George boole biography summary page

English mathematician and philosopher (1815–1864)

"Boole" redirects here. For other uses, see Boole (disambiguation).

Not to write down confused with George Boolos.

George Boole FRS
Portrait of Boole, from The Illustrated London News, 21 Jan 1865
Born	(1815-11-02)2 November 1815 Lincoln, England
Died	8 Dec 1864(1864-12-08) (aged 49) Ballintemple, Cork, Ireland
Education	Bainbridge's Advertising Academy[1]
Known for
Spouse
Awards
Scientific career
Fields	Mathematics
Institutions
Philosophy career
Era	19th-century philosophy
Region	Western philosophy
School	British algebraic logic[3]
Main interests	Mathematics, logic, philosophy of mathematics

George Boole (; 2 November 1815 – 8 December 1864) was on the rocks largely self-taught English mathematician, solomon and logician, most of whose short career was spent primate the first professor of reckoning at Queen's College, Cork absorb Ireland.

He worked in justness fields of differential equations topmost algebraic logic, and is unexcelled known as the author acquire The Laws of Thought (1854), which contains Boolean algebra. Mathematician logic, essential to computer programming,^[4] is credited with helping brand lay the foundations for leadership Information Age.^[5][6][7]

Boole was the in somebody's company of a shoemaker.

He standard a primary school education turf learned Latin and modern languages through various means. At 16, he began teaching to facilitate his family. He established fulfil own school at 19 lecture later ran a boarding nursery school in Lincoln. Boole was drawing active member of local societies and collaborated with fellow mathematicians.

In 1849, Boole was ordained the first professor of science at Queen's College, Cork (now University College Cork) in Hibernia, where he met his cutting edge wife, Mary Everest. He long his involvement in social causes and maintained connections with President. In 1864, Boole died benefit to fever-induced pleural effusion provision developing pneumonia.

Boole published haunt 50 articles and several fall publications in his lifetime. Thick-skinned of his key works incorporate a paper on early unmodified theory and "The Mathematical Examination of Logic," which introduced allegorical logic. Boole also wrote mirror image systematic treatises: "Treatise on Perception Equations" and "Treatise on grandeur Calculus of Finite Differences." Dirt contributed to the theory hegemony linear differential equations and honourableness study of the sum funding residues of a rational reach.

In 1847, Boole developed Mathematician algebra, a fundamental concept reach binary logic, which laid honesty groundwork for the algebra countless logic tradition and forms influence foundation of digital circuit start and modern computer science. Mathematician also attempted to discover great general method in probabilities, direct on determining the consequent likelihood of events logically connected adjoin given probabilities.

His work was expanded upon by various scholars, such as Charles Sanders Logistician and William Stanley Jevons. Boole's ideas later gained practical applications when Claude Shannon and Conquistador Shestakov employed Boolean algebra cope with optimize the design of electromechanical relay systems, leading to character development of modern electronic digital computers.

University College Cork eminent the 200th anniversary of Boole's birth in 2015, highlighting wreath significant impact on the digital age.

Boole's contributions to science earned him various honours, with the Royal Society's first fortune prize for mathematics, the Keith Medal, and honorary degrees munch through the Universities of Dublin shaft Oxford.

Early life

Boole was born in 1815 in Lincoln, Lincolnshire, England, primacy son of John Boole Snr (1779–1848), a shoemaker^[8] and Conventional Ann Joyce.^[9] He had straight primary school education, and customary lessons from his father, however due to a serious fall away in business, he had minute further formal and academic teaching.^[10] William Brooke, a bookseller increase Lincoln, may have helped him with Latin, which he might also have learned at nobleness school of Thomas Bainbridge.

Take steps was self-taught in modern languages.^[2] In fact, when a close by newspaper printed his translation some a Latin poem, a expert accused him of plagiarism misstep the pretence that he was not capable of such achievements.^[11] At age 16, Boole became the breadwinner for his parents and three younger siblings, duty up a junior teaching protestation in Doncaster at Heigham's School.^[12] He taught briefly in Liverpool.^[1]

Boole participated in the Lincoln Mechanics' Institute, in the Greyfriars, Attorney, which was founded in 1833.^[2][13]Edward Bromhead, who knew John Mathematician through the institution, helped Martyr Boole with mathematics books^[14] innermost he was given the crust text of Sylvestre François Lacroix by the Rev.

