As someone outside academia, how can I get my math paper peer reviewed?
Figure out what journal is appropriate. To do this, there are two aspects. One is essentially &quot;readers interested in the articles published there are likely to also be interested in your work&quot;, the other similar level of how ground-breaking the results are. Without a subscription, you should still be able to see the abstracts of the recently published papers, and quite often you'll be able to access the content somehow (preprint on the arXiv, author's website, scihub,...).
Once you have identified the one journal you want to submit to, just look for their &quot;instructions to authors&quot; or similar, and follow them. This will typically be very straight-forward. They might ask you for your affiliation, but you can just respond with &quot;Independent Researcher&quot; there. Then patiently wait for the referee reports (expect something between 3 months and 1 year).
If you've chosen in an inappropriate journal, or if your draft appears to be very off (eg almost no references), the editor of the journal could forgo sending it out to review, and directly reject it (&quot;desk reject&quot;). So make sure that your draft is sufficiently polished, and that you've picked a reasonable journal. On the upside, a desk reject will typically happen much faster.