George Boole
George Boole was an English autodidact, mathematician, philosopher and logician who served as the first professor of mathematics at Queen's College, Cork in Ireland. He worked in the fields of differential equations and algebraic logic, and is best known as the author of The Laws of Thought, which contains Boolean algebra. Boolean logic, essential to computer programming, is credited with helping to lay the foundations for the Information Age.
Boole was the son of a shoemaker. He received a primary school education and learned Latin and modern languages through various means. At 16, he began teaching to support his family. He established his own school at 19 and later ran a boarding school in Lincoln. Boole was an active member of local societies and collaborated with fellow mathematicians. In 1849, he was appointed the first professor of mathematics at Queen's College, Cork in Ireland, where he met his future wife, Mary Everest. He continued his involvement in social causes and maintained connections with Lincoln. In 1864, Boole died due to fever-induced pleural effusion after developing pneumonia.
Boole published around 50 articles and several separate publications in his lifetime. Some of his key works include a paper on early invariant theory and "The Mathematical Analysis of Logic", which introduced symbolic logic. Boole also wrote two systematic treatises: "Treatise on Differential Equations" and "Treatise on the Calculus of Finite Differences". He contributed to the theory of linear differential equations and the study of the sum of residues of a rational function. In 1847, Boole developed Boolean algebra, a fundamental concept in binary logic, which laid the groundwork for the algebra of logic tradition and forms the foundation of digital circuit design and modern computer science. Boole also attempted to discover a general method in probabilities, focusing on determining the consequent probability of events logically connected to given probabilities.
Boole's work was expanded upon by various scholars, such as Charles Sanders Peirce and William Stanley Jevons. Boole's ideas later gained practical applications when Claude Shannon and Victor Shestakov employed Boolean algebra to optimize the design of electromechanical relay systems, leading to the development of modern electronic digital computers. His contributions to mathematics earned him various honours, including the Royal Society's first gold prize for mathematics, the Keith Medal, and honorary degrees from the Universities of Dublin and Oxford. University College Cork celebrated the 200th anniversary of Boole's birth in 2015, highlighting his significant impact on the digital age.
Early life
Boole was born in 1815 in Lincoln, Lincolnshire, England, the son of John Boole Snr, a shoemaker and Mary Ann Joyce. He had a primary school education, and received lessons from his father, but due to a serious decline in business, he had little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have helped him with Latin, which he may also have learned at the school of Thomas Bainbridge. He was self-taught in modern languages. In fact, when a local newspaper printed his translation of a Latin poem, a scholar accused him of plagiarism under the pretence that he was not capable of such achievements. At age 16, Boole became the breadwinner for his parents and three younger siblings, taking up a junior teaching position in Doncaster at Heigham's School. He taught briefly in Liverpool.Boole participated in the Lincoln Mechanics' Institute, in the Greyfriars, Lincoln, which was founded in 1833. Edward Bromhead, who knew John Boole through the institution, helped George Boole with mathematics books and he was given the calculus text of Sylvestre François Lacroix by the Rev. George Stevens Dickson of St Swithin's, Lincoln. Without a teacher, it took him many years to master calculus.
At age 19, Boole successfully established his own school in Lincoln: Free School Lane. Four years later he took over Hall's Academy in Waddington, outside Lincoln, following the death of Robert Hall. In 1840, he moved back to Lincoln, where he ran a boarding school. Boole immediately became involved in the Lincoln Topographical Society, serving as a member of the committee, and presenting a paper entitled "On the origin, progress, and tendencies of polytheism, especially amongst the ancient Egyptians and Persians, and in modern India".
Boole became a prominent local figure, an admirer of John Kaye, the bishop. He took part in the local campaign for early closing. With Edmund Larken and others he set up a building society in 1847. He associated also with the Chartist Thomas Cooper, whose wife was a relation.
From 1838 onwards, Boole was making contacts with sympathetic British academic mathematicians and reading more widely. He studied algebra in the form of symbolic methods, as far as these were understood at the time, and began to publish research papers.
