BOOLE , GEORGE

Boole , George: translation

Boole came from a poor background in the English city of Lincoln and was virtually self-taught in mathematics. He discovered for himself the theory of invariants. Before he obtained an academic post Boole spent several years as a school teacher, first in Yorkshire and later at a school he opened himself. In 1849 he became professor of mathematics at Queen's College, Cork, Ireland.

Boole's main work was in showing how mathematical techniques could be applied to the study of logic. His book The Laws of Thought (1854) is a landmark in the study of logic. Boole laid the foundations for an axiomatic treatment of logic that proved essential for the further fundamental developments soon to be made in the subject by such workers at Gottlob Frege and Bertrand Russell.

Boole's own logical algebra is essentially an algebra of classes, being based on such concepts as complement and union of classes. His work was an important advance in considering algebraic operations abstractly – that is, studying the formal properties of operations and their combinations without reference to their interpretation or ‘meaning’. Fundamental formal properties like commutativity and associativity were first studied in purely abstract terms by Boole.

Boole's work led to the recognition of a new and fundamental algebraic structure the Boolean algebra alongside such structures as the field, ring, and group. The study of Boolean algebras both in themselves and their application to other areas of mathematics has been an important concern of 20th-century mathematics. Boolean algebras find important applications in such diverse fields as topology, measure theory, probability and statistics, and computing.