Though calculations based on density functional theory (DFT) are used
remarkably widely in chemistry, physics, materials science, and biomolecular
research and though the modern form of DFT has been studied for almost 60
years, some mathematical problems remain. For context, we provide an outline of
the basic structure of DFT, then pose several questions regarding both its
time-independent and time-dependent forms. Progress on any of these would aid
in development of better approximate functionals and in interpretation