Professorship and life in Cork
Boole's status as a mathematician was recognised by his appointment in 1849 as the first professor of mathematics at Queen's College, Cork in Ireland. He met his future wife, Mary Everest, there in 1850 while she was visiting her uncle John Ryall who was professor of Greek. They married in 1855. He maintained his ties with Lincoln, working there with E. R. Larken in a campaign to reduce prostitution.In 1861, Boole was involved in a Judgement in the Court of Queen's Bench in Ireland against one John Hewitt Wheatley of Craig House, Sligo for the sum of £400, whereby Wheatley's estate and interest in lands of Maghan/Mahon, County Cork became vested in Boole.
In March 1863, Boole leased Litchfield Cottage, Cork, the house in which he would live with his wife Mary until his death in December of the following year. The premises was described in the deeds as "all that and those the dwelling house called Litchfield Cottage with the premises and appurtenances thereunto belonging and the Garden and Walled in field to the rere thereof". Boole's will bequeathed all his 'estate term and interest' in the lease of Litchfield Cottage unto his wife. In August 1865, some 8 months after his death, Mary passed the house on to Francis Heard of Ballintemple, Cork, Esquire, a captain in her Majesty's 87th Regiment of South Cork.
Honours and awards
In 1844, Boole's paper "On a General Method in Analysis" won the first gold prize for mathematics awarded by the Royal Society. He was awarded the Keith Medal by the Royal Society of Edinburgh in 1855 and was elected a Fellow of the Royal Society in 1857. He received honorary degrees of LL.D. from the University of Dublin and the University of Oxford.Works
Boole's first published paper was "Researches in the theory of analytical transformations, with a special application to the reduction of the general equation of the second order", printed in the Cambridge Mathematical Journal in February 1840, and it led to his friendship with Duncan Farquharson Gregory, the editor of the journal. His works are in about 50 articles and a few separate publications.In 1841, Boole published an influential paper in early invariant theory. He received a medal from the Royal Society for his memoir of 1844, "On a General Method in Analysis". It was a contribution to the theory of linear differential equations, moving from the case of constant coefficients on which he had already published, to variable coefficients. The innovation in operational methods is to admit that operations may not commute. In 1847, Boole published The Mathematical Analysis of Logic, the first of his works on symbolic logic.
Differential equations
Boole completed two systematic treatises on mathematical subjects during his lifetime. The Treatise on Differential Equations appeared in 1859, and was followed, the next year, by a Treatise on the Calculus of Finite Differences, a sequel to the former work. Shortly after his death, Todhunter republished Boole's treatise with some of Boole's revisions, along with a supplement that was originally intended to be merged in the making of the second edition.Analysis
In 1857, Boole published the treatise "On the Comparison of Transcendent, with Certain Applications to the Theory of Definite Integrals", in which he studied the sum of residues of a rational function. Among other results, he proved what is now called Boole's identity:for any real numbers ak > 0, bk, and t > 0. Generalisations of this identity play an important role in the theory of the Hilbert transform.
Binary logic
In 1847, Boole published the pamphlet Mathematical Analysis of Logic. He later regarded it as a flawed exposition of his logical system and wanted An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities to be seen as the mature statement of his views. Contrary to widespread belief, Boole never intended to criticise or disagree with the main principles of Aristotle's logic. Rather he intended to systematise it, to provide it with a foundation, and to extend its range of applicability. Boole's initial involvement in logic was prompted by a current debate on quantification, between Sir William Hamilton who supported the theory of "quantification of the predicate", and Boole's supporter Augustus De Morgan who advanced a version of De Morgan duality, as it is now called. Boole's approach was ultimately much further reaching than either sides' in the controversy. It founded what was first known as the "algebra of logic" tradition.Among his many innovations is his principle of wholistic reference, which was later, and probably independently, adopted by Gottlob Frege and by logicians who subscribe to standard first-order logic. A 2003 article provides a systematic comparison and critical evaluation of Aristotelian logic and Boolean logic; it also reveals the centrality of holistic reference in Boole's philosophy of logic.