William Rowan Hamilton (4.08.1805—2.09.1865) was an Irish mathematician and physicist and a member of the Royal Irish Academy (1832), and its president in 1837—45. He was born in Dublin. He graduated from Trinity College of the University of Dublin (1827). From 1827 he was professor at the University of Dublin and director of the astronomical observatory. His research in physics was in the field of optics and mechanics. He developed a theory of optical phenomena (“mathematical optics”). He established (1834) an analogy between classical mechanics and geometrical optics. In other words, he showed that the mathematical apparatus he had developed for solving the problems of geometrical optics, which rests on the use of the so-called characteristic function (Hamilton's function), can also be interpreted in the language of wave theory. In 1828 he predicted the phenomenon of conical refraction in a crystal, which was soon proved experimentally and played a certain part in the establishment of the wave hypothesis of light. The analogy between corpuscular and wave optics developed by Hamilton was almost entirely forgotten for a long time, and only a hundred years later it was used by E. Schrödinger in working out his wave mechanics.
Hamilton extended his theory of optical phenomena to mechanics, developing its new general principles, and in particular the variational principle. Hamilton's mechanical principle is analogous to Fermat's optical principle. The analytical apparatus of mechanics, which Hamilton discovered on the basis of a synthesis of the problems of optics and mechanics, was developed further in the work of the German mathematician C. Jacobi and of M. V. Ostrogradsky. Hamilton's matrix apparatus is used in solving problems of quantum mechanics. In 1839 he introduced the concept of group velocity (for a long time this was credited to G. Stokes and J. Rayleigh).
He constructed a distinctive system of numbers, the quaternions.
A member of a number of academies of sciences, including the St Petersburg Academy of Sciences (1837). The Royal Medal (1836).