It's hard to be sure it really happened this way, but I feel like my PhD began more with a research challenge and then went top down into learning what I needed

It's hard to be sure it really happened this way, but I feel like my PhD began more with a research challenge and then went top down into learning what I needed to to think about the challenge, and working back up to an academic framing of how the fundamental theory was advanced. We also had comprehensive exams, so you're forced to know the overall theory of your discipline as part of the rigor of the program. I personally like the challenge approach to research, it's like what companies call their "north star" sometimes. It's not that you're working directly on that problem necessarily, it's that you're identifying what would have to be true for that problem to be solvable and working on some of those things