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George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at
Queen's College, Cork University College Cork – National University of Ireland, Cork (UCC) ( ga, Coláiste na hOllscoile Corcaigh) is a constituent university of the National University of Ireland, and located in Cork. The university was founded in 1845 as one of ...
in Ireland. He worked in the fields of
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s and
algebraic logic In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for ...
, and is best known as the author of '' The Laws of Thought'' (1854) which contains
Boolean algebra In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas i ...
. Boolean logic is credited with laying the foundations for the
Information Age The Information Age (also known as the Computer Age, Digital Age, Silicon Age, or New Media Age) is a historical period that began in the mid-20th century. It is characterized by a rapid shift from traditional industries, as established during t ...
.


Early life

Boole was born in 1815 in Lincoln, Lincolnshire, England, the son of John Boole senior (1779–1848), 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.Hill, p. 149
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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. Rhees, Rush. (1954) "George Boole as Student and Teacher. By Some of His Friends and Pupils", ''Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences''. Vol. 57. Royal Irish Academy He taught briefly in Liverpool. Boole participated in the
Lincoln Mechanics' Institute The Lincoln Mechanics' Institute or Lincoln and Lincolnshire Mechanics' Institute was founded in Lincoln, England in 1833. It was one of the many Mechanics' institutes which sprang up in the early 19th century and was the first Mechanics' Instit ...
, in the Greyfriars, Lincoln, which was founded in 1833.
Edward Bromhead Sir Edward Thomas ffrench Bromhead, 2nd Baronet FRS FRSE (26 March 1789 – 14 March 1855) was a British landowner and mathematician, best remembered as patron of the mathematician and physicist George Green and mentor of George Boole. Life Born ...
, who knew John Boole through the institution, helped George Boole with mathematics books and he was given the
calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
text of
Sylvestre François Lacroix Sylvestre François Lacroix (28 April 176524 May 1843) was a French mathematician. Life He was born in Paris, and was raised in a poor family who still managed to obtain a good education for their son. Lacroix's path to mathematics started wi ...
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 Edmund Roberts Larken (1809–1895) was an English cleric and Christian socialist, a patron of radical causes and author on social matters. Along with other unconventional views, he was noted as possibly the first parish priest of his time to wear ...
and others he set up a
building society A building society is a financial institution owned by its members as a mutual organization. Building societies offer banking and related financial services, especially savings and mortgage lending. Building societies exist in the United Kingdo ...
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 Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...
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 University College Cork – National University of Ireland, Cork (UCC) ( ga, Coláiste na hOllscoile Corcaigh) is a constituent university of the National University of Ireland, and located in Cork. The university was founded in 1845 as one of ...
(now University College Cork (UCC)) 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 some years later in 1855. He maintained his ties with Lincoln, working there with E. R. Larken in a campaign to reduce prostitution.Hill, p. 138 note 4
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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 The Keith Medal was a prize awarded by the Royal Society of Edinburgh, Scotland's national academy, for a scientific paper published in the society's scientific journals, preference being given to a paper containing a discovery, either in mathe ...
by the Royal Society of Edinburgh in 1855 and was elected a Fellow of the Royal Society (FRS) in 1857. He received honorary degrees of
LL.D. Legum Doctor (Latin: “teacher of the laws”) (LL.D.) or, in English, Doctor of Laws, is a doctorate-level academic degree in law or an honorary degree, depending on the jurisdiction. The double “L” in the abbreviation refers to the early ...
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 (Volume 2, No. 8, pp. 64–73), and it led to a friendship between Boole and
Duncan Farquharson Gregory Duncan Farquharson Gregory (13 April 181323 February 1844) was a Scottish mathematician. Education Gregory was born in Aberdeen on 13 April 1813, the youngest son of Isabella Macleod (1772–1847) and James Gregory (1753–1821). He was taught ...
, 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 Commute, commutation or commutative may refer to: * Commuting, the process of travelling between a place of residence and a place of work Mathematics * Commutative property, a property of a mathematical operation whose result is insensitive to th ...
. 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 Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
of Finite Differences'', a sequel to the former work.


