Maxwell's equations, 1873.
James Clerk Maxwell was truly a genius. Although his greatest contribution to science was his theory of electromagnetic radiation, and his second greatest contribution was his theory of the distribution of the speeds of molecules in gases, he made significant and important advances in a number of other areas as well. Altogether he wrote about 100 scientific papers and 4 books. He was also the joint scientific editor of the 9th edition of the Encyclopaedia Britannica and wrote many of the articles therein. During the last few years of his life he devoted a great deal of time to editing the un-published researches of Henry Cavendish, which is now recognized as a classic in the history of science. He tended to work on several topics simultaneously with the result that there was often an interval of several years between papers on the same subject! Indeed, twelve years elapsed between his two most important papers on the kinetic theory (1867 and 1879) and six years between his two papers on his electromagnetic theory (1855 and 1861).
Of the major achievements in science since the birth of 'modern science' in the 16th century, arguably there are two that stand out because of their significance and influence and the way they unified 'ideas'. The first was due to Newton; as we have already seen, his Principia unified, in terms of a few simple laws, pretty much everything that was known about motion. Apart from some 'corrections' required to make his ideas consistent with relativity (i.e., for objects traveling at speeds approaching that of light), which we rarely encounter except in the study of atomic and subatomic particles, his laws remain the corner-stone for the science of mechanics. Nearly two centuries later another 'unification' occurred when James Clerk Maxwell united what was known about electricity, magnetism and light. At the time of Newton, little was known about electricity and magnetism and light. Electrostatic and magnetostatic phenomena had been studied by Franklin, Gilbert and others but no one suspected any connection between them although in the decade or so beginning in 1820 some interesting phenomena were observed. For instance, in 1820 Hans Oersted (1777-1851) discovered that an electrical current would deflect a nearby magnet; Andre-Marie Ampere (1775-1836) discovered that two parallel wires carrying an electrical current would attract (or repel) each other (depending on the relative directions of the current) and in 1832 Michael Faraday (1791-1867) discovered that a changing (or moving) nagnetic field gave rise to an electrical current. Clearly, then, electrical and magnetic effects were very much related to each other. It was Maxwell who showed how the two phenomena could be unified; he provided a very neat mathematical description, now known as Maxwell's equations, appearing fully developed in 1873, that form the basis of our understanding of his electromagnetic theory. He predicted that electrical charges that were accelerating - for example, oscillating or moving in a circle - would produce electromagnetic waves that propagate through space at the speed of light. Indeed, he proposed that visible light itself is therefore an electromagnetic wave:
It is reported that he scurried around the house tracing the wiring that connected the room bells to the servant's quarters and would excitedly drag his parents around showing them his discoveries. He was privately tutored until he entered Edinburgh Academy at the age of ten. His curiosity remained unscathed although his schoolmates considered him odd and often taunted him with the nickname "Dafty". At the Academy, after a slow start, he began to display extraordinary talents, in both mathematics and the writing of English verse. He maintained an interest in building models of polyhedra and devising new ways to draw curves, and when he was 15 he won the Academy's mathematics medal for a paper he published on drawing generalized ovals with pins and thread. When he was 16 he visited William Nicol, the inventor of the polarizing prism, and on returning home he built a device to study the patterns for colored polarized light. He made careful colored drawings of his observations and sent them to Nicol. He was rewarded with a set of polarizing prisms that he treasured for the rest of his life. A few years later he presented two papers to the Royal Society; one "On the Theory of Rolling Curves" and another "On the Equilibrium of Elastic Solids". Both papers were read before the Society by somebody else because "it was not thought proper for a boy in a round jacket to mount the rostrum there." After six years at the Academy and three years at the University of Edinburgh, he entered Peterhouse College, Cambridge in 1850, where most Scottish students went. He transferred to Trinity College shortly afterwards where it was easier to obtain a fellowship. He became a favorite with his professors ... it was said that it is
He was second on the Mathematical Tripos examination and won a Trinity fellowship. He graduated with a degree in mathematics with high honors in 1854.
Maxwell remained at Trinity for another two years, studying Michael Faraday's works on electricity and following his own researches on mathematics, geometrical optics and the theory of color. In 1856 he was elected to the Professorship in Natural Philosophy at Marischal College, Aberdeen, where he completed the first of his many remarkable contributions in mathematical physics. An essay he wrote on the rings of Saturn won the Adams Prize for 1857 ; he showed that their stability could be achieved only if they comprised numerous small solid particles (an explanation now confirmed by the Voyager spacecraft). Two years later he married Katherine Dewar, the daughter of the Principal, and in a note to his aunt he said
It was also at Aberdeen that he became interested in the kinetic theory of gases and solved the problem of the distribution of velocities among the molecules of a gas, the Maxwellian distribution. While the formal proof was challenged there is no doubt of the correctness of the final result. The theory was statistical, meaning a change from the concept of certainty - heat viewed as flowing from hot to cold - to one of probability - molecules at high temperature (high velocity) have a high probability of moving towards those at low temperature (low velocity). The earlier ideas of thermodynamics were not rejected; they were simply recast in a better theory that explained observations and experiments. In 1860 a reorganization at Aberdeen left him without a position. After failing to get the vacant Chair at Edinburgh he was appointed Professor of Natural Philosophy at King's College, London in 1860, where he remained for five extremely creative years. He made the acquaintance of Faraday, who was Director of the Royal Institution until 1861. He completed his work on the theory of color, developed his theory of electricity and magnetism, refined further his kinetic theory of gases and investigated experimentally the viscosity of air at different temperatures and pressures; the latter formed the subject of a Bakerian Lecture to the Royal Society, which he presented in 1866. Also in 1866 he published a paper on the Dynamical Theory of Gases in which some errors in his earlier publication on the kinetic theory - pointed out by Rudolph Clausius (1822-1888) - were corrected. He worked also with Stewart and Jenkin in experiments to determine the absolute value of the unit of resistance, the ohm.
