Hamilton, William Rowan

William Hamilton
William Hamilton
	; William Rowan Hamilton
Born	August 4, 1805; Dublin, Ireland
Died	September 2, 1865; Dublin, Ireland;
Residence	Ireland
Nationality	Irish, of Scottish descent
Field	Mathematician, physicist, and astronomer
Institutions	Trinity College Dublin
Alma mater	Trinity College Dublin
Academic advisor	John Brinkley
Known for	Quaternions and Hamiltonians
Religious stance	Anglican
	Note that although Hamilton never had a doctoral advisor, scientific genealogy authorities regard the Reverend John Brinkley as Hamilton's equivalent mentor.

Latest revision as of 10:47, 12 May 2023

Sir William Rowan Hamilton (August 4, 1805 – September 2, 1865) was an Irish mathematical physicist who recast the the laws governing the motion of bodies in a simplified and elegant form called Hamilton's equations. He also made contributions in optics through a similar formulation of its laws. Hamilton invented quaternions, a four-dimensional extension of complex numbers.

Early life

Hamilton was the fourth of nine children of Archibald Hamilton, a solicitor, and Sarah Hutton. He was born at 36 Dominick Street, Dublin.

When he was a year-old, he was placed in the care of an uncle and aunt, James and Sydney Hamilton. Hamilton could read from the bible at age three, and by age four he was able to read some Greek, Latin and Hebrew. At six he was attempting translations of Homer and Virgil. Between the ages of nine and ten, he picked up Sanskrit, Arabic, and Persian, while mastering Italian and French. Two years later, he wrote a Syriac grammar for publication. In his later years, he would take up these pursuits as a form of relaxation.

Around this time, Hamilton encountered math prodigy Zerah Colburn, who could do elaborate calculations in his head. Hamilton competed with Colburn but was never able to match his acuity in the sphere of calculation, although it opened the budding mathematician's eyes to new possibilities.

When Hamilton was 12, he lost his mother, and two years later, his father. When he was 15, he began to tackle science and mathematics, beginning with a study of Isaac Newton's Principia. Around the age of 17, he was tackling the infinitesimal calculus and was engaged in preparation for entrance at Trinity College, Dublin, and had therefore to devote a portion of time to classics. In the summer of 1822, he began a systematic study of Pierre-Simon Laplace's Mécanique Céleste.

It was in the successful effort to open this treasure-house that Hamilton’s mind received its final temper. From that time Hamilton appears to have devoted himself almost wholly to the mathematics investigation, Hamilton detected an important defect in one of Laplace’s demonstrations dealing with the composition of forces at the beginning of the work, and he was induced by a friend to write out his remarks, that they might be shown to Dr John Brinkley, then the first Astronomer Royal for Ireland, and an accomplished mathematician. Brinkley seems at once to have perceived the vast talents of young Hamilton and to have encouraged him.

University years

Hamilton was 18 when he entered Trinity College, and during his time there achieved great honors. Amongst a number of competitors of more than ordinary merit, he was first in every subject and at every examination. In 1824, he submitted his first paper for publication touching on themes of optics that would later win him an important place in the history of physics. In the same year, he met and hoped to marry Catherine Disney, the daughter of family friends, but lost out to a clergyman who Catherine's mother thought was better situated socially. This created a deep disturbance in Hamilton's emotional life, but he managed to press through in his studies and research. He achieved the rare distinction of obtaining an optime for both Greek and for physics in 1826. He also won awards for his poetry, which would later be commented on, with reserved praise, by the famous bard William Wordsworth. Wordsworth became one of Hamilton's life-long friends.

Scientific career

Early research

Hamilton's first discovery, a method of mathematical investigation equally applicable to optics and dynamics, was contained in an early paper which in 1823 Hamilton communicated to Dr. Brinkley, by whom, under the title of “Caustics,” it was presented to the Royal Irish Academy in 1824. It was referred as usual to a committee. Their report, while acknowledging the novelty and value of its contents, recommended that, before being published, it should be still further developed and simplified. During the time between 1825 to 1828 the paper was renamed The theory of systems of rays, and grew to an immense bulk, principally by the additional details which had been inserted at the desire of the committee. But it also assumed a much more intelligible form, and the features of the new method were now easily to be seen. Hamilton himself seems not until this period to have fully understood either the nature or importance of optics, as later Hamilton had intentions of applying his method to dynamics.

Hamilton as astronomer

Hamilton's career as a student was cut short by his appointment to the Andrews Professorship of Astronomy in the University of Dublin, vacated by Brinkley in 1827. The chair was not exactly offered to him, as has been sometimes asserted, but the electors, having met and talked over the subject, authorized one of their number, who was Hamilton's personal friend, to urge Hamilton to become a candidate, a step which Hamilton's modesty had prevented him from taking. Thus, when barely 22, Hamilton was established at the Dunsink Observatory, near Dublin.

Hamilton was not specially fitted for the post, for although he had a profound acquaintance with theoretical astronomy, he had paid but little attention to the regular work of the practical astronomer. And it must be said that Hamilton’s time was better employed in original investigations than it would have been had he spent it in observations made even with the best of instruments.

Least action and conical refraction

In 1828, Hamilton published the first part of his Theory of Systems of Rays in the Transactions of the Royal Irish Academy. Supplements were published later.

The third portion of "Systems of Rays" appeared in 1832. It was in this paper that he predicted conical refraction, based on his formulation of optics using the principle of what Hamilton called varying action. but which is often referred to as least action. Conical refraction results in a conical formation of light rays from a single ray passing through certain crystal formations classified as biaxial. There was some challenge mounted to Hamilton's being the first to uncover this phenomenon, but it was later admitted that Hamilton had taken the final and necessary step toward this discovery. Humphrey Lloyd was able to confirm Hamilton's prediction experimentally by observing a conical shaft of light projected from a crystal. While information on conical refraction was included in the supplement to "System of Rays," it had been announced earlier in communications to the Royal Irish Academy.

A year after his discovery of conical refraction, Hamilton married Helen Maria Bayly. The couple had three children: a daughter and two sons.

Hamiltonian dynamics

In what is probably his greatest claim to popular fame, Hamilton published a paper entitled "On a General Method in Dynamics" in the Philosophical Transactions of 1834 and 1835. There, he utilizes the principle of least action, long known by physicists, to produce an elegant and revealing formulation of the dynamical principles of moving bodies. This opened up a new area of mathematical physics known as Hamiltonian dynamics. In this formulation, the Hamiltonian, a function that Hamilton represented by the letter "V" (later changed to "H" in his honor) can, when employed in conjunction with his equations of motion, predict the motion of a body or collection of bodies under idealized circumstances. Hamilton's equations are a more elegant formulation of those produced earlier by Isaac Newton and Joseph Louis Lagrange. They were later expanded upon and improved by the mathematician C. G. J. Jacobi.