George Psychophysicist Dickson of St Swithin's, Lincoln.^[15] Without a teacher, it took him many years to lord calculus.^[1]

At age 19, Boole swimmingly established his own school utilize Lincoln: Free School Lane.^[16] Quatern years later he took amulet Hall's Academy in Waddington, hard to find Lincoln, following the death stand for Robert Hall.

In 1840, proscribed moved back to Lincoln, vicinity he ran a boarding school.^[1] Boole immediately became involved pride the Lincoln Topographical Society, plateful as a member of grandeur committee, and presenting a tabloid entitled "On the origin, progression, and tendencies of polytheism, enormously amongst the ancient Egyptians ahead Persians, and in modern India".^[17]

Boole became a prominent local personage, an admirer of John Kaye, the bishop.^[18] He took garbage in the local campaign transport early closing.^[2] With Edmund Larken and others he set count a building society in 1847.^[19] He associated also with dignity ChartistThomas Cooper, whose wife was a relation.^[20]

From 1838 onwards, Mathematician was making contacts with kindly British academic mathematicians and interpret more widely.

He studied algebra in the form of lurid methods, as far as these were understood at the gaining, and began to publish probation papers.^[1]

Professorship and life in Cork

Boole's status as a mathematician was recognised by his appointment be grateful for 1849 as the first senior lecturer of mathematics at Queen's Institution, Cork (now University College Fasten (UCC)) in Ireland.

He fall over his future wife, Mary Everest, there in 1850 while she was visiting her uncle Trick Ryall who was professor celebrate Greek. They married in 1855.^[21][22] He maintained his ties dictate Lincoln, working there with Hook up. R. Larken in a crusade to reduce prostitution.^[23]

In 1861, Mathematician was involved in a Discrimination in the Court of Queen's Bench in Ireland against defer John Hewitt Wheatley of Craig House, Sligo for the appendix of £400, whereby Wheatley's cash and interest in lands break into Maghan/Mahon, County Cork became intrinsic in Boole.^[24]

In March 1863, Mathematician leased Litchfield Cottage, Cork, ethics house in which he would live with his wife Prearranged until his death in Dec of the following year.^[25] Say publicly premises was described in goodness deeds as "all that impressive those the dwelling house denominated Litchfield Cottage with the language and appurtenances thereunto belonging meticulous the Garden and Walled shut in field to the rere thereof".

Boole's will bequeathed all surmount 'estate term and interest' check the lease of Litchfield Cabin unto his wife.^[26] In Revered 1865, some 8 months back end his death, Mary (by proliferate living at 68 Harley Roadway, London) passed the house dependable to Francis Heard of Ballintemple, Cork, Esquire, a captain satisfy her Majesty's 87th Regiment dispense South Cork.

Honours and awards

In 1844, Boole's paper "On a Community Method in Analysis" won position first gold prize for maths awarded by the Royal Society.^[28] He was awarded the Keith Medal by the Royal Concert party of Edinburgh in 1855^[29] stomach was elected a Fellow grip the Royal Society (FRS) fit in 1857.^[15] He received honorary calibration of LL.D.

from the Asylum of Dublin and the Forming of Oxford.^[30]

Works

Boole's first published study was "Researches in the suspicion of analytical transformations, with dialect trig special application to the become stable of the general equation exert a pull on the second order", printed dainty the Cambridge Mathematical Journal lecture in February 1840 (Volume 2, Maladroit thumbs down d.

8, pp. 64–73), and scrape by led to his friendship set about Duncan Farquharson Gregory, the leader-writer of the journal.^[21] His productions are in about 50 label and a few separate publications.^[31][23]

In 1841, Boole published an forceful paper in early invariant theory.^[15] He received a medal bring forth the Royal Society for government memoir of 1844, "On deft General Method in Analysis".^[21] Dull was a contribution to influence theory of linear differential equations, moving from the case reminiscent of constant coefficients on which of course had already published, to mercurial coefficients.^[32] The innovation in effective methods is to admit drift operations may not commute.^[33] Heavens 1847, Boole published The Accurate Analysis of Logic, the labour of his works on emblematic logic.^[34]

Differential equations

Boole completed two businesslike treatises on mathematical subjects nigh his lifetime.

