Yeah, there are a lot of possible divisions and specializations in Math it's not even funny. Most of them unintelligible to "mere mortals".

Also hard to find a job, especially one that uses your work, unless you work in number theory, in this case you have a job at the NSA.

Number theory is an extremely broad field in itself. I'm pretty sure most of it is completely irrelevant to the NSA. If you do a PhD in any theoretical field you'll almost never find a job outside of academia that uses any of your work.

I've seen permanent adjuncts / post-docs. There was a guy at my old school who was there as a post doc. He did his PhD at UC Berkeley. I can't believe that he has been jumping around to different institutions as a post doc or lecturer for over 10 years. It's quite sad. My friend did his Ph.D at University of Oregon. It took him 6 years to finish it. Then he spent 2 years as a post doc at University of Toronto. He finally got a job back home at a small 4 year college. I guess he's doing what he set out to do: be a university math professor. But, I believe him being from Hawaii helped him land that gig. They prefer locals who want to go back home before considering others.

As an outsider I'm a bit frightened. I my (mostly estranged) cousin is a Maths researcher (from wikipedia it looks like he's at UCLA now). Once I was talking to a PhD student friend about him, and actually he had used my cousin's work in his field.

So I don't think there is no hope in research. Also I admit this whole citation, publication and plagiarism hunt is a toxic bullshit.