I've purposefully overstated in the title a bit, but it's sort of true. I'm a team lead likely on my way into middle/upper management as a corporate/enterprise programmer. I don't hate management. I like teaching and helping the people around me, and there are some aspects of project management and organization I find interesting. That said, I find myself thinking frequently about a quote by James Clerk Maxwell about how his proper line was in working, not "ruling." I'm much more passionate and at home when I'm solving problems and learning new things.
I'm self-taught, and I'm trying to determine what things to learn next that I can usefully apply (and market!). I've bought a lot of math books to go back and fill in the gaps I have from not studying quantitative subjects in college. I've also bought some systems programming books (in-depth stuff on Linux, database, and distributed systems). But I find that in my day-to-day as a largely CRUD dev, I don't get to apply much of this stuff.
Mainly what I like to do is discover and solve real problems. That's how I got into IT in the first place—I worked in an operational job in finance and wanted to solve my own problems. But now that I understand enough of the stack to solve those problems, what I'm really looking for is interesting problems of moderate to high complexity. But I have no idea where to go looking for those. An example of a field that looks interesting to me is bioinformatics, but I'm not sure how to approach a field like that as a self-taught person with an inapplicable degree. More than anything I just would like to find some interesting problems to work on professionally.
Any and all thoughts and suggestions are greatly appreciated!