Publishing outside acedemia

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I am an independent mathematician looking to publish an article related to number theory. It's not a very rigourous article but it's still interesting My first question is whow should I publish with? Also since I am independent, I'm not getting paid by a university. How much do journals pay for articles?

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Have you considered arXiv.org?

Renegade mathematician Grigori Perelman used this service to publish his proof of the poincaré conjecture. I don't believe he was (or is) supported by any institution.

Have you considered starting a blog to share your mathematical writings? I only bring that up because you say that your paper isn't very rigorous. This might be the most appropriate format for smaller or less academic pieces of writing. You could monetize the blog, but I wouldn't expect that it would make much money.

Like others have said, there isn't money in publishing mathematical papers--outside winning a prize for proving a famous conjecture.