In 1835, Hamilton was knighted by the lord-lieutenant. Other honors rapidly followed, including his election in 1837 to the president’s chair of the Royal Irish Academy, and the rare distinction of being made corresponding member of the Academy of St. Petersburg.

Quaternions

The other great contribution made by Hamilton to mathematical science was the introduction of quaternions, beginning in 1843.

Hamilton was looking for ways of extending complex numbers, which are expressed as the sum of a real and an imaginary number (an imaginary number is one whose square yields a negative number). Hamilton could not extend this branch of mathematics to three dimensions: in fact later mathematicians showed that this would be impossible. Eventually Hamilton tried four dimensions and, by doing so, created quaternions. According to the story Hamilton told, on October 16, he was out walking along the Royal Canal in Dublin with his wife, when the solution in the form of the equation

$i^{2}=j^{2}=k^{2}=ijk=-1$

suddenly occurred to him. Hamilton then promptly carved this equation into the side of the nearby Broom Bridge (which Hamilton called Brougham Bridge). He developed the rules for multiplication and division of quaternions, which had alluded him for many years.

The quaternion involved abandoning commutativity, a radical step for the time. Hamilton described a quaternion as an ordered four-element multiple of real numbers, and described the first element as the 'scalar' part, and the remaining three as the 'vector' part.

Hamilton introduced his first great work on the subject, Lectures on Quaternions, in 1852, and confidently declared that quaternions would become a powerful instrument of research. He popularized quaternions with several books, the last of which, Elements of Quaternions, had 800 pages and was just short of being completed at the time of his death.

Peter Guthrie Tait, among others, advocated the use of Hamilton's quaternions. However, controversy about their use grew in the late 1800s. Some of Hamilton's supporters vociferously opposed the growing fields of vector algebra and vector calculus (from developers like Oliver Heaviside and Josiah Willard Gibbs). Vector notation largely replaced the "space-time" quaternions in science and engineering by the mid-twentieth century.

Contemporary uses for quaternions

Today, the quaternions are in use by computer graphics, control theory, signal processing and orbital mechanics, mainly for representing rotations/orientations. For example, it is common for spacecraft attitude-control systems to be commanded in terms of quaternions, which are also used to telemeter their current attitude. .

Last years

Toward the end of his life, Hamilton was completing "Elements of Quaternions"—what he hoped would be an improvement over his "Lectures on Quaternions" published earlier. But during these years he drove himself exceedingly hard. He was in the habit of putting in a 12-hour work day, often laboring through the night and into the morning.

In early June of 1865, Hamilton was besieged by an intense attack of the gout, followed by convulsions. He seemed to recover, and resumed his arduous work schedule. Around this time, the National Academy of Science, an American institution, was forming, and admitted him into its roster of founding members. In August, he wrote his acceptance letter, while continuing to work on Elements, the publication costs for which were an increased source of worry for him. On September 2, 1865, Hamilton called his friend, Charles Graves, to his observatory, and confided to him that his death was imminent. After recommending the sentiments expressed in the 145th psalm of the bible, he died that very afternoon. He was buried September 7 at Mount Jerome Cemetery.

Other accomplishments

William Rowan Hamilton's mathematical career included the study of geometrical optics, adaptation of dynamic methods in optical systems, applying quaternion and vector methods to problems in mechanics and in geometry, development of theories of conjugate algebraic couple functions (in which complex numbers are constructed as ordered pairs of real numbers), solvability of polynomial equations and general quintic polynomial solvable by radicals, the analysis on Fluctuating Functions (and the ideas from Fourier analysis), linear operators on quaternions and proving a result for linear operators on the space of quaternions (which is a special case of the general theorem which today is known as the Cayley-Hamilton Theorem). Hamilton also invented "Icosian Calculus," which he used to investigate closed edge paths on a dodecahedron that visit each vertex exactly once.

Hamilton's extraordinary investigations connected with the solution of algebraic equations of the fifth degree, and his examination of the results arrived at by N. H. Abel, G. B. Jerrard, and others in their researches on this subject, form another contribution to science. There is next Hamilton's paper on Fluctuating Functions, a subject which, since the time of Joseph Fourier, has been of immense and ever increasing value in physical applications of mathematics. There is also the extremely ingenious invention of the hodograph. Of his extensive investigations into the solutions (especially by numerical approximation) of certain classes of physical differential equations, only a few items have been published, at intervals, in the Philosophical Magazine.

Hamilton had designed an entertainment called the "Icosian Game," which he sold for 25 pounds to some entrepreneurs who hoped to make a profit by mass-marketing it. The game, however, did not catch on, and the venture proved to be a financial failure.

Honors

Hamilton is recognized as one of Ireland's leading scientists and, as Ireland becomes more aware of its scientific heritage, he is increasingly celebrated. The Hamilton Institue^[1] is an applied mathematics research institute at NUI Maynooth and the Royal Irish Academy holds an annual public Hamilton lecture at which Murray Gell-Mann, Andrew Wiles, and Timothy Gowers have all spoken. 2005 was the 200th anniversary of Hamilton's birth and the Irish government designated that the Hamilton Year, celebrating Irish science. Trinity College Dublin marked the year by launching the Hamilton Mathematics Institute TCD.

Character and legacy

Character

Although his researches consumed much of his time, Hamilton was a great socializer, and a voluminous correspondent. Often a single letter of Hamilton's occupied from 50 to 100 or more closely written pages, all devoted to the minute consideration of every feature of some particular problem; for it was one of the peculiar characteristics of Hamilton's mind never to be satisfied with a general understanding of a question; Hamilton pursued the problem until he knew it in all its details. Hamilton was ever courteous and kind in answering applications for assistance in the study of his works, even when his compliance must have cost him much time. He was excessively precise and hard to please with reference to the final polish of his own works for publication; and it was probably for this reason that he published so little compared with the extent of his investigations.

He was obviously swept up by the romantic notions of his era, not only writing poetry of his own, but also spending time with the poets William Wordsworth and Samuel Taylor Coleridge. He corresponded with a great number of women, who provided inspiration for his work and a psychological release, outside of his voluminous correspondence with his scientific colleagues.

Of his marriage, Hamilton said that he was as happy as he expected, and happier than he deserved (Ball 1895, 217). Yet, his wife once took the children and lived away from her husband for almost a year. It is said that his wife was not the best housekeeper, and the chaotic state of his study was legendary. During his wife's absence, Hamilton began drinking heavily, which undoubtedly took a toll on both his physical and psychological health. He tried to quit for a time in the mid-1840s, but was shamed for doing so by a fellow scientist and fell back into the habit. Alcoholism is likely to have been a contributing cause to his early death at age 60. Be that as it may, he was a family man, and his children were devoted to him, often commenting (after his death) about what life with their father was like.

Interestingly, Hamilton had two rather distinct anomalies in his physical condition that, while not in any way connected, bear an interesting similarity. He is said to have had two distinct pitches to his voice, one high, another, low, and he used these interchangeably in conversation as well as when musing to himself.