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: :\mathrm \left\ = \frac for any real numbers ''a''''k'' > 0, ''b''''k'', and ''t'' > 0. Generalisations of this identity play an important role in the theory of the
Hilbert transform In mathematics and in signal processing, the Hilbert transform is a specific linear operator that takes a function, of a real variable and produces another function of a real variable . This linear operator is given by convolution with the funct ...
.


Symbolic 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.Witold Marciszewski (editor), ''Dictionary of Logic as Applied in the Study of Language'' (1981), pp. 194–5. Among his many innovations is his principle of
wholistic reference Wholistic reference is reference to the whole—with respect to the context. In its strongest, unqualified form, the principle of wholistic reference is the proposition that each and every proposition, regardless how limited the referents of its n ...
, 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 In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, ...
and
Boolean logic In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in ...
; it also reveals the centrality of holistic reference in Boole's philosophy of logic.


1854 definition of the universe of discourse

In every discourse, whether of the mind conversing with its own thoughts, or of the individual in his intercourse with others, there is an assumed or expressed limit within which the subjects of its operation are confined. The most unfettered discourse is that in which the words we use are understood in the widest possible application, and for them, the limits of discourse are co-extensive with those of the universe itself. But more usually we confine ourselves to a less spacious field. Sometimes, in discoursing of men we imply (without expressing the limitation) that it is of men only under certain circumstances and conditions that we speak, as of civilised men, or of men in the vigour of life, or of men under some other condition or relation. Now, whatever may be the extent of the field within which all the objects of our discourse are found, that field may properly be termed the universe of discourse. Furthermore, this universe of discourse is in the strictest sense the ultimate subject of the discourse.


Treatment of addition in logic

Boole conceived of "elective symbols" of his kind as an
algebraic structure In mathematics, an algebraic structure consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplication), and a finite set ...
. But this general concept was not available to him: he did not have the segregation standard in
abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ' ...
of postulated (axiomatic) properties of operations, and deduced properties.
Andrei Nikolaevich Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...
, Adolf Pavlovich Yushkevich, ''Mathematics of the 19th century: mathematical logic, algebra, number theory, probability theory'' (2001), pp. 15 (note 15)–16
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.
His work was a beginning to the
algebra of sets In mathematics, the algebra of sets, not to be confused with the mathematical structure of ''an'' algebra of sets, defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the re ...
, again not a concept available to Boole as a familiar model. His pioneering efforts encountered specific difficulties, and the treatment of addition was an obvious difficulty in the early days. Boole replaced the operation of multiplication by the word "and" and addition by the word "or". But in Boole's original system, + was a partial operation: in the language of set theory it would correspond only to
disjoint union In mathematics, a disjoint union (or discriminated union) of a family of sets (A_i : i\in I) is a set A, often denoted by \bigsqcup_ A_i, with an injection of each A_i into A, such that the images of these injections form a partition of A ( ...
of subsets. Later authors changed the interpretation, commonly reading it as exclusive or, or in set theory terms symmetric difference; this step means that addition is always defined. In fact, there is the other possibility, that + should be read as
disjunction In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor S ...
. This other possibility extends from the disjoint union case, where exclusive or and non-exclusive or both give the same answer. Handling this ambiguity was an early problem of the theory, reflecting the modern use of both
Boolean ring In mathematics, a Boolean ring ''R'' is a ring for which ''x''2 = ''x'' for all ''x'' in ''R'', that is, a ring that consists only of idempotent elements. An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean al ...
s and Boolean algebras (which are simply different aspects of one type of structure). Boole and Jevons struggled over just this issue in 1863, in the form of the correct evaluation of ''x'' + ''x''. Jevons argued for the result ''x'', which is correct for + as disjunction. Boole kept the result as something undefined. He argued against the result 0, which is correct for exclusive or, because he saw the equation ''x'' + ''x'' = 0 as implying ''x'' = 0, a false analogy with ordinary algebra.


