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Sir William Hamilton

1805–1865

 

As a mathematician, William Hamilton is to be ranked with Descartes and Fermat, though to many the crown of his life's work (as he saw it) seems strange and obscure.

      He was born in Dublin at midnight between 3rd and 4th August 1805.  Though there was always some dispute about his origins, he always claimed to be Irish, and hoped his life's work in mathematics would reflect on the national credit of Ireland.

      His father was a successful attorney, an exuberant and eloquent man, but one also given to overindulgence in drink.  Hamilton inherited some of his characteristics, but his brains came from his mother, who died when he was only twelve.

      By then he had been sent away to live with his uncle, a clergyman in Trim who was a formidable scholar.  He imparted his love of languages to his nephew; Hamilton read Hebrew by the age of seven, and Latin, Greek, and four European languages by the age of twelve.  By then he had also acquired a smattering of Syrian, Persian, Arabic, Sanskrit, Hindi and Malay - an extraordinary accomplishment even for a genius.  These language studies were posited on his father's notion that he might work for the East India Company.  In retrospect, all this seems to have been an extraordinary waste.

      However, even as a boy his mathematical talents became apparent.  When he was ten his mathematical skills were tested in a contest with Zerah Colburn, the now forgotten American child prodigy nicknamed 'The Calculating Boy', and did not come off too badly.  He read Euclid, doubtless in the original Greek, and soon moved on to Newton's Arithemetica Universalis and then the Principia.  By 1822, it was clear that he could understand much of this, and he continued to pursue these studies, becoming largely self-taught as a mathematician.

      At the age of seventeen, while reading the Celestial Mechanics of Laplace, his discovered an error.  This introduced him to Dr Brinkley, the astronomer royal for Ireland, whom he astonished with a paper on the osculation of certain curves of double curvature.  Clearly, this widely read young man was a mathematical genius of the first order.  He also caught the attention of Sir John Herschel and Professor George Airy, the leading British astronomers of the day.

      In 1823 he entered Trinity College in Dublin.  'This young man,' his friend Dr Brinkley remarked after Hamilton had presented his paper on light rays to the Royal Irish Academy, 'I do not say will be, but is, the first mathematician of his.'  To some it seemed that a second Newton had arrived.  He proved that certain rays of light emerge from a crystal, not as single or double rays, but as conical pencils.  This led to his convincing proof of the 'undulatory theory of light'.

      In 1827, while he was still an undergraduate, he was appointed Andrews professor of astronomy in the Dublin university.  He entered his undergraduate career by being elected Astronomer Royal at the age of twenty-two without even applying for the position, many distinguished astronomers being passed over.  But it gave him a post in which he could develop not only his astronomy, which had interested him since the age of fourteen, but have the time to do other work as well.

      This involved the elaboration of some 'curious discoveries' he had made at the age of seventeen, which he eventually published as A Theory of Systems of Rays.  The techniques he introduced were to prove of fundamental importance to the development of theoretical physics in the twentieth century.  His methods were just what was needed for the theory of wave mechanics associated today with quantum theory and the theory of atomic structure.  He presented an abstract of his work to the Royal Irish Academy in April 1827.

      He had well-developed literary tastes, and was a friend of Wordsworth and Southey.  His own poems, which one critic said, 'retain a straightforward clarity, strength, and dignity', were collected by his biographer, Robert Perceval Graves.  Wordsworth himself thought that Hamilton was one of the most remarkable men he had ever met, next only to Coleridge, his fellow poet.

      Hamilton had had two unhappy love affairs before he married an invalided lady.  It was a bad match which brought him little comfort.  After ten years he realized that he was slipping into alcoholism and gave up the conviviality that had been a feature of his younger years.  He was never quite free of this threat.

      While he and his wife were out walking one day (16th October 1843), he was suddenly struck by the notion of quaternions, his great discovery.  This was a new method of dealing with the science of space mathematically.  (It was a new system of algebra and geometry that expressed relations of space in regard to direction as well as quantity, and was based on the application of a new interpretation of what had been hitherto considered 'impossible quantities'.)  Having no paper on hand, Hamilton scratched the maths involved onto the stonework of a bridge over the Royal Canal at Ballyboggan, near Cabra.  A contemporary, Professor Peter Tait, later claimed that Hamilton's method was one 'which can only be compared with the Principia of Newton and the Mécanique Céleste of Laplace'.

      The last two decades of Hamilton's life were devoted to the elaboration of quaternions and their application to many fields; Elements of Quaternions was published after his death.  He left behind manuscript books and a huge collection of papers, which were found to be in an extraordinary muddle, largely due to his domestic difficulties.  Hidden deep in the piles of papers, dinner plates were found with still uneaten chops on them.

      The now reclusive Hamilton died in Dublin of gout on 2nd September 1865.  He had been described as the greatest man of science that Ireland ever produced.  Among the many honours that came to him (including a knighthood in 1835), none pleased him more than a last tribute awarded to him as he lay dying: he had been elected the first foreign member of the National Academy of Sciences of the United States.