## William Hamilton

astronomer
mathematician
physicist
scientist

August 4, 1805
(age 60)
Dublin, Ireland

In 1822 Hamilton submitted a paper on the osculation of certain curves of double curvature to John Brinkley, professor of astronomy at Trinity College and astronomer royal of Ireland. In 1824 he 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 the present paper, it is proposed to investigate some general properties common to all such Systems of Rays, and independent of the particular surface or particular law. It is intended in another paper to point out the application of these mathematical principles to the actual laws of Nature. " These words prefaced in effect Hamilton's lifelong program in mathematical physics. The committee appointed to report on the merits of Hamilton's paper requested him to elaborate further on the topic. In 1827 Hamilton, still an undergraduate, presented to the 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. This paper earned Hamilton not only fame but also meteoric rise in the academic world. Although still an undergraduate, he was appointed Andrews professor of astronomy (1827). Connected with the munificently endowed chair were the directorship of the Observatory of Dunsink, the title of astronomer royal of Ireland, and a spacious lodging on the observatory grounds. Furthermore, it was understood that he had no observational duties to perform lest his theoretical investigations be disturbed. The next 7 years in Hamilton's life were bathed in the sunshine of success and glory in every sense. His lectures on astronomy drew crowds that he kept spellbound with his soaring rhetoric. The prodigy was the toast of society, and he made lifelong friendships with Samuel Taylor Coleridge and William Wordsworth.
In early 1834 Hamilton made the most spectacular discovery of his career-the prediction that under certain circumstances an internal and an external conical refraction would occur. The prediction was soon verified by Humphrey Lloyd, a professor of physics at Trinity. In 1836 Hamilton became president of the Royal Irish Academy. 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. In his letter of October 15, 1858, to Tait, he described in detail what went on in his mind as he walked on October 16, 1843, toward Broughman Bridge in Dublin: "I then and there felt the galvanic circuit of thought close; and the sparks which fell from it were the fundamental equations between i, j, k; exactly such as I have used them ever since. " From another letter of his we know that on the spur of the moment Hamilton "cut with a knife on a stone of Brougham Bridge . .. the formula 12 [minus ] j2 [minus ] k2 [minus ] ijk= [minus ]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. He also worked feverishly to achieve as much as possible of his great ambition, the detailed formulation of his quaternion theory, in which he saw the geometrical regularity embodied in the physical universe. His Elements of Quaternions, a huge volume comprising the efforts of his last 10 years, was published a year after his death. He felt immense satisfaction on learning shortly before his death, on September 2, 1865, that the recently established National Academy of Sciences in the United States had elected him as its foreign associate. In fact, the academy put Hamilton's name on the top of the list by a majority vote of two-thirds.