Hamilton discovers quaternions at Broom Bridge

Background. Sir William Rowan Hamilton, born in Dublin in 1805, was a prominent Irish mathematician whose work was later judged fundamental to modern theoretical physics and made him one of the founders of modern linear algebra. By 1843, he sought to extend complex numbers, which operate in a plane, to a three-dimensional system. In his own recollection, his sons William Edwin and Archibald Henry would ask him each morning whether he could multiply triples, to which he replied that he could only add and subtract them.

The Discovery. On 16 October 1843, Hamilton walked along the Royal Canal in Dublin with his wife. During this walk, he experienced a flash of insight regarding the multiplication of quaternions. He realized that the new algebra was non-commutative, a crucial distinction from complex numbers. This moment led him to immediately record the fundamental formula, establishing the basis for quaternion algebra and its applications in three-dimensional space.

Commemoration. The site of Hamilton's insight, Broom Bridge, is named after William Broome, a director of the Royal Canal company. Hamilton's sons later referred to it as the Quaternion Bridge. Although no trace of the original carving remains, a stone plaque on the bridge's underside commemorates the event. Since 1989, the National University of Ireland, Maynooth, has organized an annual pilgrimage to the bridge to honor this discovery.