Probability theory

The second part of the ''Laws of Thought'' contained a corresponding attempt to discover a general method in probabilities. Here the goal was algorithmic: from the given probabilities of any system of events, to determine the consequent probability of any other event logically connected with those events.


Death

In late November 1864, Boole walked, in heavy rain, from his home at Lichfield Cottage in Ballintemple to the university, a distance of three miles, and lectured wearing his wet clothes. He soon became ill, developing pneumonia. As his wife believed that remedies should resemble their cause, she wrapped him in wet blankets – the wet having brought on his illness. Boole's condition worsened and on 8 December 1864, he died of fever-induced pleural effusion. He was buried in the Church of Ireland cemetery of St Michael's, Church Road,
Blackrock BlackRock, Inc. is an American multi-national investment company based in New York City. Founded in 1988, initially as a risk management and fixed income institutional asset manager, BlackRock is the world's largest asset manager, with trill ...
(a suburb of
Cork Cork or CORK may refer to: Materials * Cork (material), an impermeable buoyant plant product ** Cork (plug), a cylindrical or conical object used to seal a container ***Wine cork Places Ireland * Cork (city) ** Metropolitan Cork, also known as G ...
). There is a commemorative plaque inside the adjoining church.


Legacy

Boole is the namesake of the branch of
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...
known as
Boolean algebra In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas i ...
, as well as the namesake of the lunar crater
Boole George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Irel ...
. The keyword ''Bool'' represents a
Boolean datatype In computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted ''true'' and ''false'') which is intended to represent the two truth values of logic and Boolean algebra. It is name ...
in many programming languages, though
Pascal Pascal, Pascal's or PASCAL may refer to: People and fictional characters * Pascal (given name), including a list of people with the name * Pascal (surname), including a list of people and fictional characters with the name ** Blaise Pascal, Frenc ...
and Java, among others, both use the full name ''Boolean''. The library, underground lecture theatre complex and the Boole Centre for Research in Informatics at University College Cork are named in his honour. A road called ''Boole Heights'' in Bracknell, Berkshire is named after him.


19th-century development

Boole's work was extended and refined by a number of writers, beginning with William Stanley Jevons, who also authored the article about Boole in the ''Encyclopaedia Britannica''. Augustus De Morgan had worked on the
logic of relations In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate fo ...
, and
Charles Sanders Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for ...
integrated his work with Boole's during the 1870s. Ivor Grattan-Guinness, Gérard Bornet, ''George Boole: Selected manuscripts on logic and its philosophy'' (1997), p. xlvi
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.
Other significant figures were Platon Sergeevich Poretskii, and
William Ernest Johnson William Ernest Johnson, FBA (23 June 1858 – 14 January 1931), usually cited as W. E. Johnson, was a British philosopher, logician and economic theorist.Zabell, S.L. (2008"Johnson, William Ernest (1858–1931)"In: Durlauf S.N., Blume L.E. (e ...
. The conception of a Boolean algebra structure on equivalent statements of a propositional calculus is credited to Hugh MacColl (1877), in work surveyed 15 years later by Johnson. Surveys of these developments were published by Ernst Schröder, Louis Couturat, and
Clarence Irving Lewis Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher. He is considered the progenitor of modern modal logic and the founder of conceptual pragmatism. First a noted logic ...
.


