Collection: Hamilton's Formula

Famously carved into a stone bridge by Irish mathematician William Rowan Hamilton, this equation describes how to work with complex numbers that include the square roots of negative numbers.

This equation, set out by William Rowan Hamilton, is central to an obscure branch of mathematics called quaternion algebra. The story is that the great breakthrough in quaternions finally came on Monday 16 October 1843 in Dublin, when Hamilton was on his way to the Royal Irish Academy where he was going to preside at a council meeting. As he walked along the towpath of the Royal Canal with his wife, the concepts behind quaternions were taking shape in his mind.

When the answer dawned on him, Hamilton could not resist the urge to carve the formula for the quaternions, into the stone of Brougham Bridge as he paused on it. Although the carving has since faded away, there has been an annual pilgrimage since 1989 called the Hamilton Walk for scientists and mathematicians who walk from Dunsink Observatory to the Royal Canal bridge in remembrance of Hamilton’s discovery.

Nowadays, quaternion algebra is central to the computer graphics industry. It is used to describe the orientations of objects on the screen.