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Dominick Street, a wide thoroughfare crossing Bolton Street, was the residence of many of the aristocracy. Sir William Hamilton the great Irish mathematical genius was born in No. 36

William Rowan Hamilton's scientific career included the study of geometrical optics, classical mechanics, adaptation of dynamic methods in optical systems, applying quaternion and vector methods to problems in mechanics and in geometry, development of theories of conjugate algebraic couple functions (in which complex numbers are constructed as ordered pairs of real numbers), solvability of polynomial equations and general quintic polynomial solvable by radicals, the analysis on Fluctuating Functions (and the ideas from Fourier analysis), linear operators on quaternions and proving a result for linear operators on the space of quaternions (which is a special case of the general theorem which today is known as the Cayley–Hamilton theorem). Hamilton also invented "icosian calculus", which he used to investigate closed edge paths on a dodecahedron that visit each vertex exactly once.

Hamilton was looking for ways of extending complex numbers (which can be viewed as points on a 2-dimensional plane) to higher spatial dimensions. He failed to find a useful 3-dimensional system (in modern terminology, he failed to find a real, three-dimensional skew-field), but in working with four dimensions he created quaternions. According to Hamilton, on 16 October he was out walking along the Royal Canal in Dublin with his wife when the solution in the form of the equation i2 = j2 = k2 = ijk = −1 suddenly occurred to him; Hamilton then promptly carved this equation using his penknife into the side of the nearby Broom Bridge (which Hamilton called Brougham Bridge).This event marks the discovery of the quaternion group.

A plaque under the bridge was unveiled by the Taoiseach Éamon de Valera, himself a mathematician and student of quaternions, on 13 November 1958.

It should be noted that the new tram service that passes along Dominick Street now goes as far as Broombridge.

The equation i2 = j2 = k2 = ijk = −1