writer. I am just struggling a bit with being able to discern what is the proper level of detail at some levels. I don't feel as if I yet have the experience to recognize when "of course this part will be clear and familiar to mathemeticians, there is no need to rehash it in detail here" or "this intuition/image is not well known yet valuable, I should dedicate several paragraphs and a diagram to make it very clear to the readers how it works". I understand how to be rigorous but not how to anticipate my readers and avoid unneeded pedantry. Feb 3 at 6:58
  • I find it comparable to explaining an 8-move checkmate. while it would be valid to present a brute force search of possible outcomes, this argument would not be accessible to readers. thus, one should rely at some level to use motifs to simplify the number of possibilities at hand. and while I have broken things into motifs, but I don't know where to stop and say obviously this is checkmate. Feb 3 at 6:59
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For scholarly work, as opposed to classwork, it is fine to ask for help whether you are an undergraduate or a full professor.

However, the nature of the help needs to be considered. For simple editing and phrasing, an acknowledgement of the help within the eventual paper is probably enough. But if it crosses the line to the point where the "helpers" are contributing ideas, then they become collaborators and co-authors.

Some publishers will provide technical copy-editors if that is all you need, but I think this is more likely for books than papers. It might even be that most of the editing you need can be done by a general text-editor as long as you vet what they suggest. Sometimes they will get it wrong and you need to be able to see and correct that. But such services are likely more available than someone with experience in your field.

After submission, some reviewers will suggest rephrasing as needed. But there is no guarantee of it. Telling an editor of a journal that you need a bit of help with the language might be worth the effort, but, again, no guarantees.

And, no, having collaborators and co-authors doesn't degrade the work. Collaborations with the right people can enhance it. But if you originated the key ideas you want to assure that you get credit for that. In some fields it is being the "first author". In others it is just a short paragraph describing contributions. But at such an early stage, any publication will help you along. There aren't a lot of people who achieve that.

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Getting help is fine, and so is asking that someone collaborate with you. However, asking someone to collaborate is asking them to commit a lot of time. I can only keep at most three collaborations going at a time and am selective about this.

Asking the other mathematician to be a collaborator was perhaps a mistake. It seems like you have a result, and what you need is assistance with the writing. There are options other that asking "please read my paper" which are more likely to get a response.

Ask a professor in your math department if they know of a writing center on campus. Ask the people who ran the REU for advice on what journal to submit to. You probably need help with latex, selecting a good title, writing a good abstract.

There might be a seminar in your department where you can make a presentation. It really helps to have a forum to talk this over. Of course, seminars are not what they were in the Before Times.

Everything is slower and harder during the pandemic. This is why I suggest small things, like help with a good title. You may have "On an improvement to the glorious theorem of Dr. X" and it would take a professor five minutes to suggest "Improving the bounds in the theorem of Dr. X."

Best of luck. These are good problems to have.

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You are in excellent company.

Nobel Prize winner Paul Dirac was famous for the difficulty he found in writing papers for publication where he would agonise interminably over phrasing. His colleagues in Cambridge jokingly defined a unit called a "dirac", which was one word per hour.

Ask for writing assistance and acknowledge it in your paper.

Good luck!

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    O what a measure, great. How many Diracs are a Flaubert? Feb 1 at 18:52
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I would ask the PhD/PostDoc association of the math department at your university for support in writing the paper.

You may find someone supportive, with some spare time to help you.

Good luck with your effort and thumbs up for being so passionate to embark yourself in writing a paper at such an early stage: the learning curve is steep, but it has to be done only once (ok, maybe two :D )

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