Place: United Kingdom, England
Subject: biography, maths and statistics
English mathematician who, by being the first to employ symbolic language and notation for purely logical processes, founded the modern science of mathematical logic.
He was born in Lincoln on 2 November 1815. He received little formal education, although for a time he attended a national school in Lincoln and also a small commercial school. His interest in mathematics appears to have been kindled by his father, a cobbler with a keen amateur interest in mathematics and the making of optical instruments. Boole also taught himself Greek, Latin, French, German, and Italian. At the age of 16 he became a teacher at a school in Lincoln; he subsequently taught at Waddington; then, at the age of 20, he opened his own school. All the while his spare time was devoted to studying mathematics, especially Newton's Principia and Lagrange's Mécanique analytique. He was soon contributing papers to scientific journals and in 1844 he was awarded a Royal Society medal. In 1849, despite his lack of a university education, he was appointed professor of mathematics at the newly founded Queen's College in Cork, Ireland. He held the chair until his death on 8 December 1864.
Boole's first essay into the field of mathematical logic began in 1844 in a paper for the Philosophical Transactions of the Royal Society. In it Boole discussed ways in which algebra and calculus could be combined, and the discussion led him to the discovery that the algebra he had devised could be applied to logic. In a pamphlet of 1847 he announced, against all previous accepted divisions of human knowledge, that logic was more closely allied to mathematics than to philosophy. He argued not only that there was a close analogy between algebraic symbols and those that represented logical forms but also that symbols of quantity could be separated from symbols of operation. These were the leading ideas which received their fuller treatment in Boole's greatest work, An Investigation of the Laws of Thought on which are Founded the Mathematical Theories of Logic and Probabilities (1854).
It is not quite true to say that Boole's book reduced logic to a branch of mathematics; but it did mark the birth of the algebra of logic, later known as Boolean algebra. The basic process of Boole's system is continuous dichotomy. His algebra is essentially two-valued. By sub-dividing objects into separate classes, each with a given property, it enables different classes to be treated according to the presence or absence of the same property. Hence it involves just two numbers, 0 and 1. This simple framework has had far-reaching practical effects. Applying it to the concept of ‘on’ and ‘off’ eventually produced the modern system of telephone switching, and it was only a step beyond this to the application of the binary system of addition and subtraction in producing the modern computer.
Later mathematicians modified Boole's algebra. Friedrich Frege, in particular, improved the scope of mathematical logic by introducing new symbols, whereas Boole had restricted himself to those symbols already in use. But Boole was the true founder of mathematical logic; it was on the foundations that he laid that Bertrand Russell and Alfred Whitehead attempted to build a rigidly logical structure of mathematics.
George Boole (b. Lincoln, England, 1815; d. Cork, Ireland, 1864), see Fig. 1 , was one of those rarities in an era of increasing...
b. Lincoln, England, 1815; d. Cork, Republic of Ireland, 1864 Boolean algebra; logic; operator theory; differential equations; difference...
By replacing logical operations by symbols, Boole showed that the operations could be manipulated to give logically consistent...