Boole, George

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George Boole Summary

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George Boole.

Boole, George

English Mathematician
1815–1864

George Boole was a mathematician whose work in symbolic logic laid new foundations for modern algebra, and set the stage for contemporary computer circuitry and database search strategy syntax. Boole was born in Lincolnshire, England, in 1815, and he died December 8, 1864, in County Cork, Ireland. He received little in the way of formal education, but he was a dedicated reader and self-taught student of languages and mathematics.

At the age of sixteen, Boole became an assistant teacher for elementary school students. By age twenty, Boole had started his own school. Dismayed at what he considered to be inadequate materials available to teach mathematics to young students, Boole undertook the serious study of mathematics on his own. In subsequent years he wrote several seminal papers on the relationship between logic and mathematics. Despite his lack of university training and connections, he managed to get his works published in The Cambridge Mathematical Journal, eventually winning the professional respect of other mathematicians and logicians. In 1854 he published An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities. Considered his most influential work, this text provides the foundation for what has become known as Boolean algebra. Other significant works include the Treatise on Differential Equations (1859) and the Treatise on the Calculus of Finite Differences (1860).

Boole was a deeply religious man. He was influenced by the works of Sir Isaac Newton, Joseph LaGrange, and Pierre-Simon Laplace, as well as the philosopher Gottfried Wilhelm Leibnitz. Also a family man, Boole married Mary Everest, niece of Sir George Everest, for whom Mt. Everest was named. Boole and Everest married in 1855 and eventually had five daughters: Mary, Margaret, Alicia, Lucy, and Ethel.

Boole died of pneumonia at the age of forty-nine, when Alicia was four years old and his youngest daughter was an infant. His widow, Mary Everest Boole, made significant contributions to the field of mathematics herself, carrying on her late husband's work of helping children learn mathematics. She described her work as that of a "mathematical psychologist," and focused on understanding how children use reason and logic, physical activity, and subconscious processes to learn mathematics.

Boolean Legacies

Many mathematicians consider Boole's most significant contribution to be his Boolean algebra, which articulates a theory of relations. Boolean algebra furnishes laws of possibility among propositions. In the 1940s, early computer pioneer Claude Shannon (1916–2001) applied Boole's principles to electrical wiring and developed a mathematical theory of communication, which led to the connection between the work of George Boole and modern computer circuitry, which Boole of course could not have anticipated.

Boolean algebra is also at the center of symbolic reasoning, which is widely applied in the formation of database search statements. Often called Boolean Logic, Boole's explanation of logical operators of thought provides the foundation of computer search engine syntax. Boolean "operators" are enlisted in search statements to help online searchers to restrict or expand their search results. Boolean Logic separates concepts from each other and examines their properties relative to each other. These properties can be demonstrated through Venn diagrams and syllogistic statements.

The pragmatics of Boolean Logic are found in AND, OR, and NOT statements. Unlike in typical mathematics, AND statements limit results. For example, 2 3 5. However, in Boolean Logic, the combination of Concept A and Concept B yields only results that contain both A and B. Thus, the resulting set number is less than either of the two concepts viewed singularly. This concept is often difficult for database searchers to learn to use. Accustomed to the numerical principle that adding units together yields greater results, the most common mistake of novice online searchers is to add too many variables to their search syntax, believing that more variables will provide more results. In fact, the opposite is true.

To get more results with a Boolean search, the OR statement is needed. OR statements can be tricky, however, depending on where they appear in the search statement. For example, A OR B AND C can be interpreted as (A OR B) AND C, which is likely what the searcher intends. If the search engine interprets the statement as A OR (B AND C), very different results are given. Properly placed parentheses are recommended in virtually all cases where the OR operator is employed.

The NOT operator is also a limiter, in that it restricts the search by omitting results that contain the NOT word or concept. For example, A AND B NOT C will retrieve records that contain A and B but exclude all records that contain C, even if they contain A and B.

As is evident from Boolean operators, relationships among objects or ideas may be governed by a logic that is not necessarily congruent with conventional human reasoning. What may be rational in numbers, e.g.addition, does not "add up" when applied to the use of the Boolean "AND" in a search statement.

Boole was drawn to explore the depths of logical and mathematical reasoning, and the ways in which human thought comprehends the relationships among ideas. In ways Boole could never have foreseen, his intellectual interests provided the foundation for future generations of logicians and mathematicians whose work is enhanced by the computing and database searching technology people take for granted today.

Tom Wall