[ronald_raygun]

My two cents - I got a BS in math and an MS in stats. A ton of this stuff is really hard and takes a lot of time to understand, and it really does help to have a bunch of time to dedicate to it, a professor to guide you, and friends to try problems with. It also really helps to be exposed to a good order to learn stuff (for example I'd suggest tons of functional analysis, then prob, then stats, then finally ML)

But once this stuff clicks it becomes very easy to teach yourself. I've been learning stuff like quantum algorithm, network analysis, etc.