How did William rowan hamilton become famous?

William Rowan Hamilton became famous for his groundbreaking contributions to mathematics and physics, particularly in the development of quaternions, a system that extended complex numbers to higher dimensions. His formulation of Hamiltonian mechanics revolutionized classical mechanics by providing a new framework for understanding dynamic systems. Additionally, his work in optics and algebra earned him recognition in both scientific and academic circles, solidifying his legacy as a prominent figure in 19th-century mathematics.