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William Rowan Hamilton

William Hamilton
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William Rowan Hamilton (1805–1865)
Born (1805-08-04)4 August 1805
Dublin
Died 2 September 1865(1865-09-02) (aged 60)
Dublin
Residence Ireland
Nationality Irish
Fields Physics, astronomy, and mathematics
Institutions Trinity College, Dublin
Alma mater Trinity College, Dublin
Doctoral advisor Template:If empty
Academic advisors John Brinkley
Known for Hamilton's principle
Hamiltonian mechanics
Hamiltonians
Hamilton–Jacobi equation
Quaternions
Biquaternions
Hamiltonian path
Icosian calculus
Nabla symbol
Versor
Coining the word 'tensor'
Hamiltonian vector field
Icosian game
Universal algebra
Hodograph
Hamiltonian group
Cayley–Hamilton theorem
Influences John T. Graves
Influenced Zerah Colburn
Peter Guthrie Tait
Notable awards Royal Medal (1835)

Sir William Rowan Hamilton (midnight, 3–4 August 1805 – 2 September 1865) was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques. His best known contribution to mathematical physics is the reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism, and to the development of quantum mechanics. In pure mathematics, he is best known as the inventor of quaternions.

Hamilton is said to have shown immense talent at a very early age. Astronomer Bishop Dr. John Brinkley remarked of the 18-year-old Hamilton, 'This young man, I do not say will be, but is, the first mathematician of his age.'

Life

William Rowan Hamilton's scientific career included the study of geometrical optics, classical mechanics, 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

Hamilton was the fourth of nine children born to Sarah Hutton (1780–1817) and Archibald Hamilton (1778–1819), who lived in Dublin at 38 Dominick Street. Hamilton's father, who was from Dunboyne, worked as a solicitor. By the age of three, Hamilton had been sent to live with his uncle James Hamilton, a graduate of Trinity College who ran a school in Talbots Castle in Trim Co Meath.[1] His uncle soon discovered that Hamilton had a remarkable ability to learn languages, and from a young age, had displayed an uncanny ability to acquire them (although this 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, 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. These included the classical and modern European languages, and Persian, Arabic, Hindustani, Sanskrit, and even Marathi and Malay. He retained much of his knowledge of languages to the end of his life, often reading Persian and Arabic in his spare time, although he had long stopped studying languages, and used them just for relaxation.

In September 1813 the American calculating prodigy Zerah Colburn was being exhibited in Dublin. Colburn was 9, a year older than Hamilton. The two were pitted against each other in a mental arithmetic contest with Colburn emerging the clear victor. In reaction to his defeat, Hamilton dedicated less time to studying languages and more time to studying mathematics.[2][3][4]

Hamilton was part of a small but well-regarded school of mathematicians associated with Trinity College, Dublin, which he entered at age 18. He studied both classics and mathematics, and was appointed Professor of Astronomy in 1827, prior to his graduation taking up residence at Dunsink Observatory where he spent the rest of his life.[3]

Optics and Mechanics