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Hamilton was born on 13 December 1730 (or 12 January 1731) in either London or at Park Place, Berkshire, the fourth son of Lord Archibald Hamilton, governor of Jamaica and seventh son of the 3rd Duchess of Hamilton, and Lady Jane Hamilton, daughter of James Hamilton, 6th Earl of Abercorn.
His mother was a favourite, and possibly a mistress, of the Prince of Wales and William grew up with his son George III, who would call him his "foster brother"
Mathematics also interested Hamilton from an early age, but it was the more dramatic skill of rapid calculation that first attracted attention.
At age nine, he went to Westminster School, where he made lifelong friends of Frederick Hervey and David Murray. Hamilton used to say that he was born with an ancient name and a thousand pounds; as a younger son he would have to make his own way in life.
So, six weeks after his sixteenth birthday, he was commissioned into the 3rd Foot Guards as an ensign.
By his fifth year he was proficient in Latin, Greek, and Hebrew; and during his ninth year his father boasted of his more recent mastery of Persian, Arabic, Sanskrit, Chaldee, Syriac, Hindustani, Malay, Marathi, Bengali, “and others. ”
He was desperate to get mementos from her brother—locks of hair, poetry, a miniature that he secretly had copied in Dublin—and relieved his distress by writing his confessions to close friends, often daily, sometimes twice a day.
Matrices and even vector analysis have a parent in quaternions.
In 1818 he competed unsuccessfully against Zerah Colburn, the American “calculating boy”; he met him again in 1820.
At about this time he also began to read Newton’s Principia and developed a strong interest in astronomy, spending much time observing through his own telescope.
In 1822 he noticed an error in Laplace’s Mécanique céleste.
The result was a series of researches on properties of curves and surfaces that he sent to Brinkley.
Among them was “Systems of Right Lines in a Plane, ” which contained the earliest hints of ideas that later were developed into his famous “Theory of Systems of Rays. ”
The paper was referred to a committee which reported six months later that it was “of a nature so very abstract, and the formulae so general, as to require that the reasoning by which some of the conclusions have been obtained should be more fully developed. .. ”
Anyone who has struggled with Hamilton’s papers can sympathize with the committee, but to Hamilton it was a discouraging outcome.
Hamilton considered his “Systems of Rays” to be merely an expansion of his paper on caustics.
Actually the papers were quite different.
The characteristic function appeared only in the “Theory of Systems of Rays, ” while “On Caustics” investigated the properties of a general rectilinear congruence. Hamilton had taken the entrance examination for Trinity on 7 July 1823 and, to no one’s surprise, came out first in a field of 100 candidates.
He introduced French textbooks and caused others to be written in order to bring the students up to date on Continental methods.
These reforms were essentially completed when Hamilton arrived at Trinity.
At about this time he also began to read Newton’s Principia and developed a strong interest in astronomy, spending much time observing through his own telescope.
He returned to his labors and expanded his paper on caustics into the “Theory of Systems of Rays, ” which he presented to the Academy on 23 April 1827, while still an undergraduate at Trinity College.
He continued this auspicious beginning by consistently winning extraordinary honors in classics and science throughout his college career.
Trinity College, Dublin, offered an excellent curriculum in mathematics during Hamilton’s student years, owing in large part to the work of Bartholomew Lloyd, who became professor at the college in 1812 and instituted a revolution in the teaching of mathematics.
He still had not taken a degree, but he was chosen over several well-qualified competitors, including George Biddell Airy. As a practical astronomer Hamilton was a failure.
On 10 June 1827 Hamilton was appointed astronomer royal at Dunsink Observatory and Andrews professor of astronomy at Trinity College.
He and his assistant Thompson maintained the instruments and kept the observations with the somewhat reluctant help of three of Hamilton’s sisters who lived at the observatory.
After his first few years Hamilton did little observing and devoted himself entirely to theoretical studies.
Hamilton’s first serious venture into idealism came in 1830, when he began a careful reading of the collected works of George Berkeley, borrowed from Hamilton’s friend and pupil Lord Adare.
The “General Method in Dynamics” of 1834 was based directly on the characteristic function in optics, which he had worked out well before he studied Kant or Bošković.
The first readable book on quaternions was P. G. Tait’s Elementary Treatise on Quaternions (1867).
One can sympathize with Tait’s commitment to quaternions and his dissatisfaction with vector analysis.
