William Rowan Hamilton

Early life

William Rowan Hamilton was born on 4 August 1805 in Dublin, Ireland, the fourth of nine children of Archibald Hamilton (1778–1819) and Sarah Hutton, who lived at 29 Dominick Street (later renumbered to 36). Archibald, who was from Dublin, worked as a solicitor. By the age of 3, Hamilton had been sent to live with his uncle James Hamilton, a graduate of Trinity College Dublin who ran a school in Talbots Castle in Trim, County Meath.

Hamilton is said to have shown talent at an early age. His uncle observed that Hamilton, from a young age, had displayed an uncanny ability to acquire languages — a claim which has been disputed by some historians, who claim he had only a basic understanding of them. At the age of seven, he had already made progress in Hebrew, and before he was 13, he had acquired, under the care of his uncle, a dozen languages: classical and modern European languages, Persian, Arabic, Hindustani, Sanskrit, Marathi and Malay. The emphasis of Hamilton's early education on languages is attributed to the wish of his father to see him employed by the British East India Company.

An expert mental calculator, the young Hamilton was capable of working out some calculations to many decimal places. In September 1813, the American calculating prodigy Zerah Colburn was being exhibited in Dublin. Colburn was 9, a year older than Hamilton. The two were pitted against each other in a mental arithmetic contest, with Colburn emerging as the clear victor.

In reaction to his defeat, Hamilton spent less time studying languages, and more on mathematics. At age ten, he stumbled across a Latin copy of Euclid; and at twelve he studied Newton's Arithmetica Universalis. By age 16, he had covered much of the Principia, as well as some more recent works on analytic geometry and differential calculus.

Later life and death

Hamilton retained his faculties unimpaired to the last, and continued the task of finishing the Elements of Quaternions which had occupied the last six years of his life. He died on 2 September 1865 at the age of 60, following a severe attack of gout. He is buried in Mount Jerome Cemetery in Dublin.

Context and importance of the work

Hamiltonian mechanics was a powerful new technique for working with equations of motion. Hamilton's advances enlarged the class of mechanical problems that could be solved. His principle of "Varying Action" was based on the calculus of variations, in the general class of problems included under the principle of least action which had been studied earlier by Pierre Louis Maupertuis, Euler, Joseph Louis Lagrange and others. Hamilton's analysis uncovered a deeper mathematical structure than had been previously understood, in particular a symmetry between momentum and position. The credit for discovering what are now called the Lagrangian and Lagrange's equations also belongs to Hamilton.

Both the Lagrangian mechanics and Hamiltonian approaches have proven important in the study of continuous classical systems in physics, and quantum mechanical systems: the techniques find use in electromagnetism, quantum mechanics, relativity theory and quantum field theory. In the Dictionary of Irish Biography David Spearman writes:

The formulation that he devised for classical mechanics proved to be equally suited to quantum theory, whose development it facilitated. The Hamiltonian formalism shows no signs of obsolescence; new ideas continue to find this the most natural medium for their description and development, and the function that is now universally known as the Hamiltonian, is the starting point for calculation in almost any area of physics.

Many scientists, including Liouville, Jacobi, Darboux, Poincaré, Kolmogorov, Prigogine and Arnold, have extended Hamilton's work, in mechanics, differential equations and symplectic geometry.

In 1824, Hamilton was introduced at Edgeworthstown to the novelist Maria Edgeworth, by The Rev. Richard Butler, vicar of Trim, County Meath, to whom his uncle James Hamilton was curate. During the same period, his uncle introduced him to the Disney family at Summerhill House, County Meath. The Disney sons attended Trinity College, and Hamilton had friends among them. At Summerhill, he met Catherine Disney, their sister.

Hamilton was attracted to Catherine Disney, but her family did not approve and Catherine was required to marry the Rev. William Barlow, a brother of her elder sister's husband. The wedding took place in 1825. Hamilton wrote in 1826 about his feelings for her in an extended poem, "The Enthusiast". Over twenty years later, in 1847, he confided in John Herschel that during this period he might have become a poet.

In 1825, Hamilton met Arabella Lawrence, younger sister of Sarah Lawrence, a significant correspondent and frank critic of his poetry. It was a contact he made through Maria Edgeworth's circle. Hamilton paid a call, with Arabella, on the family of William Roscoe, who had died in 1831.

Hamilton visited Samuel Taylor Coleridge at Highgate, in 1832, helped by an unexpected letter of introduction given to him by Sarah Lawrence on a visit to Liverpool in March of that year. Coleridge introduced German philosopher Immanuel Kant's philosophy and German idealism to Britain. William Rowan Hamilton was a "devoted Coleridgean", and showed affinity with Kant's views on space and time, thus he also had an influence on Irish philosophy. Hamilton also often exchanged letters with mathematician and logician Augustus De Morgan.

Hamilton was a Christian, described as "a lover of the Bible, an orthodox and attached member of the Established Church", and as having a "profound conviction of the truth of revealed religion".

While attending Trinity College, Hamilton proposed to a friend's sister, whose refusal drove the young Hamilton to depression and illness, even to the verge of suicide. He proposed again in 1831 to Ellen de Vere, a sister of the poet Aubrey De Vere, who declined as well.

Hamilton married Helen Bayly, the daughter of The Rev. Henry Bayly, rector of Nenagh, County Tipperary, in 1833; she was a sister of neighbours to the observatory. They had three children: the journalist William Edwin Hamilton (born 1834), Archibald Henry (born 1835) and Helen Eliza Amelia (born 1840). Helen stayed with her widowed mother at Bayly Farm, Nenagh for extended periods, until her mother's death in 1837. She also was away from Dunsink, staying with sisters, for much of the time from 1840 to 1842. Hamilton's married life was reportedly difficult. In the troubled period of the early 1840s, his sister Sydney ran his household; when Helen returned, he was happier after some depression.