Hamilton also appears to have had a problem with his eyesight, because of which he saw individual images with each eye, rather than a single image from both eyes. The use of a stereoscope demonstrated to him for the first time the manner in which most people see images. This led him to remark that depth perception was not due to stereoscopic vision, and could equally be perceived by vision in a single eye.

Legacy

Any scientist contributing a new formulation to a science as influential and important as the dynamics of moving bodies will naturally be memorialized by future generations. While adding no new physics, his formulation, which builds on that of Joseph Louis Lagrange, provides a more powerful technique for working with the equations of motion. Both the Lagrangian and Hamiltonian approaches were developed to describe the motion of discrete systems, were then extended to continuous systems and in this form can be used to define vector fields. In this way, the techniques find use in electromagnetic, quantum relativity theory and field theory.

Hamilton's quaternions, while not generally celebrated any longer as a subject taught in undergraduate work, are still used in specialized fields.

Commemorations of Hamilton

Hamilton's equations are a formulation of classical mechanics.
Hamiltonian is the name of both a function (classical) and an operator (quantum) in physics, and a term from graph theory. It can be seen as the Quantum Hamiltonian.

Hamilton's publications

Hamilton, William Rowan. Introductory Lecture on Astronomy. Dublin University Review and Quarterly Magazine Vol. I, Trinity College, January 1833. Retrieved August 20, 2007.
Hamilton, William Rowan. Lectures on Quaternions. Royal Irish Academy, 1853. Retrieved August 20, 2007.
David R. Wilkins. Hamilton's Mathematical Papers. David R. Wilkins. Retrieved August 20, 2007.

Notes

↑ Hamilton Institute, Hamilton Institute. Retrieved April 15, 2008.

References
ISBN links support NWE through referral fees

Ball, Robert S. 1895. Great astronomers. London: Isbister.
Haefner, Cheryl. Sir William Rowan Hamilton. Cheryl Haefner. Retrieved August 10, 2007.
Hankins, Thomas. 1980. Sir William Rowan Hamilton. Baltimore: The Johns Hopkins University Press. ISBN 0801822033.
McCartney, Mark, and Andrew Whitaker. 2003. Physicists of Ireland: Passion and Precision. London: Fracis & Taylor. ISBN 0750308664
Wilkins, David R. Sir William Rowan Hamilton. Dublin: School of Mathematics, Trinity College. Retrieved August 10, 2007.
Wolfram Research's William Rowan Hamilton. Eric W. Weisstein. Retrieved August 10, 2007.

External links

All links retrieved May 12, 2023.

Credits

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[1] Hamilton Institute, Hamilton Institute. Retrieved April 15, 2008.

[1]

