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My goal is to find the general form for the asymptotic cardinality of a compound arithmetic progression. I'm not affiliated with a university and I certainly don't have any obligation to continue my research. However, it is very fulfilling to me. I spend my time in the library; I study through the books on the shelves and I don't really have anyone to tell me that my efforts are not good enough.
The problem comes in when I realized that if I was stronger in Analytic Number Theory, then I could start to look for the general estimate for the asymptotic cardinality of any compound arithmetic progression, and I'm terribly curious about how it works out. I am jealous of professional students with academic affiliations, access to reviewers, and journals; terribly. I admit that and it's a big obstacle. And I'm envious that they had the opportunity to enjoy more prestigious settings. I wish I could get a foot hold like that too. But at the same time I just don't think it's going to be possible for me to be published or be respected on the same level, no matter what I do.
Is it healthy for me to behave like this? Or am I being too optimistic in thinking that I have something to contribute that could blossom into graduate level, age appropriate research and/or a funded project?
The point is that I've given up looking for a degree or trying to participate in the research projects of others; it places the burden on them to find a place for me in their work and I'd rather be sharpening my own offering instead of going on a wild goose chase. Math doesn't require the same kind of budgetary overhead, or anywhere near the same level of oversight as the life sciences. I don't need a lab. I don't need dangerous chemicals or expensive equipment, and I don't need a workshop, either.
The other question (of which this was marked as a duplicate) was asked by a much more established individual that already finished a Master's degree and wanted to collaborate on somebody else's research; putting together a CV to apply for a research spot is much easier when there's something to anchor it.