Biography of William Rowan Hamilton

The Life of William Rowan Hamilton

By: Amanda Smith

Dublin, Ireland in the 1800's

Brief Biography of Hamilton

William Rowan Hamilton (4 August, 1805 -2 Septmeber 1865) was the fourth of nine children born to Sarah and Archibald Hamilton in Dublin, Ireland. Hamilton’s father, Archibald, was a solicitor and spent a lot of time away from home touring England to practice legal business. Because Archibald was always absent, William was sent to live with his uncle at the age of three. Hamilton stayed with his uncle, James Hamilton, until he attended college. At a very early age William was an exceptional student and a fast learner. While living with his uncle, William managed to learn Latin, Greek, and Hebrew. Before the age of twelve he learned various other languages. In total, twelve year old William knew nine languages.

Dublin, Ireland Today

Zerah Colburn

At age 12, William met child prodigy, Zerah Colburn. Colburn was being exhibited in Dublin for his uncanny mathematical skills. At this exhibit, Zerah and William were put against each other in a mental arithmetic contest. Zerah was the obvious victor. William, shameful in his defeat, decided to spend more time studying mathematics. Bartholomew Lloyd's "The Analytic Geometry," Euclid's "Elements," and Issac Newton's "Arithmetica universalis" were books that also contributed to William's interest in mathematics.

Euclid's "Elements"

Trinity College in 1800's

William was eighteen when he was accepted into Trinity College in Dublin, Ireland. In his freshman year of college, Hamilton was acquired ‘optime’ in Classics. An optime is a term formerly used at the University of Cambridge and is defined as a student taking second or third honors in the mathematical tripos. In 1824, Hamilton submitted his first paper titled, “On Caustics,” to the Royal Irish Academy. During his sophomore year at Trinity, William’s grades began to decline. It wasn’t until 1826 that he progressed and received another ‘optime’, but this time in both science and Classics, which was unheard of. In his final year as an undergraduate William presented, “Theory of Systems of Rays,” a memoir, to the Royal Irish Academy.

Trinity College Today

A Theory of Systems of Rays

In 1824, William presented to the Royal Irish Academy a paper, "On Caustics, " the preface of which stated:"The Problems of Optics, considered mathematically, relate for the most part to the intersections of the rays of light proceeding from known surfaces, according to known laws. In 1827 Hamilton, still an undergraduate, presented to the Royal Irish Academy the enlarged form of the paper under the title "A Theory of Systems of Rays." His starting point was the well-established principle that light rays travel between two points (extremities, he called them) along the path of least time, or along the path of least action, depending on whether the wave theory or the corpuscular theory of light was considered.

Univresity of Dublin

Dunsink Observatory

Prior to his graduation in 1827, Hamilton was offered a position at the University of Dublin as the Professor of Astronomy. By accepting this position, Hamilton not only received the title, Royal Astronomer of Ireland, but was also given the opportunity to stay at the Dunsink Observatory. Hamilton becoming a Professor of Astronomy may have been a great opportunity, but many felt that he did not posses any experience in astronomy. Majority of William’s colleagues believed he was inadequate for the position because although he had insightful knowledge of theoretical astronomy; he little to no knowledge of the regular work of the practical astronomer.

Hamilton becomes knighted and President of Royal Irish Academy

In 1835, Hamilton was knighted by the lord-lieutenant for his scientific achievements in 1837 he became president of the Royal Irish Academy.

Royal Irish Academy Today

Edmund Blair Leighton's picture of a man being knighted

Hamilton's Discovery of Quaternions

In 1843, Hamilton announced to the Royal Irish Academy the definition of quaternions; in 1848 he began his "Lectures on Quaternions" (published 1853). The discovery of the quaternions represented for Hamilton the most important event in his life. William formulated an equation for quaternions while he was walking with his wife along the Royal canal. Fearing that he may forget the equation by the time he returned home, he carved the equation into the side of the nearby Broom Bridge. The formula for quaternions is i2 − j 2 − k 2 − ijk = − 1. The theory included such points as the principles of noncommutative algebra, the generalized treatment of coordinates and momenta, and the correspondence of multiplication by imaginary numbers to rotation in space. All these topics now form indispensable parts of the mathematics of relativity and quantum mechanics.

Boom Bridge in Dublin, Ireland

Formula for Quaternions written on Boom Bridge

Quaternions Book

Hamilton's Family and Death

In 1824, William fell in love with a lady by the name of Catherine. Catherine was the daughter of the Disney family. Because Hamilton was too young to propose he left the matter alone. Eventually, Hamilton married a woman named, Helen Maria Bayley, and in 1834 they had a son named, William Edwin Hamilton. After William Edwin was born, Helen left Dunsink for nine months leaving Hamilton to fight the loneliness by throwing himself into his work even more. The same year Hamilton was knighted his wife birthed a son named, Archibald Henry. William’s cousin died and not long after Helen returned from her mother’s house and left again to England, this time leaving the children behind after the birth of a daughter, Helen Eliza Amelia. At this point, William became depressed and started to have problems with alcohol so his sister came to live at Dunsink.

Hamilton devoted the last twenty-two years of his life to the development of the theory of quaternions and related systems. During his last days, Hamilton was working on a definitive statement of quaternion science. On September 2, 1865, a severe attack of gout took Hamilton’s life. The attack was the result of his excessive drinking and overeating. After his death, Hamilton’s son published, “Elements of Quaternions,” a hefty volume of 762 pages.

Hamilton and one of his sons

Hamilton and his wife, Helen Maria Bayley

Hamilton's Gravesite

Hamilton's Legacy

Hamilton's equations are a formulation of classical mechanics.

Numerous other concepts and objects in mechanics, such as Hamilton's principle, Hamilton's principal function, and the Hamilton–Jacobi equation, 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.

Hamilton College (New York), a liberal arts college in Clinton, New York, is named in his honor.

The RCSI Hamilton Society was founded in his name in 2004.

The algebra of quaternions is usually denoted by H, or in blackboard bold by , in honor of Hamilton.

Today, quaternions are used in computer graphics, control theory, signal processing, and orbital mechanics, mainly for representing rotations/orientations.

Special Thanks To:

www.travel.nationalgeographic.com

www.brummiefamilytree.blogspot.com

www.irishhistorylinks.net

www.msha.gov

www.nexusilluminati.blogspot.com

www.ted.ie

www.understandingscience.ucc.ie

www.nndb.com

www.businessinsider.com

www.myreckonings.com

www.commons.wikimedia.org

www.cityknown.com

www.tripzireland.blogspot.com

www.hpe.com

www.ebay.com

www.census.nationalarchives.ie

www.mountjerome.ie

www.apprendre-math.info

www.maths.ted.ie

www.pballew.blogspot.com

www.amazon.com

www.math.arizona.edu

www.sophiararebooks.com

www.enwikipedia.org

http://etc.usf.edu

www.godandmath.com

www.encyclopedia.com

www.rte.ie

www.facebook.com

www.toptenpk.com

www.cuabroad.cua.edu

www.flickr.com

www.manhattanrarebooks-science.com

www.ma.hw.ac.uk

www.scienceblogs.com

www.ingeniousireland.ie

The End

May 14, 2014

Mr. Tai 6th period

Hamilton College Clinton, New York