I’m somewhat sympathetic to this. You probably don’t need the ability, prior to working on AI safety, to already be familiar with a wide variety of mathematics used in ML, by MIRI, etc.. To be specific, I wouldn’t be much concerned if you didn’t know category theory, more than basic linear algebra, how to solve differential equations, how to integrate together probability distributions, or even multivariate calculus prior to starting on AI safety work, but I would be concerned if you didn’t have deep experience with writing mathematical proofs beyond high school geometry (although I hear these days they teach geometry differently than I learned it—by re-deriving everything in Elements), say the kind of experience you would get from studying graduate level algebra, topology, measure theory, combinatorics, etc..
This might also be a bit of motivated reasoning on my part, to reflect Dagon’s comments, since I’ve not gone back to study category theory since I didn’t learn it in school and I haven’t had specific need for it, but my experience has been that having solid foundations in mathematical reasoning and proof writing is what’s most valuable. The rest can, as you say, be learned lazily, since your needs will become apparent and you’ll have enough mathematical fluency to find and pursue those fields of mathematics you may discover you need to know.
I’m somewhat sympathetic to this. You probably don’t need the ability, prior to working on AI safety, to already be familiar with a wide variety of mathematics used in ML, by MIRI, etc.. To be specific, I wouldn’t be much concerned if you didn’t know category theory, more than basic linear algebra, how to solve differential equations, how to integrate together probability distributions, or even multivariate calculus prior to starting on AI safety work, but I would be concerned if you didn’t have deep experience with writing mathematical proofs beyond high school geometry (although I hear these days they teach geometry differently than I learned it—by re-deriving everything in Elements), say the kind of experience you would get from studying graduate level algebra, topology, measure theory, combinatorics, etc..
This might also be a bit of motivated reasoning on my part, to reflect Dagon’s comments, since I’ve not gone back to study category theory since I didn’t learn it in school and I haven’t had specific need for it, but my experience has been that having solid foundations in mathematical reasoning and proof writing is what’s most valuable. The rest can, as you say, be learned lazily, since your needs will become apparent and you’ll have enough mathematical fluency to find and pursue those fields of mathematics you may discover you need to know.