One of the most imaginative mathematicians of the nineteenth century, Sir William Rowan Hamilton (1805–1865) changed the course of modern algebra with his discovery of quaternions in 1843. Although Hamilton's work was largely theoretical, his ideas came to have invaluable practical applications with the advent of quantum mechanics in the twentieth century. In this acclaimed biography, Thomas L. Hankins brings together the many aspects of Hamilton's life and work—from his significant contributions to mathematics, optics, and mechanics to his passion for metaphysics, poetry, and politics—fully portraying the brilliant man whose faith and idealism guided him in everything he did.