Can I publish a paper in a good journal without having an academic position?

Question

This community is introduced by a friend of mine about a week ago and I hope I can write my questions clearly (English is not my first language and I normally have poor communication skills...)

My story: I started my BSc in mathematics about 22 years ago (when I was age 9) and I decided (had to) quit after one painful semester that I still remember it. I studied on my own and a few years later I decided to solve the notorious impenetrable problem the Hodge conjecture. I have not achieved that goal yet but (I think) I have more than enough that people get a fields medal for that. And with my past experiences I believe that I am most probably not wrong in the technicalities (peer review need to be done though)... Nonetheless I can't continue working hard on the problem as I used to because of spending a lot more time on making money (from teaching to laboring jobs) so better to publish whatever I have to possibly get a research job than living a fading life and every-day-increasing severe-depression. But there are many obstacles I believe:

1- Can I publish an article without having an academic position and even without a university degree, at all?

2- I never care about fame and I absolutely don't care if solving some unsolved problem is attached to a particular name (=person) but handing over 18 years of my research to someone who have authority to easily publish it has a high risk of his/her plagiarism temptation thus ruining a possible would-be good life of mine. How can I trust someone?

3- Evaluation of my results is a necessity before I have any claim of that but if it turns out to be valuable enough can I get an academic position without having a physical degree and not going through all many years of official undergraduate and graduate programs in mathematics?

By the way, I hold an Iranian passport which means that I cannot travel Europe/US/Canada/... to present my research with just an invitation for a conference. (Visa-on-arrival is available for Iranian citizens in Mozambique or Samoa airports but I don't think that be helpful; no offense).

PS Please feel free to edit my post if my English is not clear. Thank you all in advance. :)

Answer 1

Variants of this question have been asked many times.

1. No, you do not need to have an academic position or be enrolled in a university to publish in journals.
2. You can prevent plagiarism (or at least make it easily detectable) by posting a preprint of your paper on arXiv. This establishes that you are the first person to come up with the idea.
3. It's doable, but rare.

Answer 2

Anyone can write a mathematics paper and anyone, degree or not, can submit it to a publisher. Some unscrupulous publishers will take your money and publish your work without thought, but that won't advance you in any way.

If you submit a paper to a reputable publisher and the editor thinks it has merit he or she will send it to a few reviewers for comment. The comments may be good or bad. Since you have been a bit isolated from the larger mathematical community is is even possible that what you have done isn't new, and you will be told that.

But if the reviewers find merit then you work can be published, possibly after some revision as suggested by the reviewers.

I suggest, however, that you also try to find a few people to help you. One, an independent mind, to look over the mathematics in your work to give you some external assurance that it is sound. The reviewers will certainly do that, but it might benefit you to have your own prior review. The other person you might want is someone more familiar with the language in which you want to publish, English or whatever it is.

For the other question about obtaining a position based on one paper, that is less likely. Ramanujan, of course, became a celebrity in the mathematical world with no advanced degrees and did some of the finest work in the previous century. But that is very rare. A Fields medal based on one piece of work would also be very rare.

For those who cannot travel to a conference venue, especially for political reasons, accommodations can be made to have a paper heard, even when the author cannot be present. The conference committee should be contacted in such cases, but the paper needs review before that can be considered.

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Let me add a note about Ramanujan. He was a brilliant mathematician who was blessed with the gift of thinking differently. But he would likely have labored in obscurity throughout his too-short life if he hadn't started his association with Hardy. It was that association that helped the world discover him.