In the mid-1800s, Maxwell discovered four powerful equations that, for the first time, set out a rigorous theoretical framework for understanding electricity, magnetism, and their intimate relationship.¹
1. For the mathematically trained reader, these four equations are
denote the electric field, the magnetic field, the electric charge density, the electric current density, the permittivity of free space, and the permeability of free space, respectively. As you can see, Maxwell's equations relate the rate of change of the electromagnetic fields to the presence of electric charges and currents. It is not hard to show that these equations imply a speed for electromagnetic waves given by 1√ε0μ0, which when evaluated is in fact the speed of light.
"The Fabric of the Cosmos" - Brian Greene