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Difference engines are strictly calculators. They crunch numbers the only way they know how - by repeated addition according to the method of finite differences. They cannot be used for general arithmetical calculation. The Analytical Engine is much more than a calculator and marks the progression from the mechanized arithmetic of calculation to fully-fledged general-purpose computation.

Physical Legacy Aside from a few partially complete mechanical assemblies and test models of small working sections, none of Babbage's designs was physically realized in its entirety in his lifetime. The major assembly he did complete was one-seventh of Difference Engine No. 1, a demonstration piece consisting of about 2,000 parts assembled in 1832. This works impeccably to this day and is the first successful automatic calculating device to embody mathematical rule in mechanism. A small experimental piece of the Analytical Engine was under construction at the time of Babbage's death in 1871. Many of the small experimental assemblies survived, as does a comprehensive archive of his drawings and notebooks. The designs for Babbage's vast mechanical computing engines rank as one of the startling intellectual achievements of the 19th century. It is only in recent decades that his work has been studied in detail and that the extent of what he accomplished becomes increasingly evident.

George Boole (1815–1864) was an English mathematician and a founder of the algebraic tradition in logic. He worked as a schoolmaster in England and from 1849 until his death as professor of mathematics at Queen's University, Cork, Ireland. He revolutionized logic by applying methods from the then-emerging field of symbolic algebra to logic. Where traditional (Aristotelian) logic relied on cataloging the valid syllogisms of various simple forms, Boole's method provided general algorithms in an algebraic language which applied to an infinite variety of arguments of arbitrary complexity.

Starting at the age of 16 it was necessary for Boole to find gainful employment, since his father was no longer capable of providing for the family. After 3 years working as a teacher in private schools, Boole decided, at the age of 19, to open his own small school in Lincoln. He would be a schoolmaster for the next 15 years, until 1849 when he became a professor at the newly opened Queen's University in Cork, Ireland. With heavy responsibilities for his parents and siblings, it is remarkable that he nonetheless found time during the years as a schoolmaster to continue his own education and to start a program of research, primarily on differential equations and the calculus of variations connected with the works of Laplace and Lagrange (which he studied in the original French).