William Rowan Hamilton

Sir William Rowan Hamilton (1805–1865) was an Irish prodigy who reportedly knew a dozen languages by his early teens and was appointed Ireland's Royal Astronomer while still an undergraduate. He turned out to be a far better mathematician than astronomer — and he gave the world a way to describe rotations in 3D that video-game engines still rely on today.

An idea for the ages

Hamilton spent years searching for a number system that could rotate things in three dimensions the way complex numbers rotate the plane. The answer needed four components, not three: the quaternions, obeying the rule he famously carved into a bridge:

i^2 = j^2 = k^2 = ijk = -1.

He also reshaped physics with Hamiltonian mechanics, the elegant energy-based view of motion that later became the language of quantum mechanics — and the same idea, the Hamiltonian and costate, drives modern optimal control.

On 16 October 1843, walking along the Royal Canal in Dublin with his wife, Hamilton was struck by the flash of insight he'd chased for a decade. Afraid he'd forget it, he pulled out a penknife and scratched the quaternion formula into the stone of Broom Bridge. The original scratch is long gone, but a plaque now marks the spot, and mathematicians make an annual pilgrimage there every October. It may be the most famous act of vandalism in the history of science.