Which physicist later gave mathematical form to Faraday's field ideas?

James Clerk Maxwell later gave mathematical form to Michael Faraday’s ideas about electric and magnetic fields.

Faraday was a remarkably powerful experimentalist, but he did not express his field concepts in the mathematical language that many nineteenth-century physicists expected. He described lines of force as physically meaningful patterns linking magnets, currents, and charges. Maxwell recognized the importance of this approach and worked to translate it into mathematical theory.

Maxwell’s 1855–56 work on Faraday’s lines of force was an early step. During the 1860s he developed equations connecting electric and magnetic phenomena, showing that changing fields can propagate through space. In 1865, his paper “A Dynamical Theory of the Electromagnetic Field” argued that light itself is an electromagnetic disturbance.

The familiar four-equation form came later, after Oliver Heaviside and others reformulated Maxwell’s more extensive system. Thus Maxwell did not simply repeat Faraday’s discoveries: he built a quantitative framework that unified electricity, magnetism, and light.