William Rowan Hamilton

Sir William Rowan Hamilton

Hamilton was the fourth of nine children born to Sarah Hutton (1780–1817) and Archibald Hamilton (1778–1819), who lived in Dublin at 29 Dominick Street, later renumbered to 36. Hamilton's father, who was from Dublin, worked as a solicitor. By the age of three, Hamilton had been sent to live with his uncle James Hamilton, a graduate of Trinity College who ran a school in Talbots Castle in Trim, County Meath.^[4][3]

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.

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.^[5]: 208

In reaction to his defeat, Hamilton spent less time studying languages, and more on mathematics.

Hamilton aimed to win a Trinity College fellowship by competitive examination,[3] but his ambition was overtaken by events^{[further explanation needed]}, after Brinkley in 1826 was made Bishop of Cloyne.^[14] Hamilton was still an undergraduate, when he was appointed in 1827 to the vacant posts left by Brinkley's departure, Andrews Professor of Astronomy and Royal Astronomer of Ireland.^[5]: 209

Personal life and poetry

In 1824, Hamilton was introduced at Edgeworthstown to the novelist Maria Edgeworth, by the Rev. Richard Butler, the vicar of Trim, County Meath to whom his uncle James Hamilton was curate.^{[15][16]: 5, 34} 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.^{[16]: 37 [17]}

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.^{[16]: 109, 113} 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.^[17]

In 1825, Hamilton met

Hamilton, now Royal Astronomer of Ireland, took up residence at Dunsink Observatory where he spent the rest of his life.^[9] He was there from 1827 until his death in 1865.^[19] In his early years at Dunsink, Hamilton observed the heavens quite regularly;^[20] He left routine observation to his assistant Charles Thompson.^[21][22] Hamilton's sisters also supported the observatory's work.^[3]

The introductory lectures by Hamilton in astronomy were celebrated; in addition to his students, they attracted scholars, poets, and women.^[23] Felicia Hemans wrote her poem The Prayer of the Lonely Student after hearing one of his lectures.^[24]

Personal life, travel and poetic visits

Hamilton invited his four sisters to come and live at the observatory in 1827, and they ran the household until his marriage in 1833. They included Eliza Mary Hamilton (1807–1851), the poet.^[3] In 1827, Hamilton wrote to his sister Grace about "some of" the Lawrence sisters having met his sister Eliza in Dublin.^[25][26]

Newly appointed to the Observatory, Hamilton set off on a tour in Ireland and England with Alexander Nimmo, who was coaching him on latitude and longitude.^[27] One call was to Sarah Lawrence's school at Gateacre, near Liverpool, where Hamilton had a chance to assess the calculator Master Noakes.^[28] They visited William Wordsworth at Rydal Mount in September of that year, where Caesar Otway was also present.^{[29][30]: 410} After the visit, Hamilton sent numerous poems to Wordsworth, becoming a "poetic disciple".^[31]

When Wordsworth visited Dublin in the summer of 1829, in a party with John Marshall and his family, he stayed at Dunsink with Hamilton.^[30]: 411 On a second tour in England with Nimmo in 1831, Hamilton parted from him at Birmingham, to visit the Lawrence sisters and family on his mother's side in the Liverpool area. They met up again in the Lake District, where they climbed Helvellyn and had tea with Wordsworth. Hamilton returned to Dublin, via Edinburgh and Glasgow.^[16][32]

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. He also paid a call, with Arabella, on the family of William Roscoe, who had died in 1831.^[33][34]

Family

While attending Trinity College, Hamilton proposed to his friend's sister, whose refusal drove the young Hamilton to depression and illness, even to the verge of suicide.^[35] He proposed again in 1831 to Ellen de Vere, a sister of the poet Aubrey De Vere (1814–1902), who declined as well.^[35] Hamilton eventually married Helen Marie Bayly in 1833,^[35] a country preacher's daughter, and had three children with her: William Edwin Hamilton (born 1834), Archibald Henry (born 1835), and Helen Elizabeth (born 1840).^[36] Hamilton's married life turned out to be difficult and unhappy as Bayly proved to be pious, shy, timid, and chronically ill.^[35]

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, following a severe attack of

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Hamilton made outstanding contributions to classical mechanics and optics.

His first discovery was in an early paper that he communicated in 1823 to John Brinkley, who presented it under the title of Caustics in 1824 to the Royal Irish Academy. It was referred as usual to a committee, which recommended further development and simplification before publication. Between 1825 and 1828 the paper was expanded, and became a clearer exposition of a novel method.^[6] Over this period, Hamilton gained an appreciation for the nature and importance of optics.^[38]

In 1827, Hamilton presented a theory of a single function, now known as

Hamilton made his discovery of the algebra of

occurred to him; Hamilton then carved this equation using his penknife into the side of the nearby Broom Bridge (which Hamilton called Brougham Bridge).^[5]: 210

The quaternions involved abandoning the

Hamilton also introduced the icosian game or Hamilton's puzzle. It is based on the concept of a Hamiltonian path in graph theory.^[3]