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 {{Infobox_Scientist
 | name = William Hamilton
-| image = Hamilton.jpg
+| image = William Rowan Hamilton portrait oval combined.png
 | caption = William Rowan Hamilton
 | birth_date = August 4, 1805
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 | alma_mater = [[Trinity College Dublin]]
 | doctoral_advisor = [[John Brinkley (astronomer)|John Brinkley]]
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 | known_for  = [[Quaternion]]s and [[Hamiltonian]]s
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-Sir '''William Rowan Hamilton''' (August 4, 1805 &ndash; September 2, 1865) was an [[Ireland|Irish]] [[mathematician]], [[physicist]], and [[astronomer]] who made important contributions to the development of [[optics]], [[dynamics (mechanics)|dynamics]], and [[algebra]]. His discovery of [[quaternion]]s is perhaps his best known investigation. [[Hamiltonian|Hamilton's work]] was later significant in the development of [[Hamiltonian (quantum mechanics)|quantum mechanics]]. Hamilton is said to have showed immense talent at a very early age, prompting astronomer Bishop Dr. [[John Brinkley (astronomer)|John Brinkley]] to remark in 1823 of Hamilton at the age of eighteen: “''This young man, I do not say will be, but is, the first mathematician of his age''.”
+Sir '''William Rowan Hamilton''' (August 4, 1805 &ndash; September 2, 1865) was an [[Ireland|Irish]] mathematical physicist who recast the the laws governing the motion of bodies in a simplified and elegant form called ''Hamilton's equations''. He also made contributions in optics through a similar formulation of its laws. Hamilton invented ''quaternions'', a four-dimensional extension of complex numbers.
+{{toc}}
+==Early life==
-== Biography ==
+Hamilton was the fourth of nine children of Archibald Hamilton, a solicitor, and Sarah Hutton. He was born at 36 Dominick Street, [[Dublin]].
-William Rowan Hamilton's mathematical career included the study of [[geometrical optics]],  adaptation of dynamic methods in optical systems, applying quaternion and vector methods to problems in mechanics and in geometry, development of theories of conjugate algebraic couple functions (in which complex numbers are constructed as ordered pairs of real numbers), solvability of polynomial equations and general quintic polynomial solvable by radicals, the analysis on Fluctuating Functions (and the ideas from [[Fourier analysis]]), linear operators on quaternions and proving a result for linear operators on the space of quaternions (which is a special case of the general theorem which today is known as the ''[[Cayley-Hamilton Theorem]]''). Hamilton also invented "''[[Icosian Calculus]]''," which he used to investigate closed edge paths on a dodecahedron that visit each vertex exactly once.
-===Early life===
+When he was a year-old, he was placed in the care of an uncle and aunt, James and Sydney Hamilton. Hamilton could read from the bible at age three, and by age four he was able to read some Greek, Latin and Hebrew. At six he was attempting translations of Homer and Virgil. Between the ages of nine and ten, he picked up [[Sanskrit]], [[Arabic language|Arabic]], and [[Persian language|Persian]], while mastering [[Italian language|Italian]] and [[French language|French]]. Two years later, he wrote a Syriac grammar for publication. In his later years, he would take up these pursuits as a form of relaxation.
-A [[child prodigy]], Hamilton was born the son of Archibald Hamilton, a solicitor, in [[Dublin]] at 36 Dominick Street, but was later put up for adoption.
-Hamilton's genius first displayed itself in the form of a power of acquiring languages. Note: Hamilton's ability to actually speak these languages is disputed by some historians, who claim he had only a very basic understanding of them. At the age of seven he had already made very considerable progress in [[Hebrew language|Hebrew]], and before he was thirteen he had acquired, under the care of his uncle (a linguist), almost as many languages as he had years of age. Among these, besides the classical European languages and the modern European languages, were included [[Persian language|Persian]], [[Arabic language|Arabic]], [[Hindustani]], [[Sanskrit]], and even [[Malay language|Malay]]. But though to the very end of his life he retained much of the singular learning of his childhood and youth, often reading Persian and Arabic in the intervals of sterner pursuits, he had long abandoned them as a study, and employed them merely as a relaxation.
-Hamilton later atttended [[Westminster School]] with [[Zerah Colburn]]. He was part of a small but well-regarded school of mathematicians associated with [[Trinity College, Dublin]], where he spent his life. He studied both classics and science, and was appointed Professor of [[Astronomy]] in 1827, prior to his graduation.
+Around this time, Hamilton encountered math prodigy Zerah Colburn, who could do elaborate calculations in his head. Hamilton competed with Colburn but was never able to match his acuity in the sphere of calculation, although it opened the budding mathematician's eyes to new possibilities.
-===Mathematical studies===
+When Hamilton was 12, he lost his mother, and two years later, his father. When he was 15, he began to tackle science and mathematics, beginning with a study of [[Isaac Newton]]'s ''Principia''. Around the age of 17, he was tackling the infinitesimal calculus and was engaged in preparation for entrance at Trinity College, Dublin, and had therefore to devote a portion of time to classics. In the summer of 1822, he began a systematic study of [[Pierre-Simon Laplace]]'s ''[[Celestial mechanics|Mécanique Céleste]]''.
-Hamilton's [[mathematics|mathematic]]al studies seem to have been undertaken and carried to their full development without any assistance whatsoever, and the result is that his writings belong to no particular "''school''," unless indeed we consider them to form, as they are well entitled to do, a school by themselves. As an [[arithmetic]]al calculator Hamilton was not only an expert, but he seems to have occasionally found a positive experience in working out to an enormous number of places of decimals the result of some irksome calculation. At the age of twelve Hamilton engaged [[Zerah Colburn (math prodigy)|Zerah Colburn]], the [[United States|American]] "''[[mental calculator|calculating boy]]''," who was then being exhibited as a curiosity in Dublin, and he had not always the worst of the encounter. But, two years before, he had accidentally fallen in with a [[Latin]] copy of [[Euclid]], which he eagerly devoured; and at twelve Hamilton studied [[Isaac Newton|Newton]]’s ''[[Arithmetica Universalis]]''. This was his introduction to modern [[Mathematical analysis|analysis]]. Hamilton soon commenced to read the ''[[Philosophiae Naturalis Principia Mathematica|Principia]]'', and at sixteen Hamilton had mastered a great part of that work, besides some more modern works on [[analytical geometry]] and the [[differential calculus]].
-About this period Hamilton was also engaged in preparation for entrance at [[Trinity College, Dublin|Trinity College]], Dublin, and had therefore to devote a portion of time to classics. In the summer of 1822, in his seventeenth year, he began a systematic study of [[Laplace]]'s ''[[Celestial mechanics|Mécanique Céleste]]''. Nothing could be better fitted to call forth such mathematical powers as those of Hamilton; for Laplace's great work, rich to profusion in analytical processes alike novel and powerful, demands from the student careful and often laborious study.
+It was in the successful effort to open this treasure-house that Hamilton’s mind received its final temper. From that time Hamilton appears to have devoted himself almost wholly to the mathematics investigation, Hamilton detected an important defect in one of Laplace’s demonstrations dealing with the composition of forces at the beginning of the work, and he was induced by a friend to write out his remarks, that they might be shown to Dr [[John Brinkley (astronomer)|John Brinkley]], then the first [[Astronomer Royal for Ireland]], and an accomplished [[mathematician]]. Brinkley seems at once to have perceived the vast talents of young Hamilton and to have encouraged him.
-It was in the successful effort to open this treasure-house that Hamilton’s mind received its final temper, "''Dês-lors il commença à marcher seul''" (from that time it began to go alone), to use the words of the biographer of another great mathematician. From that time Hamilton appears to have devoted himself almost wholly to the mathematics investigation, though he ever kept himself well acquainted with the [[History of science and technology|progress of science]] both in Britain and abroad. Hamilton detected an important defect in one of Laplace’s demonstrations, and he was induced by a friend to write out his remarks, that they might be shown to Dr [[John Brinkley (astronomer)|John Brinkley]], then the first [[Astronomer Royal for Ireland]], and an accomplished [[mathematician]]. Brinkley seems at once to have perceived the vast talents of young Hamilton, and to have encouraged him in the kindest manner.
