William Rowan Hamilton

William Rowan Hamilton was an Irish mathematician and physicist whose reach across disciplines was almost embarrassing. Born in Dublin in 1805, he was reading Latin, Greek and Hebrew by age five, had a working knowledge of a dozen languages by his early teens, and was appointed Andrews Professor of Astronomy at Trinity College Dublin — and Royal Astronomer of Ireland — while still an undergraduate. He held the post for the rest of his life.

His contributions to physics begin with optics, where in the 1820s and 1830s he developed a variational principle that treated rays of light as paths that extremised a characteristic function. It was inside this programme, in a paper read to the Royal Irish Academy in 1839, that he wrote down the formula v_g = dω/dk and distinguished it explicitly from the phase velocity of an individual ray. Rayleigh would later generalise the argument, but the identity is Hamilton's.

Hamilton then transposed the same variational machinery onto classical mechanics, producing the Hamilton-Jacobi equation and the Hamiltonian formulation that underlies most of modern physics — quantum mechanics in particular was built on Hamilton's framework a century after his death. Along the way he invented the quaternions (famously carved into Dublin's Broom Bridge in 1843 when he worked them out on a walk), introduced the term 'scalar' and 'vector', and laid the groundwork for modern linear algebra.