Publications

• Hamilton, Sir W.R. (1853), Lectures on Quaternions Dublin: Hodges and Smith
• Hamilton, Sir W.R., Hamilton, W.E. (ed) (1866), Elements of Quaternions London: Longmans, Green, & Co.
• Hamilton, W.R. (1833), Introductory Lecture on Astronomy Dublin University Review and Quarterly Magazine Vol. I, Trinity College Dublin
• For Hamilton's mathematical papers see David R. Wilkins, Sir William Rowan Hamilton (1805–1865): Mathematical Papers

Hamilton introduced, as a method of analysis, both quaternions and biquaternions, the extension to eight dimensions by the introduction of complex number coefficients. When his work was assembled in 1853, the book Lectures on Quaternions had "formed the subject of successive courses of lectures, delivered in 1848 and subsequent years, in the Halls of Trinity College, Dublin". Hamilton confidently declared that quaternions would be found to have a powerful influence as an instrument of research.

When he died, Hamilton was working on a definitive statement of quaternion science. His son William Edwin Hamilton brought the Elements of Quaternions, a hefty volume of 762 pages, to publication in 1866. As copies ran short, a second edition was prepared by Charles Jasper Joly, when the book was split into two volumes, the first appearing in 1899 and the second in 1901. The subject index and footnotes in this second edition improved the Elements accessibility.

Honours and awards

Hamilton was twice awarded the Cunningham Medal of the Royal Irish Academy.^[47] The first award, in 1834, was for his work on conical refraction, for which he also received the Royal Medal of the Royal Society the following year.^[48] He was to win it again in 1848.

In 1835, being secretary to the meeting of the

A plaque under the Broom Bridge, associated with the discovery of quaternions, was unveiled by

• Hamilton's equations
  are a formulation of classical mechanics.
• Numerous other concepts and objects in mechanics, such as
  Hamilton's principal function, the Hamilton–Jacobi equation, Cayley-Hamilton theorem
  are named after Hamilton.
• The Hamiltonian is the name of both a function (classical) and an operator (quantum) in physics, and, in a different sense, a term from graph theory.
• The algebra of
  quaternions is usually denoted by H, or in blackboard bold
  by ${\displaystyle \mathbb {H} }$, in honour of Hamilton.
• The Hamilton Building at Trinity College Dublin is named after him.[55]

In literature

It is believed by some modern mathematicians that Hamilton's work on quaternions was satirized by

Hamilton married Helen Bayly, daughter of Rev Henry Bayly, Rector of Nenagh, County Tipperary, in 1833; she was a sister of neighbours to the observatory.[58]^[16]: 108 They had three children: William Edwin Hamilton (born 1834), Archibald Henry (born 1835) and Helen Eliza Amelia (born 1840).^[59] 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.^[60] Hamilton's married life was reportedly difficult.^[5]: 209 In the troubled period of the early 1840s, his sister Sydney ran his household; when Helen returned, he was happier after some depression.^{[16]: 125, 126}

See also

• List of astronomers
• List of things named after William Rowan Hamilton
• Theoretical physics

References

Sources

• Hankins, Thomas L. (1980). William Rowan Hamilton. Baltimore and London: Johns Hopkins University Press.
• Graves, Robert Perceval (1882). "Life of Sir William Rowan Hamilton, Volume I". Dublin: Hodges, Figgis, & Co.
• Graves, Robert Perceval (1885). "Life of Sir William Rowan Hamilton, Volume II". Dublin: Hodges, Figgis, & Co.
• Graves, Robert Perceval (1889). "Life of Sir William Rowan Hamilton, Volume III". Dublin: Hodges, Figgis, & Co.
• Barker, Juliet R. V. (2001). Wordsworth: A Life. Penguin. p. 411.
  ISBN 978-0-14-026162-2
  .
• Bruno, Leonard C. (2003) [1999]. Math and mathematicians: the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L.
  OCLC 41497065
  .
• Robert Fountain, Jan van Koningsveld (2013). The Mental Calculator's Handbook. Lulu.com.
  ISBN 978-1-300-84665-9
  .
• Chow, Tai L. (2013). Classical Mechanics: Chaper 5: Hamilton Formulation of Mechanics: Description of Motion in Phase Spaces. CRC Press,
  ISBN 978-1466569980

External links

Wikisource has the text of the 1911 Encyclopædia Britannica article "Hamilton, Sir William Rowan".

• William Rowan Hamilton at the Mathematics Genealogy Project
• O'Connor, John J.; Robertson, Edmund F., "Sir William Rowan Hamilton", MacTutor History of Mathematics Archive, University of St Andrews
• Wilkins, David R., Sir William Rowan Hamilton. School of Mathematics, Trinity College, Dublin.
• Wolfram Research's William Rowan Hamilton
• Cheryl Haefner's Sir William Rowan Hamilton
• Hamilton Trust
• The Hamilton year 2005 web site
• The Hamilton Mathematics Institute, TCD
• Hamilton Institute
• Hamilton biography