+==University years==
-Hamilton’s career at College was perhaps unexampled. Amongst a number of competitors of more than ordinary merit, he was first in every subject and at every examination. He achieved the rare distinction of obtaining an [[optime]] for both [[Greek language|Greek]] and for [[physics]]. The amount of many more such honours Hamilton might have attained it is impossible to say; but Hamilton was expected to win both the [[gold medal]]s at the degree examination, had his career as a student not been cut short by an unprecedented event. This was Hamilton’s appointment to the [[Andrews Professorship of Astronomy]] in the [[University of Dublin]], vacated by Dr Brinkley in 1827. The chair was not exactly offered to him, as has been sometimes asserted, but the electors, having met and talked over the subject, authorized one of their number, who was Hamilton's personal friend, to urge Hamilton to become a candidate, a step which Hamilton's modesty had prevented him from taking. Thus, when barely twenty-two, Hamilton was established at the [[Dunsink Observatory]], near Dublin.
+Hamilton was 18 when he entered Trinity College, and during his time there achieved great honors. Amongst a number of competitors of more than ordinary merit, he was first in every subject and at every examination. In 1824, he submitted his first paper for publication touching on themes of optics that would later win him an important place in the history of physics. In the same year, he met and hoped to marry Catherine Disney, the daughter of family friends, but lost out to a clergyman who Catherine's mother thought was better situated socially. This created a deep disturbance in Hamilton's emotional life, but he managed to press through in his studies and research. He achieved the rare distinction of obtaining an [[optime]] for both [[Greek language|Greek]] and for [[physics]] in 1826. He also won awards for his poetry, which would later be commented on, with reserved praise, by the famous bard William Wordsworth. Wordsworth became one of Hamilton's life-long friends.
-Hamilton was not specially fitted for the post, for although he had a profound acquaintance with [[theoretical astronomy]], he had paid but little attention to the regular work of the practical [[astronomer]]. And it must be said that Hamilton’s time was better employed in original investigations than it would have been had he spent it in observations made even with the best of instruments. Hamilton was intended by the university authorities who elected him to the professorship of astronomy to spend his time as Hamilton best could for the advancement of [[science]], without being tied down to any particular branch. If Hamilton devoted himself to practical astronomy, the University of Dublin would assuredly have furnished him with instruments and an adequate staff of assistants.
+==Scientific career==
+===Early research===
-In 1835, being secretary to the meeting of the [[British Association for the Advancement of Science|British Association]] which was held that year in Dublin, he was [[knight]]ed by the [[Lord Lieutenant of Ireland|lord-lieutenant]]. Other honours rapidly succeeded, among which his election in 1837 to the [[president]]’s chair in the [[Royal Irish Academy]], and the rare distinction of being made corresponding member of the [[Academy]] of [[St Petersburg]]. These are the few salient points (other, of course, than the epochs of Hamilton's more important discoveries and inventions presently to be considered) in the uneventful life of Hamilton.
+Hamilton's first discovery, a method of mathematical investigation equally applicable to optics and dynamics, was contained in an early paper which in 1823 Hamilton communicated to Dr. Brinkley, by whom, under the title of “''Caustics'',” it was presented to the [[Royal Irish Academy]] in 1824. It was referred as usual to a committee. Their report, while acknowledging the novelty and value of its contents, recommended that, before being published, it should be still further developed and simplified. During the time between 1825 to 1828 the paper was renamed ''The theory of systems of rays'', and grew to an immense bulk, principally by the additional details which had been inserted at the desire of the committee. But it also assumed a much more intelligible form, and the features of the new method were now easily to be seen. Hamilton himself seems not until this period to have fully understood either the nature or importance of optics, as later Hamilton had intentions of applying his method to dynamics.
-===Optics and dynamics===
+===Hamilton as astronomer===
-He made important contributions to [[optics]] and to [[dynamics (mechanics)|dynamics]]. Hamilton's papers on optics and dynamics demonstrated [[theoretical dynamics]] being treated as a branch of pure mathematics. Hamilton's first discovery was contained in one of those early papers which in 1823 Hamilton communicated to Dr Brinkley, by whom, under the title of “''Caustics'',” it was presented in 1824 to the [[Royal Irish Academy]]. It was referred as usual to a committee. Their report, while acknowledging the novelty and value of its contents recommended that, before being published, it should be still further developed and simplified. During the time between 1825 to 1828 the paper grew to an immense bulk, principally by the additional details which had been inserted at the desire of the committee. But it also assumed a much more intelligible form, and the features of the new method were now easily to be seen. Hamilton himself seems not until this period to have fully understood either the nature or importance of optics, as later Hamilton had intentions of applying his method to dynamics.
-In 1827, Hamilton presented a theory that provided a single function that brings together mechanics, optics and mathematics. It helped in establishing the wave theory of light. He proposed for it when he first predicted its existence in the third supplement to his "''Systems of Rays''," read in 1832. The Royal Irish Academy paper was finally entitled “''Theory of Systems of Rays'',” (April 23, 1827) and the first part was printed in 1828 in the ''Transactions of the Royal Irish Academy''. It is understood that the more important contents of the second and third parts appeared in the three voluminous supplements (to the first part) which were published in the same Transactions, and in the two papers “''On a General Method in Dynamics'',” which appeared in the Philosophical Transactions in 1834 and 1835.
+Hamilton's career as a student was cut short by his appointment to the [[Andrews Professorship of Astronomy]] in the [[University of Dublin]], vacated by Brinkley in 1827. The chair was not exactly offered to him, as has been sometimes asserted, but the electors, having met and talked over the subject, authorized one of their number, who was Hamilton's personal friend, to urge Hamilton to become a candidate, a step which Hamilton's modesty had prevented him from taking. Thus, when barely 22, Hamilton was established at the [[Dunsink Observatory]], near [[Dublin]].
-The principle of “''Varying Action''“ is the great feature of these papers; and it is, indeed, that the one particular result of this theory which, perhaps more than anything else that Hamilton has done, something which should have been easily within the reach of [[Augustin Fresnel]] and others for many years before, and in no way required Hamilton’s new conceptions or methods, although it was by Hamilton’s new theoretical dynamics that he was led to its discovery. This singular result is still known by the name “''conical refraction''.”
+Hamilton was not specially fitted for the post, for although he had a profound acquaintance with [[theoretical astronomy]], he had paid but little attention to the regular work of the practical [[astronomer]]. And it must be said that Hamilton’s time was better employed in original investigations than it would have been had he spent it in observations made even with the best of instruments.
-The step from optics to dynamics in the application of the method of “''Varying Action''” was made in 1827, and communicated to the Royal Society, in whose ''[[Philosophical Transactions]]'' for 1834 and 1835 there are two papers on the subject. These display, like the “''Systems of Rays'',” a mastery over symbols and a flow of mathematical language almost unequalled. But they contain what is far more valuable still, the greatest addition which dynamical [[science]] had received since the strides made by Sir [[Isaac Newton]] and [[Joseph Louis Lagrange]]. [[C. G. J. Jacobi]] and other mathematicians have extended Hamilton's processes, and have thus made extensive additions to our knowledge of [[differential equations]].
