Chapter 4: Gates and Circuits
Boolean algebra is named for its inventor, English mathematician George Boole, born in 1815. His father, a tradesman, began teaching him mathematics at an early age. But Boole was initially more interested in classical literature, languages, and religion-- interests he maintained throughout his life. By the time he was 20, he had taught himself French, German, and Italian. He was well versed in the writings of Aristotle, Spinoza, Cicero, and Dante, and wrote several philosophical papers himself.
At 16 he took a position as a teaching assistant in a private school to help support his family. His work there plus a second teaching job left him little time to study. A few years later, he opened a school and began to learn higher mathematics on his own. In spite of his lack of formal training, his first scholarly paper was published in the Cambridge Mathematical Journal when he was just 24. In 1849, he was appointed professor of mathematics at Queen's College in Cork, Ireland. He became chair of mathematics and spent the rest of his career there. Boole went on the publish over 50 papers and several major works before he died in 1864, at the peak of his career.
Boole's The Mathematical Analysis of Logic was published in 1847. It would eventually form the basis for the development of digital computers. In the book, Boole set forth the formal axioms of logic (much like the axioms of geometry) on which the field of symbolic logic is built. Boole drew on the symbols and operations of algebra in creating his system of logic. He associated the value 1 with the universal set (the set representing everything in the universe) and the value 0 with the empty set, and restricted his system to these quantities. He then defined operations that are analogous to subtraction, addition, and multiplication.
In 1854, Boole published An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities. This book described theorems built on his axioms of logic and extended the algebra to show how probabilities could be computed in a logical system. Five years later, Boole published Treatise on Differential Equations, followed by Treaties on the Calculus of Finite Differences. The latter is one of the cornerstones of numerical analysis, which deals with the accuracy of computations.
Boole received little recognition and few honors for his work. Given the importance of Boolean algebra in modern technology, it is hard to believe that his system of logic was not taken seriously until the early twentieth century. George Boole was truly one of the founders of computer science.