If you care about actually reading the nournals, as I do, and you had a very poor math education (as mine was abysmally opposed to both math and science as enemies of religion) then here are things I've determined I need to know to read journals:
- Core statistics. You need to be familiar with how statisticians treat data, because it comes up a lot.
- Calculus. You do not need to be a wizard at working the numbers but you do need to understand how to describe the process of differentiation and integration over multiple variables comfortably.
- Linear algebra. It's essentially the basis for everything, even more than statistics.
- Numerical nethods for computing. I constantly have to refer to references to understand why people make the choices they do.
- Theory of computation and the research clustered around it. Familiarity here helps a lot. Sometimes I even catch errors or am able to recognize improvements available. Also there is a lot of crossover, as one would expect. An example: everyone is remembering how good automatic differentiation is! And given that properly combined differentiable equations are also differentiable, AD let's you optimize over your optimization process. It's differentiable turtles all the way down.
My next big challenge is nonparametric statistics. Many researchers tell me that this is a very fruitful place to be and many methods there are increasingly making improvements in ML.