+===Least action and conical refraction===
-And though differential equations, optics and theoretical dynamics of course are favored in which any such contribution to science can be looked at, the other must not be despised. It is characteristic of most of Hamilton's, as of nearly all great discoveries, that even their indirect consequences are of high value.
+In 1828, Hamilton published the first part of his ''Theory of Systems of Rays'' in the ''Transactions of the Royal Irish Academy''. Supplements were published later.
+The third portion of "Systems of Rays" appeared in 1832. It was in this paper that he predicted ''conical refraction'', based on his formulation of optics using the principle of what Hamilton called ''varying action''. but which is often referred to as ''least action''. Conical refraction results in a conical formation of light rays from a single ray passing through certain crystal formations classified as ''biaxial''. There was some challenge mounted to Hamilton's being the first to uncover this phenomenon, but it was later admitted that Hamilton had taken the final and necessary step toward this discovery. Humphrey Lloyd was able to confirm Hamilton's prediction experimentally by observing a conical shaft of light projected from a crystal. While information on conical refraction was included in the supplement to "System of Rays," it had been announced earlier in communications to the Royal Irish Academy.
+A year after his discovery of conical refraction, Hamilton married Helen Maria Bayly. The couple had three children: a daughter and two sons.
+===Hamiltonian dynamics===
+In what is probably his greatest claim to popular fame, Hamilton published a paper entitled "On a General Method in Dynamics" in the ''Philosophical Transactions'' of 1834 and 1835. There, he utilizes the principle of ''least action'', long known by physicists, to produce an elegant and revealing formulation of the dynamical principles of moving bodies. This opened up a new area of mathematical physics known as ''Hamiltonian dynamics''. In this formulation, the Hamiltonian, a function that Hamilton represented by the letter "V" (later changed to "H" in his honor) can, when employed in conjunction with his equations of motion, predict the motion of a body or collection of bodies under idealized circumstances. Hamilton's equations are a more elegant formulation of those produced earlier by [[Isaac Newton]] and [[Joseph Louis Lagrange]]. They were later expanded upon and improved by the mathematician [[C. G. J. Jacobi]].
+In 1835, Hamilton was [[knight]]ed by the [[Lord Lieutenant of Ireland|lord-lieutenant]]. Other honors rapidly followed, including his election in 1837 to the [[president]]’s chair of the [[Royal Irish Academy]], and the rare distinction of being made corresponding member of the [[Academy]] of [[St. Petersburg]].
 ===Quaternions===
 [[Image:Quaternion Plague on Broom Bridge.jpg|right|Quaternion Plague on Broome Bridge]]
-The other great contribution made by Hamilton to mathematical science was his discovery of [[quaternion]]s in 1843.
+The other great contribution made by Hamilton to mathematical science was the introduction of [[quaternion]]s, beginning in 1843.
-Hamilton was looking for ways of extending [[complex number]]s (which can be viewed as [[Point (geometry)|point]]s on a 2-dimensional [[plane (mathematics)|plane]]) to higher spatial dimensions. Hamilton could not do so for 3 dimensions: in fact later mathematicians showed that this would be impossible.  Eventually Hamilton tried 4 dimensions and created quaternions. According to the story Hamilton told, on October 16 Hamilton was out walking along the [[Royal Canal]] in [[Dublin]] with his [[Helen Maria Bayly|wife]] when the solution in the form of the equation
+Hamilton was looking for ways of extending [[complex number]]s, which are expressed as the sum of a real and an imaginary  number (an imaginary number is one whose square yields a negative number). Hamilton could not extend this branch of mathematics to three dimensions: in fact later mathematicians showed that this would be impossible. Eventually Hamilton tried four dimensions and, by doing so, created quaternions. According to the story Hamilton told, on October 16, he was out walking along the [[Royal Canal]] in [[Dublin]] with his [[Helen Maria Bayly|wife]], when the solution in the form of the equation
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-suddenly occurred to him; Hamilton then promptly carved this equation into the side of the nearby [[Broom Bridge]] (which Hamilton called Brougham Bridge.)  Since 1989, the [[National University of Ireland, Maynooth]] has organized a pilgrimage, where mathematicians take a walk from Dunsink observatory to the bridge where, unfortunately, no trace of the carving remains, though a stone plaque does commemorate the discovery.
+suddenly occurred to him. Hamilton then promptly carved this equation into the side of the nearby [[Broom Bridge]] (which Hamilton called Brougham Bridge). He developed the rules for multiplication and division of quaternions, which had alluded him for many years.
+The quaternion involved abandoning [[commutativity]], a radical step for the time. Hamilton described a quaternion as an ordered four-element multiple of real numbers, and described the first element as the 'scalar' part, and the remaining three as the 'vector' part.
-The quaternion involved abandoning [[commutativity]], a radical step for the time. Not only this, but Hamilton had in a sense invented the cross and dot products of vector algebra. Hamilton also described a quaternion as an ordered four-element multiple of real numbers, and described the first element as the 'scalar' part, and the remaining three as the 'vector' part.
+Hamilton introduced his first great work on the subject, ''Lectures on Quaternions'', in 1852, and confidently declared that quaternions would become a powerful instrument of research. He popularized quaternions with several books, the last of which, ''Elements of Quaternions'', had 800 pages and was just short of being completed at the time of his death.
-In 1852, Hamilton introduced quaternions as a method of analysis. His first great work is ''Lectures on Quaternions'' (Dublin, 1852). Hamilton confidently declared that quaternions would be found to have a powerful influence as an instrument of research.
+[[Peter Guthrie Tait]], among others, advocated the use of Hamilton's quaternions. However, controversy about their use grew in the late 1800s. Some of Hamilton's supporters vociferously opposed the growing fields of vector algebra and vector calculus (from developers like [[Oliver Heaviside]] and [[Josiah Willard Gibbs]]). Vector notation largely replaced the "''[[space-time]]''" quaternions in science and engineering by the mid-twentieth century.
-He popularized quaternions with several books, the last of which, ''Elements of Quaternions'', had 800 pages and was published shortly after his death.
-[[Peter Guthrie Tait]] among others, advocated the use of Hamilton's quaternions.  They were made a mandatory examination topic in Dublin, and for a while they were the only advanced mathematics taught in some American
+===Contemporary uses for quaternions===
-universities.  However, controversy about the use of quaternions grew in the late 1800s. Some of Hamilton's supporters vociferously opposed the growing fields of vector algebra and vector calculus (from developers like [[Oliver Heaviside]] and [[Willard Gibbs]]), because quaternions provide superior notation. While this is undeniable for four dimensions,  quaternions cannot be used with arbitrary dimensionality (though extensions like [[Clifford algebra]]s can). Vector notation largely replaced the "''[[space-time]]''" quaternions in science and engineering by the mid-20th century.
+Today, the quaternions are in use by [[computer graphics]], [[control theory]], [[signal processing]] and orbital mechanics, mainly for representing rotations/orientations. For example, it is common for spacecraft attitude-control systems to be commanded in terms of quaternions, which are also used to telemeter their current attitude. .
-Today, the quaternions are in use by [[computer graphics]], [[control theory]], [[signal processing]] and orbital mechanics, mainly for representing rotations/orientations. For example, it is common for spacecraft attitude-control systems to be commanded in terms of quaternions, which are also used to telemeter their current attitude. The rationale is that combining many quaternion transformations is more numerically stable than combining many matrix transformations.  In pure mathematics, quaternions show up significantly as