It was difficult enough to give up the commutative property in quaternion multiplication, but vector analysis required much greater sacrifices.
It accepted two kinds of multiplication, the dot product and the cross product.
The dot product was not a real product at all, since it did not preserve closure; that is, the product was not of the same nature as the multiplier and the multiplicand.
Both products failed to satisfy the law of the moduli, and both failed to give an unambiguous method of division.
Moreover the cross product (in which closure was preserved) was neither associative nor commutative.
No wonder a devout quaiernionist like Tait looked upon vector analysis as a “hermaphrodite monster. ”
Nevertheless vector analysis proved to be the more useful tool, especially in applied mathematics.
The controversy did not entirely die, however, and as late as 1940 E. T. Whittaker argued that quaternions “may even yet prove to be the most natural expression of the new physics [quantum mechanics]. ”
The quaternions were not the only contribution that Hamilton made to mathematics.
On one occasion in 1843 he was called to task for not having maintained a satisfactory program of observations, but this protest did not seriously disturb his more congenial mathematical researches.
Life at the observatory gave Hamilton time for his mathematical and literary pursuits, but it kept him somewhat isolated.
His reputation in the nineteenth century was enormous; yet no school of mathematicians grew up around him, as might have been expected if he had resided at Trinity College.
In the scientific academies Hamilton was more active.
A prominent early member of the British Association for the Advancement of Science, he was responsible for bringing the annual meeting of the association to Dublin in 1835.
On that occasion he was knighted by the lord lieutenant.
In 1837 he corrected Abel’s proof of the impossibility of solving the general quintic equation and defended the proof against G. B. Jerrard, who claimed to have found such a solution.
He also became interested in the study of polyhedra and developed in 1856 what he called the “Icosian Calculus, ” a study of the properties of the icosahedron and the dodecahedron.
This study resulted in an “Icosian Game” to be played on the plane projection of a dodecahedron.
He sold the copyright to a Mr. Jacques of Piccadilly for twenty-five pounds.
His characteristic function in optics did not hit at the controversy then current over the physical nature of light, and it became important for geometrical optics only sixty years later when Bruns rediscovered the characteristic function and called it the method of the eikonal.
His dynamics was saved from oblivion by the important additions of Jacobi, but even then the Hamiltonian method gained a real advantage over other methods only with the advent of quantum mechanics.
The quaternions, too, which were supposed to open the doors to so many new fields of science turned out to be a disappointment.
Yet quaternions were the seed from which other noncommutative algebras grew.
Over the long run the success of Hamilton’s work has justified his efforts.
The high degree of abstraction and generality that made his papers so difficult to read has also made them stand the test of time, while more specialized researches with greater immediate utility have been superseded.
Hermann Günther Grassmann working independently of Hamilton published his Ausdehnungslehre in 1844 in which he treated n-dimensional geometry and hypercomplex systems in a much more general wav than Hamilton; but Grassmann’s book was extremely difficult and radical in its conception and so had very few readers.
Hamilton’s books on quaternions were also too long and too difficult to attract much of an audience.
His Lectures on Quaternions (1853) ran to 736 pages wifh a sixtyfour-page preface.
Any reader can sympathize with John Hersehel’s request that Hamilton make his principles “clear and familiar down to the level of ordinary unmetaphysical apprehension” and to “introduce the new phrases as strong meat gradually given to babes. ”
After a short period as a Member of Parliament, he served as British Ambassador to the Kingdom of Naples from 1764 to 1800.
He studied the volcanoes Vesuvius and Etna, becoming a Fellow of the Royal Society and recipient of the Copley Medal.
He joined the Royal Irish Academy in 1832 and served as its president from 1837 to 1845.
The Royal Society awarded him the Copley Medal in 1770 for his paper.
(Excerpt from Philosophical Transactions: An Account of th...)
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In 1761 Hamilton entered Parliament as Member for Midhurst.
He was a member of the Royal Irish Academy in 1832
He was robust and energetic, with a good sense of humor.
In 1831 he was rejected by Ellen De Vere, sister of his good friend the poet Aubrey De Vere, and in 1833 he married Helen Bayly.
His second wife was Emma Hamilton, famed as Horatio Nelson's mistress.
The fourth of nine children, Hamilton was raised and educated from the age of three by his uncle James Hamilton, curate of Trim, who quickly recognized his fabulous precocity.
