Boolean Algebra

Leibniz initiated the search for a system of symbols with rules of their combination in his De Arte Combinatoria of 1666, as well as developing the binary notation. In 1854, George Boole (1815-1864), Professor of Mathematics at Cork from 1849 despite having no first degree, formalised a set of such rules in the seminal work entitled, perhaps optimistically, An Investigation of the Laws of Thought. Boole's aim was to identify the rules of reasoning in a rigorous framework and revolutionised formal logic after thousands of years of little progress. They transformed logic from a philosophical into a mathematical discipline. These rules have subsequently become known as Boolean algebra and the design of all modern binary digital computers has depended on the results of this work. These logical operations, normally implemented as electronic gates, are all that are required to perform more complicated operations such as arithmetic.

Charles Lutwidge Dodgson (1832-1898) [1], a Mathematics Lecturer at Christ Church, Oxford from 1855 to 1881, was influenced by the work of Boole. He had a general interest in algebra and also teaching. In May 1855 he noted in his diary:

I began arranging a scheme for teaching systematically the first part of Algebraic Geometry: a thing which no one hitherto seems to have attempted - I find it exceedingly difficult to do it in anything like a satisfactory way.

He subsequently produced works on The Fifth Book of Euclid proved Algebraically and A Syllabus of Plan Algebraical Geometry as well as collections of algebraic and arithmetic formulae to aid examination candidates.

Much later, in his diaries of 1884 Dodgson noted: ``In these last few days I have been working on a Logical Algebra and seem to be getting to a simpler notation than Boole's.'' In 1885 he notes: ``I have occupied myself at Guildford in teaching my new `Logical Algebra' to Louisa, Margaret and the two boys.'' In March 1885 he mentions ``A Symbolic Logic, treated by my algebraic method.'' He published a number of works on logic, including Symbolic Logic, Part I: Elementary in 1896 under his more famous alias of Lewis Carroll. Unfortunately Part II never appeared.