+===Last years===
-one of the four finite-dimensional [[normed division algebra]]s over the real numbers, with applications throughout algebra and geometry.
+Toward the end of his life, Hamilton was completing "Elements of Quaternions"—what he hoped would be an improvement over his "Lectures on Quaternions" published earlier. But during these years he drove himself exceedingly hard. He was in the habit of putting in a 12-hour work day, often laboring through the night and into the morning.
-Hamilton also contributed an alternative formulation of the mathematical theory of classical mechanics. While adding no new physics, this formulation, which builds on that of [[Joseph Louis Lagrange]], provides a more powerful technique for working with the equations of motion. Both the [[Lagrangian]] and [[Hamiltonian mechanics|Hamiltonian]] approaches were developed to describe the motion of [[discrete system]]s, were then extended to [[continous theory|continuous system]]s and in this form can be used to define [[vector field]]s. In this way, the techniques find use in [[electromagnetic]], [[quantum theory|quantum]] [[relativity theory]] and [[field theory]].
+In early June of 1865, Hamilton was besieged by an intense attack of the gout, followed by convulsions. He seemed to recover, and resumed his arduous work schedule. Around this time, the National Academy of Science, an American institution, was forming, and admitted him into its roster of founding members. In August, he wrote his acceptance letter, while continuing to work on ''Elements'', the publication costs for which were an increased source of worry for him. On September 2, 1865, Hamilton called his friend, Charles Graves, to his observatory, and confided to him that his death was imminent. After recommending the sentiments expressed in the 145th psalm of the bible, he died that very afternoon. He was buried September 7 at Mount Jerome Cemetery.
-===Other originality===
+==Other accomplishments==
-Hamilton originally matured his ideas before putting pen to paper. The discoveries, papers and treatises previously mentioned might well have formed the whole work of a long and laborious life. But not to speak of his enormous collection of books, full to overflowing with new and original matter, which have been handed over to [[Trinity College, Dublin]], the previous mentioned works barely form the greater portion of what Hamilton has published. Hamilton developed the [[variational principle]], which was reformulated later by [[Carl Gustav Jacob Jacobi]]. He also introduced ''Hamilton's puzzle'' which can be solved using the concept of a [[Hamiltonian path]].
+William Rowan Hamilton's mathematical career included the study of [[geometrical optics]], adaptation of dynamic methods in optical systems, applying quaternion and vector methods to problems in mechanics and in geometry, development of theories of conjugate [[algebra]]ic couple functions (in which complex numbers are constructed as ordered pairs of real numbers), solvability of polynomial equations and general quintic [[polynomial]] solvable by radicals, the analysis on Fluctuating Functions (and the ideas from [[Fourier analysis]]), linear operators on quaternions and proving a result for linear operators on the space of quaternions (which is a special case of the general theorem which today is known as the ''[[Cayley-Hamilton Theorem]]''). Hamilton also invented "''[[Icosian Calculus]]''," which he used to investigate closed edge paths on a dodecahedron that visit each vertex exactly once.
 Hamilton's extraordinary investigations connected with the solution of algebraic equations of the fifth [[degree (mathematics)|degree]], and his examination of the results arrived at by [[Niels Henrik Abel|N. H. Abel]], [[George Birch Jerrard|G. B. Jerrard]], and others in their researches on this subject, form another contribution to science. There is next Hamilton's paper on [[Fluctuating Function]]s, a subject which, since the time of [[Joseph Fourier]], has been of immense and ever increasing value in physical [[applications of mathematics]]. There is also the extremely ingenious invention of the [[hodograph]]. Of his extensive investigations into the solutions (especially by [[numerical approximation]]) of certain classes of physical differential equations, only a few items have been published, at intervals, in the ''[[Philosophical Magazine]]''.
-Besides all this, Hamilton was a voluminous correspondent. Often a single letter of Hamilton's occupied from fifty to a hundred or more closely written pages, all devoted to the minute consideration of every feature of some particular problem; for it was one of the peculiar characteristics of Hamilton's mind never to be satisfied with a general understanding of a question; Hamilton pursued the problem until he knew it in all its details. Hamilton was ever courteous and kind in answering applications for assistance in the study of his works, even when his compliance must have cost him much time. He was excessively precise and hard to please with reference to the final polish of his own works for publication; and it was probably for this reason that he published so little compared with the extent of his investigations.
+Hamilton had designed an entertainment called the "Icosian Game," which he sold for 25 pounds to some entrepreneurs who hoped to make a profit by mass-marketing it. The game, however, did not catch on, and the venture proved to be a financial failure.
-===Death and afterwards===
+==Honors==
-Hamilton retained his faculties unimpaired to the very last, and steadily continued till within a day or two of his death, which occurred on 2 September 1865, the task of finishing the “''[[Elements of Quaternions]]''” which had occupied the last six years of his life.
+Hamilton is recognized as one of [[Ireland]]'s leading scientists and, as Ireland becomes more aware of its scientific heritage, he is increasingly celebrated. The Hamilton Institue<ref>[http://www.hamilton.ie Hamilton Institute], Hamilton Institute. Retrieved April 15, 2008.</ref> is an applied mathematics research institute at [[National University of Ireland, Maynooth|NUI Maynooth]] and the [[Royal Irish Academy]] holds an annual public Hamilton lecture at which [[Murray Gell-Mann]], [[Andrew Wiles]], and [[Timothy Gowers]] have all spoken. 2005 was the 200th anniversary of Hamilton's birth and the Irish government designated that the ''Hamilton Year, celebrating Irish science''. [[Trinity College Dublin]] marked the year by launching the Hamilton Mathematics Institute TCD.
-Hamilton is recognized as one of Ireland's leading scientists and, as Ireland becomes more aware of its scientific heritage, he is increasingly celebrated. The [http://www.hamilton.ie Hamilton Institute] is an applied mathematics research institute at [[National University of Ireland, Maynooth|NUI Maynooth]] and the [[Royal Irish Academy]] holds an annual public Hamilton lecture at which [[Murray Gell-Mann]], [[Andrew Wiles]] and [[Timothy Gowers]] have all spoken. 2005 was the 200th anniversary of Hamilton's birth and the Irish government designated that the ''Hamilton Year, celebrating Irish science''. [[Trinity College Dublin]] marked the year by launching the Hamilton Mathematics Institute TCD.
+==Character and legacy==
+===Character===
-== Commemorations of Hamilton==
+Although his researches consumed much of his time, Hamilton was a great socializer, and a voluminous correspondent. Often a single letter of Hamilton's occupied from 50 to 100 or more closely written pages, all devoted to the minute consideration of every feature of some particular problem; for it was one of the peculiar characteristics of Hamilton's mind never to be satisfied with a general understanding of a question; Hamilton pursued the problem until he knew it in all its details. Hamilton was ever courteous and kind in answering applications for assistance in the study of his works, even when his compliance must have cost him much time. He was excessively precise and hard to please with reference to the final polish of his own works for publication; and it was probably for this reason that he published so little compared with the extent of his investigations.
-*[[Hamilton's equations]] are a formulation of classical mechanics.
-*[[Hamiltonian (disambiguation)|Hamiltonian]] is the name of both a function (classical) and an operator (quantum) in physics, and a term from [[graph theory]]. It can be seen as the Quantum Hamiltonian.
-== Quotations ==
