What is the best way for an amateur Mathematician to get their paper reviewed?

Question

Good Day All,

I am an amateur Mathematician humbly seeking your advice. I have just completed a math paper and would like someone to review it. I'm not an academic so I can't post it to sites such as arxiv.org but I can upload to vixra.org. However I'm aware vixra.org gets many crank submissions since anyone can post there. Do I have any other options or being an amateur, automatically places me in a position where I should post to sites of lower repute to have them viewed? Also, should I submit to a publisher immediately or seek to submit on a pre-printing site for review first? Any recommendations would be appreciated.

Thank you in advance.

Answer 1

Here is my comment with more details:

Quoting from https://arxiv.org/help/endorsement

If you're looking for an endorsement, you can find somebody qualified to endorse by clicking on the link titled "Which of these authors are endorsers?" at the bottom of every abstract. You can then find the email addresses of the submitter on the abstract page at the top of the"Submission history" section. It's best for you to find an endorser who (i) you know personally and (ii) is knowledgeable in the subject area of your paper -- a good choice for graduate students would be your thesis advisor or another professor in your department working in your field. If you do not personally know anyone who is eligible to endorse, you can search for recent submissions in your field of interest and then verify that the submitter is eligible to endorse. It is often a good idea to send eligible endorsers a copy of your proposed submission along with the endorsement request. Please note, however, that it is inappropriate to email large numbers of potential endorsers at once, or to repeatedly email the same endorser with a request for endorsement.

I.e. pick a paper relevant to the work (possibly one you cite) and find it on the arXiv (assuming it is there). Then find an author who is an endorser using the link mentioned (may take a few tries depending on how lucky you are). Then contact this person about your work and ask to be endorsed.

Here is some general advice when asking to be endorsed:
Make sure you explain precisely in the email what results you have proven, and preferably also the methods used. This will allow the person to get a first impression on the suitability.
As part of this, make sure the paper is presented nicely (use $\LaTeX$!) You will need to show the paper to the person (it is also mentioned on the arXiv page I linked that people should not endorse someone without checking the paper). But they need not do a full review of the paper, they just need to check that it seems like you know what you are doing (this is specifically mentioned on that page). So the time requirement is not particularly high.
That said, it may still easily take you several tries to find someone who wants to take the time to look at the paper (and each one may end up taking a long time to reply, simply because this sort of request is not of the highest priority).
To mitigate the above, make sure you pick the person you can find who is the most relevant, so they can see that they have not been picked at random. It may also help if they seem unlikely to receive a lot of such requests (not sure how to gauge this though). For example, I would probably not mind looking over a paper in my field for this purpose, but I am not an endorser, so I have no idea how many such requests people typically get. It will certainly also depend on the field (I am in a field where very few amateurs publish, whereas someone in number theory will be much more likely to be swamped by requests).