George Boole - Biography, Legacy

Mathematician and logician, born in Lincoln, Lincolnshire, EC England, UK. He was largely self-taught, and though without a degree was appointed professor of mathematics at Cork in 1849. He did important work on finite differences and differential equations, but is primarily known for his Mathematical Analysis of Logic (1847) and Laws of Thought (1854), pioneering works in modern symbolic logic.

Western Philosophy 19th-century philosophy George Boole
Name:	George Boole
Birth:	November 2, 1815 ( Lincoln, Lincolnshire, England )
Death:	December 8, 1864 ( Ballintemple, Cork City, Ireland )
School/tradition:	Mathematical foundations of computer science
Main interests:	Mathematics, Logic, Philosophy of mathematics
Notable ideas:	Boolean algebra
Influences:	Aristotle, Spinoza, Newton
Influenced:	Modern computer scientists, Jevons, De Morgan, Peirce, Johnson, Shannon

George Boole [buːl], (November 2, 1815 – December 8, 1864) was a British mathematician and philosopher.

As the inventor of Boolean algebra, the basis of all modern computer arithmetic, Boole is regarded in hindsight as one of the founders of the field of computer science, although computers did not exist in his day.

Biography

George Boole's father was a tradesman of limited means, but of studious character and active mind. but the extraordinary mathematical talents of George Boole did not manifest themselves in early life. Almost the only changes which can be called events are his successful establishment of a school at Lincoln, its removal to Waddington, his appointment in 1849 as the first professor of mathematics of then Queen's College, Cork (now University College Cork, where the library is named in his honour) in Ireland, and his marriage in 1855 to Miss Mary Everest (niece of George Everest), who, as Mrs. Boole, afterwards wrote several useful educational works on her husband's principles.

To the public Boole was known only as the author of numerous abstruse papers on mathematical topics, and of three or four distinct publications which have become standard works. His earliest published paper was one upon the "Theory of Analytical Transformations," printed in the Cambridge Mathematical Journal for 1839, and it led to a friendship between Boole and D.F. A long list of Boole's memoirs and detached papers, both on logical and mathematical topics, will be found in the Catalogue of Scientific Memoirs published by the Royal Society, and in the supplementary volume on Differential Equations, edited by Isaac Todhunter. To the Cambridge Mathematical Journal and its successor, the Cambridge and Dublin Mathematical Journal, Boole contributed in all twenty-two articles. The works of Boole are thus contained in about fifty scattered articles and a few separate publications.

Only two systematic treatises on mathematical subjects were completed by Boole during his lifetime. These treatises are valuable contributions to the important branches of mathematics in question, and Boole, in composing them, seems to have combined elementary exposition with the profound investigation of the philosophy of the subject in a manner hardly admitting of improvement. In the sixteenth and seventeenth chapters of the Differential Equations we find, for instance, a lucid account of the general symbolic method, the bold and skilful employment of which led to Boole's chief discoveries, and of a general method in analysis, originally described in his famous memoir printed in the Philosophical Transactions for 1844. Boole was one of the most eminent of those who perceived that the symbols of operation could be separated from those of quantity and treated as distinct objects of calculation.

During the last few years of his life Boole was constantly engaged in extending his researches with the object of producing a second edition of his Differential Equations much more complete than the first edition;

With the exception of Augustus de Morgan, Boole was probably the first English mathematician since the time of John Wallis who had also written upon logic. Speculations concerning a calculus of reasoning had at different times occupied Boole's thoughts, but it was not till the spring of 1847 that he put his ideas into the pamphlet called Mathematical Analysis of Logic. Boole afterwards regarded this as a hasty and imperfect exposition of his logical system, and he desired that his much larger work, An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities (1854), should alone be considered as containing a mature statement of his views.

He did not regard logic as a branch of mathematics, as the title of his earlier pamphlet might be taken to imply, but he pointed out such a deep analogy between the symbols of algebra and those which can be made, in his opinion, to represent logical forms and syllogisms, that we can hardly help saying that logic is mathematics restricted to the two quantities, 0 and 1. Boole showed that elective symbols of this kind obey the same primary laws of combination as algebraic symbols, whence it followed that they could be added, subtracted, multiplied and even divided, almost exactly in the same manner as numbers. Given any propositions involving any number of terms, Boole showed how, by the purely symbolic treatment of the premises, to draw any conclusion logically contained in those premises.

Though Boole published little except his mathematical and logical works, his acquaintance with general literature was wide and deep.

The personal character of Boole inspired all his friends with the deepest esteem.

The Booles had five daughters:

Mary, who married the mathematician and author Charles Howard Hinton and had three children (Howard, William and Joan) Margaret, whose son Geoffrey Ingram Taylor became a mathematician and a Fellow of the Royal Society Alicia, who made important contributions to four-dimensional geometry Lucy, a chemist Ethel Lilian, who married the Polish scientist and revolutionary Wilfrid Michael Voynich and is the author of the novel The Gadfly.

Legacy

Boole's work was extended and refined by William Stanley Jevons, Augustus De Morgan, Charles Peirce, and William Ernest Johnson.

Boole's work (as well as that of his intellectual progeny) was relatively obscure except among logicians, and seemed to have no practical use. Approximately seventy years after Boole's death, Claude Shannon discovered Boolean algebra while taking a philosophy class at the University of Michigan.