Electricity and magnetism were studied as two separate, if related, branches of physics for most of scientific history — electric charges did one set of things, magnets did another, with connections between them noticed but not yet unified into a single coherent theory. James Clerk Maxwell's four equations, formulated in the 1860s, changed that permanently, describing electric and magnetic fields as two aspects of a single underlying phenomenon. Almost as a side effect of that unification, the equations made a prediction nobody had been looking for: a wave of oscillating electric and magnetic fields, travelling through space at a specific calculable speed — which turned out to match the known speed of light exactly.
Four equations, one unified electromagnetic theory
Maxwell's equations describe, in mathematical form, how electric charges create electric fields, how electric currents create magnetic fields, how changing magnetic fields create electric fields (the principle behind electromagnetic induction), and how changing electric fields create magnetic fields in turn. Individually, earlier scientists including Coulomb, Ampère, and Faraday had already discovered pieces of this picture. Maxwell's crucial contribution was bringing all four relationships together into one consistent mathematical framework, and in doing so, adding a term that hadn't previously been recognised as necessary — a changing electric field itself generating a magnetic field, completing a symmetry the earlier separate laws hadn't captured on their own.
An unexpected wave, moving at exactly the speed of light
Once assembled into a complete, self-consistent set, Maxwell's equations implied something startling: a changing electric field generates a magnetic field, and a changing magnetic field generates an electric field, meaning the two can sustain each other, propagating outward together as a self-perpetuating wave, entirely independent of any physical medium being disturbed. Maxwell calculated the speed such an electromagnetic wave should travel at, based purely on known electrical and magnetic constants measured in laboratory experiments unrelated to light — and the number that fell out of the calculation matched the experimentally measured speed of light to within the precision available at the time. That match wasn't a coincidence Maxwell had gone looking for; it was an unplanned, striking consequence of the mathematics itself, and it led him to the conclusion that light is an electromagnetic wave, unifying optics with electricity and magnetism into a single theory covering all three.
What we're still unsure about
Maxwell's equations remain a completely settled, extraordinarily well-tested cornerstone of classical physics, underpinning an enormous range of modern technology from radio to fibre optics, and there's no scientific dispute about their validity within their domain. What later physics revealed is a more subtle limitation rather than an error: Maxwell's equations, as originally derived, describe electromagnetism classically and don't, on their own, account for the quantum nature of light and electromagnetic interactions that quantum electrodynamics later incorporated — a refinement and extension of the classical picture rather than a correction of some mistake, reflecting how even a deeply successful theory can later be understood as an excellent approximation within a still broader framework.
This sits inside Maxwell's Equations, one of eight topics in Electromagnetism, one of five domains in Physics, one of seventeen subjects the app can quiz you on.