+He was obviously swept up by the romantic notions of his era, not only writing poetry of his own, but also spending time with the poets [[William Wordsworth]] and [[Samuel Taylor Coleridge]]. He corresponded with a great number of women, who provided inspiration for his work and a psychological release, outside of his voluminous correspondence with his scientific colleagues.
-* "Time is said to have only one dimension, and space to have three dimensions. ... The mathematical quaternion partakes of both these elements; in technical language it may be said to be "time plus space," or "space plus time": and in this sense it has, or at least involves a reference to, four dimensions. And how the One of Time, of Space the Three, Might in the Chain of Symbols girdled be." &mdash; William Rowan Hamilton (Quoted in [[Robert Percival Graves]]' "''Life of Sir William Rowan Hamilton''" (3 vols., 1882, 1885, 1889))
-* "He used to carry on, long trains of algebraic and arithmetical calculations in his mind, during which he was unconscious of the earthly necessity of eating; we used to bring in a ‘snack’ and leave it in his study, but a brief nod of recognition of the intrusion of the chop or cutlet was often the only result, and his thoughts went on soaring upwards." &mdash; [[William Edwin Hamilton]] (his elder son)
+Of his marriage, Hamilton said that he was as happy as he expected, and happier than he deserved (Ball 1895, 217). Yet, his wife once took the children and lived away from her husband for almost a year. It is said that his wife was not the best housekeeper, and the chaotic state of his study was legendary. During his wife's absence, Hamilton began drinking heavily, which undoubtedly took a toll on both his physical and [[psychology|psychological]] health. He tried to quit for a time in the mid-1840s, but was shamed for doing so by a fellow scientist and fell back into the habit. Alcoholism is likely to have been a contributing cause to his early death at age 60. Be that as it may, he was a family man, and his children were devoted to him, often commenting (after his death) about what life with their father was like.
-== Publications ==
+Interestingly, Hamilton had two rather distinct [[anomaly|anomalies]] in his physical condition that, while not in any way connected, bear an interesting similarity. He is said to have had two distinct pitches to his voice, one high, another, low, and he used these interchangeably in conversation as well as when musing to himself.
-* Hamilton, William Rowan (Royal Astronomer Of Ireland), "''[http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/Lectures/AstIntro.html Introductory Lecture on Astronomy]''." Dublin University Review and Quarterly Magazine Vol. I, Trinity College, January 1833.
+Hamilton also appears to have had a problem with his eyesight, because of which he saw individual images with each eye, rather than a single image from both eyes. The use of a stereoscope demonstrated to him for the first time the manner in which most people see images. This led him to remark that depth perception was not due to stereoscopic vision, and could equally be perceived by vision in a single eye.
-* Hamilton, William Rowan, "''[http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=05230001&seq=9 Lectures on Quaternions]''." Royal Irish Academy, 1853.
-* David R. Wilkins's collection of [http://www.maths.soton.ac.uk/EMIS/classics/Hamilton/ Hamilton's Mathematical Papers].
-== References ==
+===Legacy===
-* ''Sir William Rowan Hamilton'' by Thomas Hankins, 1980 published by The Johns Hopkins University Press, 474 pages.  Primarily biographical but covers the math and physics Hamilton worked on in sufficient detail to give a flavor of the work.
+Any scientist contributing a new formulation to a science as influential and important as the dynamics of moving bodies will naturally be memorialized by future generations. While adding no new physics, his formulation, which builds on that of [[Joseph Louis Lagrange]], provides a more powerful technique for working with the equations of motion. Both the [[Lagrangian]] and [[Hamiltonian mechanics|Hamiltonian]] approaches were developed to describe the motion of [[discrete system]]s, were then extended to [[continuous theory|continuous system]]s and in this form can be used to define [[vector field]]s. In this way, the techniques find use in [[electromagnetic]], [[quantum theory|quantum]] [[relativity theory]] and [[field theory]].
-* Wilkins, David R., ''[http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/ Sir William Rowan Hamilton]''.  School of Mathematics, Trinity College, Dublin.
-* [http://scienceworld.wolfram.com/biography/HamiltonWilliamRowan.html Wolfram Research's William Rowan Hamilton]
-* Cheryl Haefner's [http://www.engr.iupui.edu/~orr/webpages/cpt120/mathbios/hamil.htm Sir William Rowan Hamilton]
-== External links ==
+Hamilton's ''quaternions'', while not generally celebrated any longer as a subject taught in undergraduate work, are still used in specialized fields.
-* MacTutor's [http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Hamilton.html Sir William Rowan Hamilton]. School of Mathematics, [[University of St Andrews]].
+== Commemorations of Hamilton==
-* [http://31.1911encyclopedia.org/H/HA/HAMILTON_SIR_WILLIAM_ROWAN.htm 1911 ''Britannica Hamilton]''
+*[[Hamilton's equations]] are a formulation of classical mechanics.
-* [http://www.hamilton-trust.org.uk/ Hamilton Trust]
+*[[Hamiltonian (disambiguation)|Hamiltonian]] is the name of both a function (classical) and an operator (quantum) in physics, and a term from [[graph theory]]. It can be seen as the Quantum Hamiltonian.
-* [http://www.hamilton2005.ie/ The Hamilton year 2005 web site]
-* [http://www.hamilton.tcd.ie/ The Hamilton Mathematics Institute, TCD]
-* [http://www.hamilton.ie Hamilton Institute]
 == See also ==
+* [[Calculus]]
+* [[Isaac Newton]]
+* [[Joseph Louis Lagrange]]
 *[[List of people on stamps of Ireland]]
 *[[Tarik O'Regan]] (great, great, great grandson)
 *[[Against the Day]]
-<!-- Metadata: see [[Wikipedia:Persondata]] —>
+== Hamilton's publications ==
-{{Persondata
-|NAME= Hamilton, William
+* Hamilton, William Rowan. [http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/Lectures/AstIntro.html Introductory Lecture on Astronomy]. Dublin University Review and Quarterly Magazine Vol. I, Trinity College, January 1833. Retrieved August 20, 2007.
-|ALTERNATIVE NAMES=
+* Hamilton, William Rowan. [http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=05230001&seq=9 Lectures on Quaternions]. Royal Irish Academy, 1853. Retrieved August 20, 2007.
-|SHORT DESCRIPTION= [[Mathematician]], [[physicist]], and [[astronomer]]
+* David R. Wilkins. [http://www.maths.soton.ac.uk/EMIS/classics/Hamilton/ Hamilton's Mathematical Papers]. David R. Wilkins. Retrieved August 20, 2007.
-|DATE OF BIRTH= August 4, 1805
-|PLACE OF BIRTH=  [[Dublin]], [[Ireland]]
+==Notes==
-|DATE OF DEATH= September 2, 1865
+<references/>
-|PLACE OF DEATH=  [[Dublin]], [[Ireland]]
-}}
+== References ==
+*Ball, Robert S. 1895. ''Great astronomers''. London: Isbister.
+*Haefner, Cheryl. [http://www.engr.iupui.edu/~orr/webpages/cpt120/mathbios/hamil.htm Sir William Rowan Hamilton]. Cheryl Haefner. Retrieved August 10, 2007.
+* Hankins, Thomas. 1980. ''Sir William Rowan Hamilton''. Baltimore: The Johns Hopkins University Press. ISBN 0801822033.
+*McCartney, Mark, and Andrew Whitaker. 2003. Physicists of Ireland: Passion and Precision. London: Fracis & Taylor. ISBN 0750308664
+* Wilkins, David R. [http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/ Sir William Rowan Hamilton]. Dublin: School of Mathematics, Trinity College. Retrieved August 10, 2007.
+* [http://scienceworld.wolfram.com/biography/HamiltonWilliamRowan.html Wolfram Research's William Rowan Hamilton]. Eric W. Weisstein. Retrieved August 10, 2007.
+== External links ==
+All links retrieved May 12, 2023.
+* [http://www.hamilton-trust.org.uk/ Hamilton Trust].
+* [http://www.hamilton.ie Hamilton Institute].
-{{DEFAULTSORT:Hamilton, William Rowan}}
-[[Category:Physical sciences]]
+[[Category:Mathematicians]]
-[[Category:Biographies of Scientists and Mathematicians]]
-[[Category:Biography]]
-[[Category:Mathematics]]
 [[Category:Physics]]
 [[Category:Astronomy]]
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William Hamilton
William Rowan Hamilton
Born	August 4, 1805 Dublin, Ireland
Died	September 2, 1865 Dublin, Ireland
Residence	Ireland
Nationality	Irish, of Scottish descent
Field	Mathematician, physicist, and astronomer
Institutions	Trinity College Dublin
Alma mater	Trinity College Dublin
Academic advisor	John Brinkley
Known for	Quaternions and Hamiltonians
Religious stance	Anglican
Note that although Hamilton never had a doctoral advisor, scientific genealogy authorities regard the Reverend John Brinkley as Hamilton's equivalent mentor.