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.