William Rowan Hamilton

William Rowan Hamilton was an Irish mathematician, physicist and astronomer who reformulated the equations of classical mechanics into a new form, now called Hamiltonian mechanics, that describes the motion of a physical system through a single function representing its total energy rather than through Newton's original force-based equations. This reformulation turned out to be far more than a matter of mathematical convenience: its structure carried directly over into the later development of quantum mechanics in the twentieth century, making it one of the most consequential single contributions to theoretical physics. In 1843, while walking along Dublin's Royal Canal, Hamilton had a sudden insight into a new four-dimensional number system he called quaternions, which extend the two-dimensional complex numbers and required him to abandon the ordinarily assumed commutative law of multiplication, a radical step at the time that helped open the door to modern abstract algebra. Hamilton also made significant contributions to optics, correctly predicting the previously unobserved phenomenon of conical refraction in certain crystals, and he spent much of his career as Andrews Professor of Astronomy at Trinity College Dublin and director of Dunsink Observatory, receiving a knighthood in 1835 and the Royal Society's Royal Medal the same year.