20th-century development

In 1921, the economist
John Maynard Keynes John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946), was an English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in ...
published a book on probability theory, ''A Treatise of Probability''. Keynes believed that Boole had made a fundamental error in his definition of independence which vitiated much of his analysis. In his book ''The Last Challenge Problem'', David Miller provides a general method in accord with Boole's system and attempts to solve the problems recognised earlier by Keynes and others. Theodore Hailperin showed much earlier that Boole had used the correct mathematical definition of independence in his worked out problems. Boole's work and that of later logicians initially appeared to have no engineering uses.
Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory". As a 21-year-old master's degree student at the Massachusetts Insti ...
attended a philosophy class at the University of Michigan which introduced him to Boole's studies. Shannon recognised that Boole's work could form the basis of mechanisms and processes in the real world and that it was therefore highly relevant. In 1937 Shannon went on to write a master's thesis, at the Massachusetts Institute of Technology, in which he showed how Boolean algebra could optimise the design of systems of electromechanical
relay A relay Electromechanical relay schematic showing a control coil, four pairs of normally open and one pair of normally closed contacts An automotive-style miniature relay with the dust cover taken off A relay is an electrically operated switch ...
s then used in telephone routing switches. He also proved that circuits with relays could solve Boolean algebra problems. Employing the properties of electrical switches to process logic is the basic concept that underlies all modern electronic
digital computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These prog ...
s.
Victor Shestakov Victor Ivanovich Shestakov (Russian: ) (1907–1987) was a Russian/Soviet logician and theoretician of electrical engineering. In 1935 he discovered the possible interpretation of Boolean algebra of logic in electro-mechanical relay circuits. He g ...
at Moscow State University (1907–1987) proposed a theory of electric switches based on Boolean logic even earlier than
Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory". As a 21-year-old master's degree student at the Massachusetts Insti ...
in 1935 on the testimony of Soviet logicians and mathematicians
Sofya Yanovskaya Sofya Aleksandrovna Yanovskaya (also Janovskaja; russian: Софи́я Алекса́ндровна Яно́вская; 31 January 1896 – 24 October 1966) was a Soviet mathematician and historian, specializing in the history of mathematics, math ...
, Gaaze-Rapoport, Roland Dobrushin, Lupanov, Medvedev and Uspensky, though they presented their academic theses in the same year, 1938. But the first publication of Shestakov's result took place only in 1941 (in Russian). Hence, Boolean algebra became the foundation of practical digital circuit design; and Boole, via Shannon and Shestakov, provided the theoretical grounding for the
Information Age The Information Age (also known as the Computer Age, Digital Age, Silicon Age, or New Media Age) is a historical period that began in the mid-20th century. It is characterized by a rapid shift from traditional industries, as established during t ...
.


21st-century celebration

The year 2015 saw the 200th anniversary of Boole's birth. To mark the bicentenary year, University College Cork joined admirers of Boole around the world to celebrate his life and legacy. UCC's George Boole 200 project, featured events, student outreach activities and academic conferences on Boole's legacy in the digital age, including a new edition of Desmond MacHale's 1985 biography '' The Life and Work of George Boole: A Prelude to the Digital Age'', 2014. The search engine Google marked the 200th anniversary of his birth on 2 November 2015 with an algebraic reimaging of its Google Doodle.


