I saw this cool BBC documentary "Scotland's Einstein: James Clerk Maxwell - The Man Who Changed the World" few days ago, and as far I remember, Maxwell was good in math while his colleague and friend Faraday was an expert to EM. Maxwell accomplished to describe Faraday’s findings mathematically ending up with his famous set of equations. And when Maxwell tried to use his equations to calculate the speed of an EM wave, he found that the resulted speed was close to the (already measure at that time) speed of light. Consequently, he claimed (mathematically of course) that light is an EM.