William Rowan Hamilton discovers quaternions on 16 October 1843 while walking along the Royal Canal in Dublin, carving the fundamental formula i²=j²=k²=ijk=−1 into Broom Bridge. Quaternions extend complex numbers to four dimensions and are the first non-commutative algebraic system in history. Hamilton publishes them in Lectures on Quaternions (1853). Although for decades Gibbs and Heaviside's vectors overshadowed them in practical use, quaternions are today indispensable in 3D computer graphics, robotics, inertial navigation, and theoretical particle physics.