You can send it to a journal as a private individual, but probably a better way would to post a manuscript on arxiv.org, and once it generates certain buzz (if the problem is interesting and well solved) then either submit it to a journal yourself or partner with other mathematician to polish it, etc. and then submit.

To be able to submit to arXiv, one needs to be endorsed by someone in the domain, which could be a potential hurdle for someone not in academia. (and I'm not about to suggest viXra as a way to get around that)

Yeah, I actually used to be a math post-graduate and have a draft of a paper with an interesting result, so I wanted to publish it but I had no idea how to get "endorsed". This was like 10 years ago and I switched to a career in programming so I doubt I'll even understand my own proof now.