As a student where should he first approach for review of his paper, even more so a first one, before submitting to peer reviewed journal? Teachers tend to be busy with school and personal work, soliciting or emailing a person out of the blue may not be the ideal etiquette, while students in one's class may not have the required background. What to do in this situation?
Do any websites exist (other than arXiv) that allows for a process that critique papers?
Thank you.
There seems to be a disconnect here: If your result is anywhere near something that can be published in a journal, it will be infinitely more interesting for your professors to read than grading homework. It makes no sense to compare how busy they are with one, to how much time they'd have for the other. That's like thinking someone is so busy with washing dishes that they'd never have time to come eat a slice of your home-baked cake. Sure, the cake may or may not be horrible, but you're not going to judge that by how many dishes they wash.
So if you are enrolled as a student in a relevant program, the first and obvious people you should consult are your teachers. They will be excited and delighted if it turns out you have discovered something publishable, and if not, well, then it's part of their job to let you know in a gentle way.
As a practical matter, your first approach probably shouldn't be about the paper itself, but about the result. Instead of
say something like
Possible responses then include: