William Rowan Hamilton

Mathematician and physicist — William Rowan Hamilton (Dublin 1805 – Dublin 1865) was an Irish mathematician, physicist and astronomer, a child prodigy who as a boy already knew numerous languages. In 1827, while still a student, he was appointed Royal Astronomer of Ireland. He made fundamental contributions to optics and mechanics, reformulating the latter in an elegant and powerful form, Hamiltonian mechanics, based on the total energy of the system. This formulation later proved decisive for the development of statistical mechanics and, above all, quantum mechanics, where the Hamiltonian operator is central. In mathematics he is famous for inventing quaternions, an extension of complex numbers.

Trivia

On 16 October 1843, during a walk along the Royal Canal in Dublin, he had the flash of insight that led to quaternions and carved the fundamental formula $i^2=j^2=k^2=ijk=-1$ into the stone of Broom Bridge with his knife.

Theories and contributions

• Hamiltonian mechanics — Reformulation of mechanics based on the Hamiltonian $H$ (total energy) and the equations $\dot{q}=\frac{\partial H}{\partial p}$, $\dot{p}=-\frac{\partial H}{\partial q}$.
• Quaternions — Hypercomplex numbers with three imaginary units: $i^2=j^2=k^2=ijk=-1$; useful for describing rotations in space.

Featured in chapters

19

Linked atoms

1 linked atom.

19 Le equazioni di Maxwell e le onde elettromagnetiche

• Maxwell in differential form