Hamilton carved his breakthrough equation into a Dublin bridge with a penknife
On 16 October 1843, walking beside Dublin's Royal Canal with his wife, William Rowan Hamilton suddenly saw how to multiply numbers in four dimensions. Afraid to lose the idea, he pulled out a penknife and scratched the formula for his new quaternions into the stone of Broom Bridge.
He had spent years trying to extend complex numbers, which live on a flat plane, into higher dimensions, and three would not work; four did. Quaternions helped make him a founder of modern linear algebra, though in 1840 Olinde Rodrigues had reached essentially the same result without the name. Hamilton devoted his last six years to a book on them, still unfinished when he died in 1865 after a severe attack of gout.
Born in Dublin in 1805, the fourth of nine children of a solicitor, he was sent at three to an uncle who ran a school in Trim. His father hoped he would join the East India Company, so languages came first: by 13 he reportedly had a dozen, including Persian, Arabic and Sanskrit, though some historians doubt how deep that knowledge went. At eight he lost a mental arithmetic contest to the American prodigy Zerah Colburn and switched his energies to mathematics, reading Euclid at ten and much of Newton's Principia by 16.
Spotting what he thought was an error in Laplace's celestial mechanics brought him to John Brinkley, Ireland's Royal Astronomer, who declared the teenager already the first mathematician of his age. Entering Trinity College Dublin at 17, he came first in every examination, and in 1827, still an undergraduate, succeeded Brinkley as professor of astronomy and director of Dunsink Observatory, which stayed his home until he died. His lectures drew poets, and he befriended William Wordsworth, sending him many poems.
His Theory of Systems of Rays predicted conical refraction, in which light entering certain crystals emerges as a hollow cone. Applying the same approach to motion, he produced Hamiltonian mechanics, revealing a symmetry between position and momentum. The function now called the Hamiltonian remains a starting point for calculation across quantum theory, relativity and nearly every other branch of physics.
Source: William Rowan Hamilton
