Everyone has heard of E = mc2 but there's another important discovery in physics that underpins most of modern technology and our understanding of the universe. In 1865, physicists were investigating three separate phenomena: light, electricity, and magnetism. It wasn't a single breakthrough in electricity or magnetism experiments that sparked the breakthrough, but the aggregation of multiple results that brought together a set of equations that provided a unified theory of light, electricity, and magnetism that become collectively known as Maxwell's equations.

By 1865, there was an inkling that these things could be connected, but it wasn't known how. Michael Faraday was actually the first try to form a unified theory, but his attempt was incomplete. James Clerk Maxwell, a younger physicist that had arrived at King's College London where Faraday was also stationed. Maxwell thought that Faraday was on the right path and eventually put together the unified theory.

Maxwell's equations are a set of 4 equations (originally it was 20, but we figured out how to simplify it). Really, only one equation can be attributed to Maxwell himself – Gauss's law for electricity, Gauss's law for magnetism, Maxwell-Faraday equation, and Ampère's circuital law (see Stigler's Law of Eponymy).

The real breakthrough was aggregating seemingly disparate results into one system. It's a different type of innovation than we usually see but sometimes more powerful. Lisp has been described by Alan Kay as the "Maxwell's Equation of Software" – see this interview. Building bridges between two vastly different things can lead to some of the most surprising results.

You can read Maxwell's paper in his original A Dynamical Theory of the Electromagnetic Field.