BOOLE, GEORGE

born Nov. 2, 1815, Lincoln, Lincolnshire, Eng. died Dec. 8, 1864, Ballintemple, County Cork, Ire. English mathematician who helped establish modern symbolic logic and whose algebra of logic, now called Boolean algebra, is basic to the design of digital computer circuits. Boole was given his first lessons in mathematics by his father, a tradesman, who also taught him to make optical instruments. Aside from his father's help and a few years at local schools, however, Boole was self-taught in mathematics. When his father's business declined, George had to work to support the family. From the age of 16 he taught in village schools in the West Riding of Yorkshire, and he opened his own school in Lincoln when he was 20. During scant leisure time he read mathematics journals in the Mechanics Institute, founded about that time for science education. There he wrestled with the Principia of the 17th-century English physicist and mathematician Isaac Newton, the Trait de mcanique cleste of Pierre-Simon Laplace, and the Mcanique analytique of Joseph-Louis Lagrange, both 18th- and early 19th-century French mathematicians, and began to solve advanced problems in algebra. Boole submitted a stream of original papers to the new Cambridge Mathematical Journal, beginning in 1839 with his Researches on the Theory of Analytical Transformations. These papers were on differential equations and the algebraic problem of linear transformation, emphasizing the concept of invariance. In 1844 he discussed how methods of algebra and calculus may be combined in an important paper in the Philosophical Transactions of the Royal Society. That same year he was awarded a medal by the Royal Society for his contributions to analysis (i.e., using algebra and calculus to deal with the infinitely large and the infinitely small). Boole soon saw that his algebra could also be applied in logic. Developing novel ideas on logical method, and confident in the symbolic reasoning he had derived from his mathematical investigations, he published in 1847 a pamphlet, Mathematical Analysis of Logic, in which he argued persuasively that logic should be allied with mathematics, not philosophy. He won the admiration of the English logician Augustus De Morgan, who published Formal Logic the same year. On the basis of his publications, Boole in 1849 was appointed professor of mathematics at Queen's College, County Cork, even though he had no university degree. In 1854 he published An Investigation into the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities, which he regarded as a mature statement of his ideas. The next year he married Mary Everest, niece of Sir George Everest, for whom the mountain is named. The Booles had five daughters. One of the first Englishmen to write on logic, Boole pointed out the analogy between the algebraic symbols and those that can represent logical forms and syllogisms, showing how the symbols of quantity can be separated from those of operation. With Boole in 1847 and 1854 began the algebra of logic, or what is now called Boolean algebra. It is basically two-valued in that it involves a subdivision of objects into separate classes, each with a given property. Different classes can then be treated as to the presence or absence of the same property. Boole's original and remarkable general symbolic method of logical inference, fully stated in Laws of Thought (1854), enables one, given any propositions involving any number of terms, to draw conclusions, by the symbolic treatment of the premises, that are logically contained in the premises. He also attempted a general method in probabilities, which would make it possible from the given probabilities of any system of events to determine the consequent probability of any other event logically connected with the given events. In 1857 he was elected a Fellow of the Royal Society. The influential Treatise on Differential Equations appeared in 1859 and was followed the next year by its sequel, Treatise on the Calculus of Finite Differences. Used as texts for many years, these works embody an elaboration of Boole's more important discoveries. Boole's abstruse reasoning led to applications of which he never dreamed: telephone switching and electronic computers use binary digits, which allow a series of dual alternative routines in the mathematical sequence of instructions to these devices. Additional reading For details about Boole's life and contributions to logic, see William Kneale, Boole and the Revival of Logic, Mind, 57:149175 (1948), with bibliography; see also Boole by T.A.A. Broadbent in the Dictionary of Scientific Biography, vol. 2 (1970); and E.T. Bell, Men of Mathematics (1937, reprinted 1961).