# William Rowan Hamilton

**Sir William Rowan Hamilton** LL.D, DCL, MRIA (3 August 1805 – 2 September 1865)[1] was an Irish mathematician, Andrews Professor of Astronomy at Trinity College Dublin, and Royal Astronomer of Ireland. He worked in both pure mathematics and mathematics for physics. He made important contributions to optics, classical mechanics and algebra. Although Hamilton was not a physicist–he regarded himself as a pure mathematician–his work was of major importance to physics, particularly his 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.

Sir William Rowan Hamilton | |
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Born | Dublin, Ireland | 4 August 1805

Died | 2 September 1865 60) Dublin, Ireland | (aged

Nationality | Irish |

Alma mater | Trinity College, Dublin |

Known for | Hamilton's principle Hamiltonian mechanics Hamiltonians Hamilton–Jacobi equation Quaternions Biquaternions Hamiltonian path Icosian calculus Nabla symbol Versor Coining the word 'tensor' Coining the word 'scalar' cis notation Hamiltonian vector field Icosian game Universal algebra Hodograph Hamiltonian group Cayley–Hamilton theorem |

Spouse(s) | Helen Maria Bayly |

Children | William Edwin Hamilton, Archibald Henry Hamilton, Helen Eliza Amelia O'Regan Hamilton |

Awards | Royal Medal (1835) |

Scientific career | |

Fields | Mathematics, astronomy, physics |

Institutions | Trinity College, Dublin |

Academic advisors | John Brinkley |

Influences | Zerah Colburn John T. Graves |

Influenced | Peter Guthrie Tait |

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.