At the end of the 1865 academic session, shortly after finishing his paper on the Dynamical Theory of Gases, he resigned his professorship and moved to his estate, Glenair, near Edinburgh. There, he could devote more time to his scientific studies and to the study of English literature. During the next few years he completed the major part of his treatise on electromagnetic theory, although it was not published until 1873 . Meanwhile at Cambridge, it was felt that students were not receiving an adequate background in the growing field of experimental physics. Maxwell partly inspired and lent active support to the movement to establish a new school of physics, with a Chair in experimental physics, and a fine physical laboratory. In 1871 the University approved the Chair and Maxwell was appointed professor of experimental physics and director of the newly established Cavendish Laboratory, named after Henry Cavendish.
Maxwell devoted a good deal of time and effort to the building and furnishing of the new Cavendish Laboratory. It was officially opened in 1874 and rose rapidly to prominence to become one of the premier laboratories in the world. His personal interests during this period were given chiefly to lecturing and to editing the unpublished papers of Henry Cavendish  whose work on electricity greatly impressed Maxwell not only because of its originality - outlined in the brief biography of Cavendish - but because it anticipated several discoveries made later by others. Sadly, he did not live to see his crowning achievement - the theory of the electromagnetic field - verified by experiment, for he died at the age of 48 years in November 1879, some eight years before Hertz demonstrated the existence of electric waves. It was after Hertz verification that Maxwell's genius was fully recognized.
As a lecturer, Maxwell was often too far above the heads of his audience, but as a teacher his curiosity and enthusiasm excited his students. As Director of the Cavendish Laboratory he brought his dog, Toby, to his office. He remained just outside the social mainstream, in a world of his own; he hated starched clothes, he recycled everything he could, he traveled 3rd class preferring the hard seats, he never drank wine, and would be distracted by such simple things by the refraction of light by water glasses. He adored poetry and wrote a good deal himself, both serious and humorous.
Maxwell gave mathematical form to Faraday's ideas of electrical phenomena. He derived a set of equations that relate all known electric and magnetic phenomena; the equations give quantitative relations between electric and magnetic fields, and the charges, currents and time-varying currents producing these fields. They contain Coulomb's law of the force between electrical charges as well as the corresponding law for magnetic poles; Oersted's discovery, in 1820, that moving charges, i.e., an electrical current, could produce a magnetic field, an effect that Ampere studied in detail over the next seven years; Faraday's discovery that a changing magnetic field would induce an electrical current in a circuit and Lenz's law on the direction of the induced current. The equations contain all of this information plus a lot more for they include Maxwell's hypothesis that electric waves should proceed from oscillating electrical currents and travel through space at the velocity of light. Given the electric and magnetic forces at some initial time, Maxwell's equations allow one to determine them for all future time. It was Richard Feynman who said
For years there appeared to be no way to test Maxwell's theory. However, Heinrich Hertz (1857-1894) succeeded in producing and detecting electromagnetic waves. Although his life was relatively short, Hertz was very much a "hands-on" scientist. By generating sparks between two metal spheres, which he was able to detect at some distance from the source, he proved the presence of electromagnetic waves. By moving the detector around he found that the signal increased and decreased in intensity, just like a standing wave. He measured the wavelength and frequency of these waves and deduced that they traveled with the speed of light, as Maxwell had predicted. Hertz also went on to show that these waves could be reflected, refracted, polarized and made to interfere. He showed that in every way his waves behaved exactly like light waves. Hertz' studies led to the development of radio communications, which, today, represent one of the major branches of our civilization.
 The Prize, established in 1848 and awarded at intervals for the best solution to some problem of great scientific importance proposed by the examiners, put Maxwell among the highest ranks of his contemporaries in science.
 J.C. Maxwell, A Treatise on Electricity and Magnetism (1st ed., 1873; 2nd ed. 1881, 3rd ed. 1891).
 J.C. Maxwell, The Electrical Researches of the Hon. Henry Cavendish (Cambridge University; Cambridge, England, 1879).
M. Shamos Great Experiments in Physics (Dover Publications Inc., New York, 1987).