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. Hamilton was born in Dublin and educated there at Trinity College. In 1827, while still an undergraduate, he was appointed professor of astronomy and royal astronomer of Ireland. Hamilton showed that the sum of two complex numbers could be represented 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, for ij = - ji 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.