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Hamilton's advances enlarged greatly the class of mechanical problems that could be solved and they represent perhaps the greatest addition which dynamics had received since the work of Isaac Newton and Lagrange. Today the quaternions are used in computer graphics control theory signal processing and orbital mechanics mainly for representing rotations/orientations. The Hamiltonian is the name of both a function (classical) and an operator (quantum) in physics and in a different sense a term from graph theory.
In mathematics he is perhaps best known as the inventor of quaternions. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques. Sir William Rowan Hamilton (4 August 1805 – 2 September 1865) was an Irish physicist astronomer and mathematician who made important contributions to classical mechanics optics and algebra.