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1854

Boolean Algebra

George Boole (1815–1864), Claude Shannon (1916–2001)

“George Boole was born into a shoemaker’s family in Lincolnshire, England, and schooled at home, where he learned Latin, mathematics, and science. But Boole’s family landed on hard times, and at age 16 he was forced to support his family by becoming a school teacher—a profession he would continue for the rest of his life. In 1838, he wrote his first of many papers on mathematics, and in 1849 he was appointed as the first professor of mathematics at Queen’s College in Cork, Ireland.

Today Boole is best known for his invention of mathematics for describing and reasoning about logical prepositions, what we now call Boolean logic. Boole introduced his ideas in his 1847 monograph, “The Mathematical Analysis of Logic,” and perfected them in his 1854 monograph, “An Investigation into the Laws of Thought.”

Boole’s monographs presented a general set of rules for reasoning with symbols, which today we call Boolean algebra. He created a way—and a notation—for reasoning about what is true and what is false, and how these notions combine when reasoning about complex logical systems. He is also credited with formalizing the mathematical concepts of AND, OR, and NOT, from which all logical operations on binary numbers can be derived. Today many computer languages refer to such numbers as Booleans or simply Bools in recognition of his contribution.

Boole died at the age of 49 from pneumonia. His work was carried on by other logicians but didn’t receive notice in the broader community until 1936, when Claude Shannon, then a graduate student at the Massachusetts Institute of Technology (MIT), realized that the Boolean algebra he had learned in an undergraduate philosophy class at the University of Michigan could be used to describe electrical circuits built from relays. This was a huge breakthrough, because it meant that complex relay circuits could be described and reasoned about symbolically, rather than through trial and error. Shannon’s wedding of Boolean algebra and relays let engineers discover bugs in their diagrams without having to first build the circuits, and it allowed many complex systems to be refactored, replacing them with relay systems that were functionally equivalent but had fewer components.”

SEE ALSO Binary Arithmetic (1703), Manchester SSEM (1948)

“A circuit diagram analyzed using George Boole’s “laws of thought”—what today is called Boolean algebra. Boole’s laws were used to analyze complicated telephone switching systems.”