Someone asked me about this, so here are my quick thoughts.

Although I've learned a lot of math over the last year and a half, it still isn't my comparative advantage. What I do instead is,

Find a problem

that seems plausibly important to AI safety (low impact), or a phenomenon that's secretly confusing but not really explored (instrumental convergence). If you're looking for a problem, corrigibility strikes me as another thing that meets these criteria, and is still mysterious.

Think about the problem

Stare at the problem on my own, ignoring any existing thinking as much as possible. Just think about what the problem is, what's confusing about it, what a solution would look like. In retrospect, this has helped me avoid anchoring myself. Also, my prior for existing work is that it's confused and unhelpful, and I can do better by just thinking hard. I think this is pretty reasonable for a field as young as AI alignment, but I wouldn't expect this to be true at all for e.g. physics or abstract algebra. I also think this is likely to be true in any field where philosophy is required, where you need to find the right formalisms instead of working from axioms.

Therefore, when thinking about whether "responsibility for outcomes" has a simple core concept, I nearly instantly concluded it didn't, without spending a second glancing over the surely countless philosophy papers wringing their hands (yup, papers have hands) over this debate. This was the right move. I just trusted my own thinking. Lit reviews are just proxy signals of your having gained comprehension and coming to a well-considered conclusion.

Concrete examples are helpful: at first, thinking about vases in the context of impact measurement was helpful for getting a grip on low impact, even though it was secretly a red herring. I like to be concrete because we actually need solutions - I want to learn more about the relationship between solution specifications and the task at hand.

Make simplifying assumptions wherever possible. Assume a ridiculous amount of stuff, and then pare it down.

Don't formalize your thoughts too early - you'll just get useless mathy sludge out on the other side, the product of your confusion. Don't think for a second that having math representing your thoughts means you've necessarily made progress - for the kind of problems I'm thinking about right now, the math has to sing with the

...