Hamilton, William Rowan (1805–1865)

Irish mathematician whose formulation of Isaac Newton's dynamics proved adaptable to quantum theory, and whose ‘quarternion’ theory was a forerunner of the branch of mathematics known as vector analysis. He was knighted in 1835.

Hamilton was born in Dublin. A precocious boy, he was reading Hebrew when just 7 years old, and had a good knowledge of 13 languages by the age of 13. In later life, he read Sanskrit and Persian for recreation. In 1827, while still an undergraduate at Trinity College, he was appointed professor of astronomy and royal astronomer of Ireland. His Theory of Systems of Rays was published by the Royal Irish Academy in 1828, followed by three supplements in 1830, 1831, and 1837. This work dealt with reflections from a curved mirror using what Hamilton termed the ‘characteristic function’ (and which is now known as the Hamiltonian). Later he used the same method to investigate systems of moving objects.

Hamilton showed that the sum of two complex numbers could be represented three-dimensionally by a parallelogram and that complex numbers could be used, in general, as a useful tool in plane geometry. From couples Hamilton went on to investigate triples and this led him to his great work on quaternions. He began to lecture on them in 1848, and revealed that for quaternions the ordinary commutative principle of multiplication (that is 3 x 4 = 4 x 3) did not work. This forced mathematicians to abandon their belief in the commutative principle as an axiom.

It was Hamilton who coined the word ‘vector’, and he made it possible to deal with lines in all possible positions and directions and freed them from dependence on Cartesian axes of reference.

Although Hamilton was famous and widely respected in his time, none of his ideas were utilized by other mathematicians and physicists until after his death, when the Hamiltonian function became important in the new science of quantum mechanics. The quaternions prompted 20th-century mathematicians to investigate other algebraic structures that are not commutative. He was renowned for writing incomprehensible books of great length; three volumes of his collected Mathematical Papers have been published (1931–67).