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I am an independent researcher in mathematics. I wrote a research paper and I intend to publish it.

It is my first math research paper, I have no prior experience in this.

I submitted my paper to multiple journals, but they found out about the multiple submissions and replied negatively.

I tried to list my article on arXiv, but they require endorsement, which is hard to get.

These days I have been sending about 40 emails per day to either universities professors and to authors on arXiv and ask for the endorsement.

So far zero success.

My article is about number theory. First year at uni math knowledge should be enough to understand.

Can I please have an advice?

Publishing an article seems to be a real nightmare.

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    Your question seems to be more or less: What do I have to know in order to get a manuscript published smoothly? That's a rather broad question, probably too broad to be answered properly here. It would be best if you knew somebody personally who has experience with publishing and can guide you. Anyway, what you have learned already is that simultaneous submission to multiple journals is strongly frowned upon. There are various questions on this site about that. Dec 27, 2022 at 16:53
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    A research paper should prove theorems that no mathematician currently knows and no mathematician could figure out easily from what they know. Given how much number theory is already known, it is extremely unlikely that a paper that can be understood with first year uni math knowledge has theorems no mathematician currently knows (or could easily figure out). Dec 27, 2022 at 17:27
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    Don't most journals require authors to make a declaration at submission time that the manuscript isn't under consideration by any other journals? If so, one good piece of advice to OP might be "don't lie in declarations, and if you must lie in declarations, don't get caught". Dec 27, 2022 at 18:21
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    I think Bryan Krause has given an excellent answer to this question, thereby demonstrating that the question is answerable as it is. Thus, I voted to reopen.
    – Arno
    Dec 28, 2022 at 11:30
  • Here is some more advice. The first option is to break up your paper into questions suitable/acceptable to math.SE. There's plenty of expertise on that website capable of determining the correctness of your ideas. If the math.SE option doesn't work, consider googling the following phrase: math PhD tutor. There is a surprising number of math PhDs offering their services as math tutors. They can quickly determine the correctness of your work, where the faults are if they exist, and what to do about it if it's correct...
    – ShyPerson
    Jan 14, 2023 at 2:15

2 Answers 2

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It is my first math research paper, I have no prior experience in this.

The purpose of PhD programs is to train people to do research, including the process of publishing papers. If you're an independent researcher with no prior training, you should not expect this to be easy and likely not even possible. Imagine if instead your post was "I'm an independent carpenter with no prior experience. I have some wood and I'd like to build a house; I put in some nails but no one wants to live there even though I've been handing out pictures of my wood pile to people on the city bus. Please help." I don't write this to be rude, I write this to help explain that doing and publishing research is a trained profession, and no one without training should expect they can do it without training, and that this is totally okay and does not mean you don't have potential to publish good research or talent any more than someone with interest and talent in carpentry is not expected to build houses from scratch with just that interest and talent.

I submitted my paper to multiple journals, but they found out about the multiple submissions and replied negatively.

Yes, they replied negatively because this is extremely rude behavior - reviewing a manuscript in academia takes volunteer time. You've asked a bunch of different volunteers to simultaneously spend their valuable time all on your manuscript rather than the many others they've received to review. An advisor would have helped you avoid this.

I tried to list my article on arXiv, but they require endorsement, which is hard to get.

ArXiv requires endorsement because they're trying to limit the amount of junk that gets posted on their site. An advisor could help you with both the endorsement part and with knowing whether your paper is useful or junk.

These days I have been sending about 40 emails per day to either universities professors and to authors on arXiv and ask for the endorsement.

This is also rude. Don't do this.

My article is about number theory. First year at uni math knowledge should be enough to understand.

If your article is understandable with just first year university math knowledge, it might be a good demonstration of what you understand about first year university math, but it is almost certainly not useful research-level mathematics, the kind that gets published in journals. An advisor would help you understand what sorts of papers are useful to publish and whether yours fits this category.

Can I please have an advice?

You need a research advisor/mentor. One way to obtain such a mentor is to apply for graduate programs - PhD programs and many masters programs provide mentorship in research; for PhD programs it's the main point. It may be possible to find someone to mentor you even without formally enrolling in a program, but this is also difficult - possibly more difficult than applying the normal way (why should a professor spend time mentoring someone who isn't admitted to their program, when they have other students who are admitted that also have questions?). You're more likely to convince someone to be your mentor if they appreciate your potential for research rather than this paper in particular.

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    Hmmm. The advice is good, but you are a bit harsh on a newbie in the first paragraph. A newbie on several levels, actually.
    – Buffy
    Dec 27, 2022 at 17:30
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    @Buffy I don't consider it harsh to let someone know that they shouldn't expect to be able to do something that requires training without having training. It doesn't reflect poorly on them at all to be unable to publish research without training in publishing research.
    – Bryan Krause
    Dec 27, 2022 at 17:43
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    I think the first paragraph is a work of art. The carpentry quote is a worthy candidate for the Academia.SE Hall of Fame, right along with the Holy Grail, or some other famous cup.
    – cag51
    Dec 27, 2022 at 17:57
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    The advice in this answer may be “a bit harsh”, but it is also truthful, informative, and useful. In other words, it is just the sort of advice people come to this site to receive. I’ll take such advice any day over the polite but mostly useless advice that some people here seem to prefer.
    – Dan Romik
    Dec 28, 2022 at 4:59
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    @stevec: In modern math, it is next to impossible to have "brilliant subject knowledge" without proper training. At the same time, amateurs sometimes do solve important math problems (in areas where very little depth of knowledge is required, see e.g. here). Dec 29, 2022 at 3:18
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First, congratulations on your result!

One of the rules is that you can't submit a paper to more than one place at the same time. Also, there are different kinds of mathematical journals. If you submit a paper to a journal, you want to make sure your paper is suitable to that journal.

The reason your e-mails are not getting responses is because mathematicians do in fact receive e-mails from people who are almost certainly writing faulty proofs, so their "default" position is to not respond to your e-mail.

I recommend that you find an established and trusted mathematician who agrees to take the time to understand your result. Is there a local college or university you can go to? Going to a secretary at a physical location would probably be a better bet than e-mailing. I think a liberal arts college (if you're in the US) would likely be more welcoming than a research university.

Do you know anyone who knows the mathematical background to determine correctness? Maybe an undergraduate math major?

Wait a minute: was your paper by any chance about the Riemann hypothesis? I got an e-mail from someone about this a couple days ago.

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