Electrodynamics is a different kind of field theory because it is universal, true on all scales. Maxwell's equations are remarkably accurate inside nuclei of atoms and between stars. Electrical forces are strong and often dominate behavior. One per cent charge imbalance is enough to lift the earth. Electrodynamics implies a universal conservation of current. Current is not just the flux of charge. Current includes Maxwell's displacement current  where  is a property of the vacuum found between stars and inside atoms.  is a true constant that never varies anywhere, anytime. Current exists in three spatial dimensions so ordinary differential equations in time---including the well stirred approximations of classical chemistry---have difficulty conserving current. Many classical models must be amended to conserve current. Applying field theory to chemical, biochemical, and biological systems creates great opportunities for mathematics, as illustrated by applications to the electrical properties of biological cells and ion channels.