Hamilton, Sir William Rowan, 1805–65, Irish mathematician and astronomer, b. Dublin. A child prodigy, he had mastered 13 languages by the age of 13 and was still an undergraduate when he became professor of astronomy at the Univ. of Dublin (1827). Hamilton was one of the most original and creative mathematicians of his time. In his *Theory of Systems of Rays* (1828) he predicted the existence of conical refraction (later confirmed experimentally by H. Lloyd) and unified the field of optics under the principle of varying action, which he later extended to dynamics and which has become of fundamental importance in modern physics, particularly quantum theory. His later years, which were marred by personal problems, were largely devoted to the invention and development of his theory of quaternions. Although he believed this work to be his most important, quaternions have been superseded in many applications by the methods of vector and tensor analysis. Of some import, however, was his discovery that the algebra of quaternions does not follow the commutative law; it opened the way for the discovery and development of numerous types of abstract algebras by later mathematicians.

See E. T. Bell, *Men of Mathematics* (1937).

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.