Credited to Ireland. Olinde Rodrigues described quaternions and their use for rotations in print in 1840 in all but name. Hamilton discovered them independently in 1843, named them, and developed the theory.
How it began
By 1843 William Rowan Hamilton knew that complex numbers could be treated as points in a plane, and he had spent years trying to find a comparable system for points in space by multiplying triples of numbers. On October 16, 1843 he was walking with his wife along the Royal Canal in Dublin. As they came to Brougham Bridge, now Broom Bridge, he saw that the multiplication worked for quadruples. He carved the rule into the stone of the bridge: i² = j² = k² = ijk = −1.
How it works
A quaternion is a quadruple of numbers with one real part and three imaginary units, i, j and k, multiplied according to Hamilton's rule. Three of the four numbers can serve as the coordinates of a point in space. Unlike ordinary multiplication, the order in which two quaternions are multiplied matters.
What changed first
Hamilton named the new numbers quaternions and devoted the rest of his life to studying and teaching them. Two months later, on December 26, 1843, his friend John Graves wrote to him with a system of eight parts, which he called octaves. Graves had earlier interested Hamilton in algebra.
Where it stands today
Quaternions are commonly used in computer graphics, robotics and physics because they describe rotations efficiently. A plaque on Broom Bridge marks the spot where Hamilton found the formula; his original carving has not survived. The 175th anniversary was commemorated on October 16, 2018.
