of Electricity and Magnetism, making use of the mathematics of potential theory developed by Continental mathematicians. But this paper fell on deaf ears until William Thomson read it, realised its significance, and had it re-printed in 1850. Green's work became a source of inspiration for the Cambridge school of mathematical physicists, which included Thomson himself, George Gabriel Stokes, and James Clerk Maxwell. Green's Essay contained what became known as Green's theorem, a basic result in vector calculus, Green's identities, and the notion of Green's functions, which appears in the study of differential equations. Thomson went on to prove Stokes' theorem, which earned that name after Stokes asked students to prove in the Smith's Prize exam in 1854. Stokes learned it from Thomson in a letter in 1850. Stokes' theorem generalises Green's theorem, which itself is a higher-dimensional version of the Fundamental Theorem of Calculus. Research in physics—in particular elasticity, heat conduction, hydrodynamics, and electromagnetism—motivated the development of vector calculus in the nineteenth century. Arthur Cayley is credited with the creation of the theory of matrices—rectangular arrays of numbers—as distinct objects from determinants, studied since the mid-eighteenth century. The term matrix was coined by James Joseph Sylvester, a major contributor to the theory of determinants. It is difficult to overestimate the value of matrix theory to modern theoretical physics. Peter Tait wrote, prophetically, that Cayley was "forging the weapons for future generations of physicists." Theoretical mechanics and optics Early contributions study of elasticity—how objects behave under stresses, pressures, and loads— employed ad hoc hypotheses to solve specific problems. It was during the nineteenth century that scientists began to work out a thorough theory. In 1821, using an analogy with elastic bodies, French professor of mechanics Claude-Louis Navier arrived at the basic equations of motion for viscous fluids. George Gabriel Stokes re-derived them in 1845 using continuum mechanics in a paper titled "On the Theories of Internal Friction of Fluids in Motion." In it, Stokes sought to develop a mathematical description for all known fluids that take into account viscosity, or internal friction. These are now referred to as the Navier–Stokes equations. In 1852, Stokes showed that light polarisation can be described in terms of what are now known as the Stokes parameters. The Stokes parameters for a given wave may be viewed as a vector. Founded in the eighteenth century, the calculus of variations grew into a much favored mathematical tool