Views

Boole's views were given in four published addresses: ''The Genius of Sir Isaac Newton''; ''The Right Use of Leisure''; ''The Claims of Science''; and ''The Social Aspect of Intellectual Culture''. The first of these was from 1835 when
Charles Anderson-Pelham, 1st Earl of Yarborough Charles Anderson-Pelham, 1st Earl of Yarborough (8 August 1781 – 5 September 1846), styled Hon. Charles Anderson-Pelham from 1794 to 1823, was one of the founders of the Royal Yacht Squadron and its first Commodore. He lived at Appuldurcombe H ...
gave a bust of Newton to the Mechanics' Institute in Lincoln. The second justified and celebrated in 1847 the outcome of the successful campaign for early closing in Lincoln, headed by Alexander Leslie-Melville, of
Branston Hall Branston Hall is a country house in the village of Branston, Lincolnshire, England. The hall, a Grade II listed building, is set in 88 acres (3.56 square kilometres) of wooded parkland and lakes. Originally commissioned as the family seat of ...
. ''The Claims of Science'' was given in 1851 at Queen's College, Cork. ''The Social Aspect of Intellectual Culture'' was also given in Cork, in 1855 to the Cuvierian Society. Though his biographer Des MacHale describes Boole as an "agnostic deist", Boole read a wide variety of Christian theology. Combining his interests in mathematics and theology, he compared the Christian trinity of Father, Son, and Holy Ghost with the three dimensions of space, and was attracted to the Hebrew conception of God as an absolute unity. Boole considered converting to Judaism but in the end was said to have chosen Unitarianism. eference?/sup> Boole came to speak against what he saw as "prideful" scepticism, and instead favoured the belief in a "Supreme Intelligent Cause". He also declared "I firmly believe, for the accomplishment of a purpose of the Divine Mind." In addition, he stated that he perceived "teeming evidences of surrounding design" and concluded that "the course of this world is not abandoned to chance and inexorable fate." Two influences on Boole were later claimed by his wife,
Mary Everest Boole Mary Everest Boole (11 March 1832 in Wickwar, Gloucestershire – 17 May 1916 in Middlesex, England) was a self-taught mathematician who is best known as an author of didactic works on mathematics, such as ''Philosophy and Fun of Algebra'', an ...
: a universal mysticism tempered by Jewish thought, and Indian logic.Jonardon Ganeri (2001), ''Indian Logic: a reader'', Routledge, p. 7,
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Mary Boole stated that an adolescent mystical experience provided for his life's work:
My husband told me that when he was a lad of seventeen a thought struck him suddenly, which became the foundation of all his future discoveries. It was a flash of psychological insight into the conditions under which a mind most readily accumulates knowledge ..For a few years he supposed himself to be convinced of the truth of "the Bible" as a whole, and even intended to take orders as a clergyman of the English Church. But by the help of a learned
Jew Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
in Lincoln he found out the true nature of the discovery which had dawned on him. This was that man's mind works by means of some mechanism which "functions normally towards Monism."Boole, Mary Everest ''Indian Thought and Western Science in the Nineteenth Century'', Boole, Mary Everest ''Collected Works'' eds. E. M. Cobham and E. S. Dummer, London, Daniel 1931 pp.947–967
In Ch. 13 of ''Laws of Thought'' Boole used examples of propositions from
Baruch Spinoza Baruch (de) Spinoza (born Bento de Espinosa; later as an author and a correspondent ''Benedictus de Spinoza'', anglicized to ''Benedict de Spinoza''; 24 November 1632 – 21 February 1677) was a Dutch philosopher of Portuguese-Jewish origin, b ...
and Samuel Clarke. The work contains some remarks on the relationship of logic to religion, but they are slight and cryptic. Boole was apparently disconcerted at the book's reception just as a mathematical toolset:
George afterwards learned, to his great joy, that the same conception of the basis of Logic was held by
Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathema ...
, the contemporary of Newton. De Morgan, of course, understood the formula in its true sense; he was Boole's collaborator all along. Herbert Spencer, Jowett, and Robert Leslie Ellis understood, I feel sure; and a few others, but nearly all the logicians and mathematicians ignored 53the statement that the book was meant to throw light on the nature of the human mind; and treated the formula entirely as a wonderful new method of reducing to logical order masses of evidence about external fact.
Mary Boole claimed that there was profound influence – via her uncle George Everest – of Indian thought in general and Indian logic, in particular, on George Boole, as well as on Augustus De Morgan and
Charles Babbage Charles Babbage (; 26 December 1791 – 18 October 1871) was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer. Babbage is considered ...
:
Think what must have been the effect of the intense Hinduizing of three such men as Babbage, De Morgan, and George Boole on the mathematical atmosphere of 1830–65. What share had it in generating the
Vector Analysis Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subjec ...
and the mathematics by which investigations in physical science are now conducted?
Boole maintained that:


