Is there any way a pure math guy can get his rigorous math fix while simultaneously moving fusion research forward? Is fusion simply too complicated to take a pure math approach? What open math questions are there pertaining to fusion?
There's a lot of research being done in computational magnetohydrodynamics. This is the study of the flow of ionic fluids, usually in confined magnetic fields. The governing equations of magnetohydrodynamics are a coupling of both the Navier-Stokes equations and Maxwell's equations of electromagnetism. In pure/applied mathematics there is the famous problem of smoothness in solutions to the Navier-Stokes equations.
Most of the problems in fusion energy are mostly engineering problems but there is still a lot of theoretical work being done.