Working on MIRI's current technical agenda mostly requires a background in computer science with an unusually strong focus on logic: see details here. That said, the scope of MIRI's research program should be expanding over time. E.g. see Patrick's recent proposal to model goal stability challenges in a machine learning system, which would require more typical AI knowledge than has usually been the case for MIRI's work so far.
MIRI's research isn't really what a mathematician would typically think of as "math research" — it's more like theory-heavy computer science research with an unusually significant math/logic component, as is the case with a few other areas of computer science research, e.g. program analysis.
Also see the "Our recommended path for becoming a MIRI research fellow" section on our research fellow job posting.
Currently I am planning to start a mathematics degree when I enter university, however my interest has shifted largely to computational neuroscience and related fields, so I'm now planning to switch to an AI degree when I go to study. Having said that, MIRI has always posed interesting problems to me, and I have entertained the thought of trying to do some work for MIRI before. And so my question boils down to this: Would there be any problem with taking the AI degree if I ever wanted to try my hand at doing some math for MIRI? Is a maths degree essential or would an AI degree with a good grasp on mathematics related to MIRI work just as well? Any thoughts or musings would be appreciated :)