William Rowan Hamilton | Biography

Hamilton was a brilliant child prodigy. When he was five years old he knew Latin, Greek, and Hebrew, and before he was ten, he was fluent in Persian, Arabic, Sanskrit, Hindustani, and a host of other eastern languages. His father's hope was that he would eventually land a clerk position with the East India Company. But the young Hamilton had other interests. Science and mathematics fascinated him. As a teenager, Hamilton had absorbed Isaac Newton's Principia and began to develop a keen interest in astronomy. In 1822 he reported a mathematical error in the astronomer Pierre Laplace's Mécanique celeste. Thus was the genius of the impetuous Hamilton brought to the attention of the general scientific community.

Hamilton entered Trinity College in Dublin and so impressed his teachers with his brilliance that before he graduated, he was offered the position of Andrews Professor of Astronomy at the university. With the appointment went the title of Astronomer Royal of Ireland and the directorship of the Dunsink Observatory. Despite his mathematical genius, Hamilton had little skill as an observational astronomer, nor was he particularly interested in the observing programs then under way. Instead, Hamilton devoted his time to mathematical research.

His most important work was in the realm of complex numbers and a new branch of mathematics, which he invented, known as the algebra of quaternions. (A quaternion is a type of complex number of the form a + bi + cj + dk, where a, b, c, and d are real numbers and i, j, and k are imaginary.) Basically, his theory used geometric principles to manipulate complex numbers. He realized that the commutative principle of multiplication (i.e., 2 x 3 = 3 x 2) could not hold for his quaternions, a revolutionary idea in algebra. Hamilton's goal was that quaternions could be used to solve complex physics problems in 3-dimensions in a similar way that vectors, a term he coined after the work of Hermann Günther Grassmann (1809-1877) on vector analysis, could be used to represent forces. He used them, for example, in applications to geometry, optics, and mechanics. His dream came to fruition, a century later, when a non-commutative algebra became an integral component of the quantum theory of atomic structure.

Hamilton's professional successes did not carry over into his personal life. During most of his adult years, he mourned an unrequited love affair he had endured in 1825. After further rejections by other women, he eventually married Helen Bayly. The marriage was difficult, however, for Bayly was often in ill health and plagued by an almost morbid timidity. Although Hamilton, himself, was often energetic and full of good humor, he also experienced periods of depression and struggled with alcholism for much of the last decade of his life. He died from gout in 1865.