W. R. Hamilton

William Hamilton
William Rowan Hamilton (1805–1865)
Born	(1805-08-04)4 August 1805 Dublin, Ireland
Died	2 September 1865(1865-09-02) (aged 60) Dublin, Ireland
Residence	Ireland
Nationality	Irish
Fields	Physics, astronomy, and mathematics
Institutions	Trinity College, Dublin
Alma mater	Trinity College, Dublin
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 PRIA FRSE (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.'

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.