How does one get into financial math? I’m an algebraic number theory guy with a background that includes quite a few things under the sun (lots of analysis, algebra and more pure math of various flavors) but I’ve long neglected applied math (outside of some mathematical physics). I took a course in statistics many years ago which went over enough to do an actuarial exam but that’s about it.

I’m interested in learning some financial math on the side but I don’t know which topics would be most relevant for getting started nor how one really gets started. I’d imagine some math stats (a book recommendation would be appreciated since I’m clueless on this stuff) would be among a start but are there other topics which may be useful (game theory, machine learning, etc.)?