How did James Clerk Maxwell show that light is an electromagnetic wave?

James Clerk Maxwell demonstrated that light is an electromagnetic wave by mathematically unifying the laws of electricity and magnetism into a set of four equations, now known as Maxwell’s equations.12

By manipulating these equations, Maxwell derived a wave equation that described the propagation of transverse electric and magnetic disturbances through the electromagnetic field. Crucially, his theory predicted that these waves would travel at a specific velocity determined by the constants of electrostatics and magnetostatics.13

When Maxwell calculated this theoretical speed using available experimental measurements, the result was approximately $3\times {10}^8$ metres per second—a value that matched the known speed of light at the time. This coincidence convinced Maxwell that light was an electromagnetic disturbance propagated through the field. He formally asserted this conclusion in his 1864 lecture, "A Dynamical Theory of the Electro-Magnetic Field," effectively unifying the fields of electricity, magnetism, and optics.134