I was a former math college student with a 3.9+ GPA (overall, and in my math classes). I took most of the key classes to go to grad school, e.g. groups, rings, and fields, upper-level real analysis, graduate-level complex analysis, mathematical logic, point-set topology, etc. I chickened out of applying to math graduate programs because I was intimidated by my peers and didn't think I had a shot at a top program. I wasn't an Olympiad winner, didn't do research, etc. I'm now realizing that was a mistake. In retrospect, while I wasn't about to get into MIT or anything, I definitely should've given graduate school applications a meaningful shot before chickening out.
Now, I'm at a great law school. It's fine, but it's definitely not where I feel like I'm meant to be. I'm signing up for math classes next year at the Faculty of Arts & Sciences in algebraic topology, groups, rings and fields (to brush up), and topology (again, to brush up).
I'm wondering if someone could give me a realistic picture of what applications will look like. I want to apply to math programs now. I'm considering both Masters (to wet my feet again, and buy myself some time) and PhD programs. I will have good references. The school I'm at has a top math graduate department, so hopefully good grades in my math classes next year will give a slight boost to my application to this particular school.
There's a part of me that is still unsure whether lack of research experience or a contest math track record will significantly disadvantage me from getting into a top PhD program. I don't think it would be a good decision given my priorities to go to any PhD program I get into. It'd just set me back a few years to get into roughly the same jobs in industry/law/finance, but I would definitely set aside the law for a few years to "indulge" my passion if I get into a top program that could promise a meaningful academic career or a very math-heavy career in industry/government, e.g. NSA, robotics, AI, etc. My peers, whom I outperformed, are at great schools (top 20), but not the best. I wasn't very confident in college, but I'm wondering if that means I have a decent shot at a top 10 program. (This is not to put them down! I guess I just had a very fragile sense of self-esteem then...)
As far as my interests go, my comparative advantage and my biggest passion was in abstract algebra and complex analysis, so I'm leaning towards algebraic topology, algebraic geometry, or a related field.