Family

In 1855, Boole married Mary Everest (niece of George Everest), who later wrote several educational works on her husband's principles. The Booles had five daughters: * Mary Ellen (1856–1908) who married the mathematician and author
Charles Howard Hinton Charles Howard Hinton (1853 – 30 April 1907) was a British mathematician and writer of science fiction works titled ''Scientific Romances''. He was interested in higher dimensions, particularly the fourth dimension. He is known for coining t ...
and had four children: George (1882–1943), Eric (*1884), William (1886–1909) and Sebastian (1887–1923), inventor of the
Jungle gym A jungle gym (called a climbing frame in British English) is a piece of playground equipment made of many pieces of material, such as metal pipes or ropes, on which participants can climb, hang, sit, and—in some configurations—slide. Monkey ...
. After the sudden death of her husband, Mary Ellen committed suicide in
Washington, D.C. ) , image_skyline = , image_caption = Clockwise from top left: the Washington Monument and Lincoln Memorial on the National Mall, United States Capitol, Logan Circle, Jefferson Memorial, White House, Adams Morgan, Na ...
in May 1908. Sebastian had three children: ** Jean Hinton (married name Rosner) (1917–2002), a peace activist. **
William H. Hinton William Howard Hinton (; February 2, 1919 – May 15, 2004) was an American Maoist intellectual, best known for his work on Communism in China. A Marxist, he is best known for his book '' Fanshen'', published in 1966, a "documentary of revo ...
(1919–2004) visited China in the 1930s and 40s and wrote an influential account of the Communist land reform. ** Joan Hinton (1921–2010) worked for the Manhattan Project and lived in China from 1948 until her death on 8 June 2010; she was married to Sid Engst. * Margaret (1858–1935), married Edward Ingram Taylor, an artist. ** Their elder son
Geoffrey Ingram Taylor Sir Geoffrey Ingram Taylor OM FRS FRSE (7 March 1886 – 27 June 1975) was a British physicist and mathematician, and a major figure in fluid dynamics and wave theory. His biographer and one-time student, George Batchelor, described him as " ...
became a mathematician and a Fellow of the Royal Society. ** Their younger son Julian Taylor was a professor of surgery. * Alicia (1860–1940), who made important contributions to
four-dimensional geometry A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called '' dimensions'' ...
. ** Her son Leonard Stott, a medical doctor and tuberculosis pioneer, invented a portable X-ray machine, a pneumothorax apparatus, and system of navigation based on spherical coordinates.D. MacHale, ''The Life and Work of George Boole: A Prelude to the Digital Age'', Cork University Press, 2014. cited in
The Extraordinary Case of the Boole Family
'' by Moira Chas
* Lucy Everest (1862–1904), who was the first female professor of chemistry in England. * Ethel Lilian (1864–1960), who married the Polish scientist and revolutionary
Wilfrid Michael Voynich Wilfrid Voynich (born Michał Habdank-Wojnicz; Telšiai, Деятели революционного движения в России: Био-библиографический словарь: От предшественников декабри� ...
and was the author of the novel '' The Gadfly''.


See also


Concepts

*
Boolean algebra In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas i ...
, a logical calculus of truth values or set membership *
Boolean algebra (structure) In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a gen ...
, a set with operations resembling logical ones *
Boolean circuit In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible input ...
, a mathematical model for digital logical circuits. *
Boolean data type In computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted ''true'' and ''false'') which is intended to represent the two truth values of logic and Boolean algebra. It is name ...
is a data type, having two values (usually denoted true and false) *
Boolean expression In computer science, a Boolean expression is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean ...
, an expression in a programming language that produces a Boolean value when evaluated *
Boolean function In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth functio ...
, a function that determines Boolean values or operators *
Boolean model (probability theory) For statistics in probability theory, the Boolean-Poisson model or simply Boolean model for a random subset of the plane (or higher dimensions, analogously) is one of the simplest and most tractable models in stochastic geometry. Take a Poisson ...
, a model in stochastic geometry *
Boolean network A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function (possibly different for each variable) assigned to it which takes inputs from a subset of those variables and output that determines the sta ...
, a certain network consisting of a set of Boolean variables whose state is determined by other variables in the network *
Boolean processor The Intel MCS-51 (commonly termed 8051) is a single chip microcontroller (MCU) series developed by Intel in 1980 for use in embedded systems. The architect of the Intel MCS-51 instruction set was John H. Wharton. Intel's original versions were po ...
, a 1-bit variables computing unit *
Boolean ring In mathematics, a Boolean ring ''R'' is a ring for which ''x''2 = ''x'' for all ''x'' in ''R'', that is, a ring that consists only of idempotent elements. An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean al ...
, a ring consisting of idempotent elements *
Boolean satisfiability problem In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfie ...
* Boole's syllogistic is a logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the "empty set". *
Laws of thought The laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based. The formulation and clarification of such rules have a long tradition in the history of philosophy and logic. Generally they ...
* Principle of wholistic reference


