George Boole

English mathematician and logician

• Born: November 2, 1815; Lincoln, England
• Died: December 8, 1864; Ballintemple, Ireland

Nineteenth-century British mathematician and logician George Boole is best known for developing the concept of modern symbolic logic and the creation of what is now known as Boolean algebra. Prior to Boole, logic was considered part of philosophy, not mathematics. His linguistic algebra, consisting of three basic operations (AND, OR and NOT), has formed the basis of modern computer languages, systems, and circuits.

Primary fields: Mathematics; computer science

Specialties: Logic; algebra; mathematical analysis

Early Life

George Boole was born on November 2, 1815 in Lincoln, Lincolnshire, England, the first son of John Boole and Mary Ann Joyce. His father was a shoemaker and his mother was a maid. Nine years after George’s birth, the couple had three other children: Mary Ann, William, and Charles. Although a cobbler by trade, Boole’s father had a keen interest in mathematics and science. He enjoyed building kaleidoscopes, telescopes, and cameras with his eldest son.

Even as a boy, Boole possessed great intelligence, an outstanding memory, and a penchant for rigorous study. After attending a school for the children of tradesmen and later a commercial school, he went to primary school and developed an interest in foreign languages. His father hired a tutor to teach him Latin and he later taught himself Greek, French, and German. At fourteen, he found himself in the middle of a public disagreement when his father published one of his translations of a poem by the Greek author Meleager; a local schoolmaster protested that it could not be the work of an adolescent.

Despite his innate gifts, Boole did not continue his education. For a time, he thought of becoming an Anglican priest. When he was sixteen, his father’s business closed. In order to support his family, Boole became an assistant teacher at Heigham’s School in Doncaster. Four years later, at age twenty, he opened his own school in Lincoln. It was during this period that Boole began to study higher mathematics. He was inspired to do so by the poor quality of the mathematics texts available to his students. He mastered Sir Isaac Newton’s three-volume Principia Mathematica and Joseph-Louis Lagrange’s two-volume Mécanique Analytique. He based his first scientific paper, published in 1835, on an address he wrote at the dedication of a bust of Newton in Lincolnshire.

In 1855, Boole married Mary Everest, the niece of Sir George Everest, after whom Mount Everest is named. They had five daughters together: Mary Ellen, Margaret, Alicia Stott, Lucy Everest, and Ethel Lilian. Following Boole’s death, his widow taught each of their daughters mathematics and contributed to the mathematical field herself, writing about the ways in which children use logic and reason to learn math.

Life’s Work

Boole produced a number of pioneering mathematical and scientific papers over the course of his career. In 1840, he published several articles on algebraic problems and differential equations in the Cambridge Mathematical Journal and wrote pieces on calculus and algebra for the Royal Society in London. Four years later, his paper on the calculus of operators, submitted to the Royal Society, earned him the organization’s gold medal. The award helped to solidify his reputation as an influential mathematician.

In 1847, Boole published a slim pamphlet titled The Mathematical Analysis of Logic. In this pioneering work, he establishes the concept of modern symbolic logic (the system of signs used to represent quantities and relationships) and makes a compelling case that logic, long associated with the ancient Greek philosopher Aristotle, should in fact be considered a mathematical discipline. He argues that Aristotle’s elaborate debates could be effectively broken down into two algebraic quantities, 1 and 0, with 1 representing discussed objects and 0 being an empty set. Boole’s binary system, or dual system, was influenced by the work of seventeenth-century German mathematician and philosopher Gottfried Wilhelm von Leibniz. In 1849, Boole’s paper helped earn him a position as professor of mathematics at Queen’s College in Cork, Ireland, despite the fact he had never earned a college degree.

In 1854, Boole elaborated on his ideas in a publication titled An Investigation of the Laws of Thought on which Are Founded the Mathematical Theories of Logic and Probabilities. Considered by many to be his most significant work, the treatise delineates Boole’s complete thoughts on mathematical logic, now known as Boolean algebra. This branch of mathematics has become central to the development of many scientific fields, including combinatorial theory, computer design, information theory, probability, and switching theory.

Boolean algebra, which uses the logical operators of AND, OR, and NOT, is a theory of relations in which elements have either one or two values. It also provides for the creation of laws of possibility among proportions. Boole demonstrated that comparisons, or basic mathematical functions, could be performed using these three simple functions, revolutionizing the way operators are seen. The operator AND, for example, in Boolean logic limits results, while an AND operator in other mathematics adds results together. (For example, a Boolean logic search in a computer database for George AND Washington would limit results to information pertaining only to the first US president.) Moreover, by reducing the complexity of Aristotle’s philosophic logic to this simple algebra, Boole moved logic firmly into the world of mathematics.

Boole’s later works included two textbooks that remained in popular use in Great Britain decades after his death: Treatise on Differential Equations (1859) and Treatise on the Calculus of Finite Differences (1860). As a teacher, he was committed to his students, despite health problems that plagued him with the onset of middle age. Boole died of pneumonia in Ballintemple, County Cork, Ireland, on December 8, 1864. He was forty-nine years old.

Impact

During Boole’s lifetime, his work appeared to have little use outside of the world of higher mathematics. However, his name is better known today than it has ever been, due in large part to the fact that “Boolean searches” underpin much of computer science. These searches are used to look up information on the Internet, and in computer databases. By using Boole’s operators AND, OR, and NOT, among others, researchers are able to limit, widen, or define a database search and thereby produce better search results.

Boole’s work does not simply affect the way people search for information on computers; it is central to the very architecture of modern computers. In the 1930s, nearly seventy years after Boole’s death, an American mathematician and electrical engineer named Claude Shannon used Boole’s concepts to jettison the complicated and random arrangements of electrical circuits then in use to create far simpler electromechanical relays. Shannon then used these new and more effective relay systems to compute Boolean algebra problems. Today, Boole’s work in restricting logic to two quantities (1 and 0) applies to the creation and development of the binary code and computer circuits that allow a global network of computer systems to function.

Bibliography

Davis, Martin. The Universal Computer: The Road from Leibniz to Turing. Boca Raton: CRC, 2012. Print. Examines the development of modern computers through the lives of seven mathematicians (including Boole) whose theories and ideas made computer science possible.

Jacquette, Dale. On Boole. Belmont: Wadsworth/Thomson Learning, 2002. Print. Presents an overview of Boole’s work as it relates to philosophy.

MacHale, Des. George Boole: His Life and Work. Dublin: Boole, 1985. Print. Presents a full-length biography of Boole, including illustrations and providing key details about his life and his contributions to mathematics.

Nahin, Paul J. The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age. Princeton: Princeton UP, 2012. Print. Examines the lives of Boole and Claude Shannon, an American mathematician and electrical engineer who, in the mid-twentieth century, founded the field of information theory that supports much of modern digital computing.