Other

*
List of Boolean algebra topics This is a list of topics around Boolean algebra and propositional logic. Articles with a wide scope and introductions * Algebra of sets * Boolean algebra (structure) * Boolean algebra * Field of sets * Logical connective * Prop ...
*
List of pioneers in computer science This is a list of people who made transformative breakthroughs in the creation, development and imagining of what computers could do. Pioneers : ''To arrange the list by date or person (ascending or descending), click that column's small "up-do ...


Notes


References

* Walker, A. (ed) (2019) ''George Boole's Lincoln, 1815–49.'' The Survey of Lincoln, Vol.16. * University College Cork, ''George Boole 200 Bicentenary Celebration''
GeorgeBoole.com
* Ivor Grattan-Guinness, ''The Search for Mathematical Roots 1870–1940''. Princeton University Press. 2000. *
Francis Hill Sir James William Francis Hill (15 September 1899 – 6 January 1980) was a British solicitor and leading historian of Lincoln and Lincolnshire. He was the third Chancellor of the University of Nottingham. He also served as a Councillor, Alderm ...
(1974), ''Victorian Lincoln''
Google Books
. *
Des MacHale Des is a masculine given name, mostly a short form (hypocorism) of Desmond. People named Des include: People * Des Buckingham, English football manager * Des Corcoran, (1928–2004), Australian politician * Des Dillon (disambiguation), seve ...
, '' George Boole: His Life and Work''
Boole Press
1985. *
Des MacHale Des is a masculine given name, mostly a short form (hypocorism) of Desmond. People named Des include: People * Des Buckingham, English football manager * Des Corcoran, (1928–2004), Australian politician * Des Dillon (disambiguation), seve ...
, '' The Life and Work of George Boole: A Prelude to the Digital Age'' (new edition)
Cork University Press
. 2014 * Stephen Hawking, ''
God Created the Integers ''God Created the Integers: The Mathematical Breakthroughs That Changed History'' is a 2005 anthology, edited by Stephen Hawking, of "excerpts from thirty-one of the most important works in the history of mathematics." The title of the book is a ...
''. Running Press, Philadelphia. 2007.


External links


Roger Parsons' article on Boole
* *

by George Boole; a transcription of an article which originally appeared in ''Cambridge and Dublin Mathematical Journal'', Vol. III (1848), pp. 183–98.
George Boole's work as first Professor of Mathematics in University College, Cork, Ireland

George Boole website

Author profile
in the database
zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructu ...
* {{DEFAULTSORT:Boole, George 1815 births 1864 deaths 19th-century British mathematicians 19th-century British non-fiction writers 19th-century British philosophers 19th-century British writers 19th-century English mathematicians 19th-century English non-fiction writers 19th-century English philosophers 19th-century English writers 19th-century essayists 19th-century translators Academics of Queens College Cork Boolean algebra British deists British essayists British innovators British male non-fiction writers British mathematicians British translators British Unitarians Respiratory disease deaths in Ireland English essayists English innovators English logicians English mathematicians English non-fiction writers English translators English Unitarians Fellows of the Royal Society History of algebra History of logic History of mathematics History of philosophy History of science Mathematical logicians People from Lincoln, England Philosophers of logic Philosophers of mathematics Probability theorists Royal Medal winners Victorian writers