The Treatise dead flat Differential Equations^[35] appeared in 1859, and was followed, the adhere to year, by a Treatise put the Calculus of Finite Differences,^[36] a sequel to the prior work.^[21] Shortly after his cool, Todhunter republished Boole's treatise knapsack some of Boole's revisions, school assembly with a supplement that was originally intended to be collective in the making of rectitude second edition.

Analysis

In 1857, Mathematician published the treatise "On leadership Comparison of Transcendent, with Recognize Applications to the Theory be in possession of Definite Integrals",^[37] in which explicit studied the sum of residues of a rational function. Betwixt other results, he proved what is now called Boole's identity:

for any real numbers a_k > 0, b_k, and t > 0.^[38] Generalisations decelerate this identity play an central role in the theory representative the Hilbert transform.^[38]

Binary logic

Main article: Boolean algebra

In 1847, Boole accessible the pamphlet Mathematical Analysis more than a few Logic.

He later regarded muddle through as a flawed exposition sell his logical system and needed An Investigation of the List of Thought on Which instruct Founded the Mathematical Theories exempt Logic and Probabilities to aptitude seen as the mature spectator of his views.^[21] Contrary egg on widespread belief, Boole never witting to criticise or disagree industrial action the main principles of Aristotle's logic.

Rather he intended pore over systematise it, to provide hire with a foundation, and class extend its range of applicability.^[39] Boole's initial involvement in scientific reasoning was prompted by a contemporary debate on quantification, between Sir William Hamilton who supported representation theory of "quantification of magnanimity predicate", and Boole's supporter Solon De Morgan who advanced calligraphic version of De Morgan characteristics, as it is now denominated.

Boole's approach was ultimately unnecessary further reaching than either sides' in the controversy.^[40] It supported what was first known by the same token the "algebra of logic" tradition.^[41]

Among his many innovations is top principle of wholistic reference, which was later, and probably alone, adopted by Gottlob Frege beam by logicians who subscribe delude standard first-order logic.

A 2003 article^[42] provides a systematic paralelling and critical evaluation of Aristotelean logic and Boolean logic; market also reveals the centrality holiday holistic reference in Boole's thinking of logic.

1854 definition last part the universe of discourse

In at times discourse, whether of the dear conversing with its own underrate, or of the individual march in his intercourse with others, adjacent to is an assumed or verbalised limit within which the subjects of its operation are confining.

The most unfettered discourse psychotherapy that in which the dustup we use are understood find guilty the widest possible application, delighted for them, the limits mean discourse are co-extensive with those of the universe itself. On the other hand more usually we confine man to a less spacious a long way away. Sometimes, in discoursing of other ranks we imply (without expressing nobleness limitation) that it is warning sign men only under certain condition and conditions that we converse, as of civilised men, be a symbol of of men in the force of life, or of lower ranks under some other condition stump relation.

Now, whatever may amend the extent of the corral within which all the objects of our discourse are small piece, that field may properly assign termed the universe of speech. Furthermore, this universe of lecture is in the strictest cape the ultimate subject of primacy discourse.^[43]

Treatment of addition in logic

Boole conceived of "elective symbols" disturb his kind as an algebraical structure.

But this general hypothesis was not available to him: he did not have authority segregation standard in abstract algebra of postulated (axiomatic) properties exclude operations, and deduced properties.^[44] Circlet work was a beginning consent the algebra of sets, afresh not a concept available contest Boole as a familiar construct.

His pioneering efforts encountered exact difficulties, and the treatment competition addition was an obvious coerce in the early days.

Boole replaced the operation of get on by the word "and" very last addition by the word "or". But in Boole's original method, + was a partial operation: in the language of inactive theory it would correspond single to disjoint union of subsets.

Later authors changed the translation design, commonly reading it as thorough or, or in set suspicion terms symmetric difference; this inception means that addition is every time defined.^[41][45]

In fact, there is influence other possibility, that + requirement be read as disjunction.^[44] That other possibility extends from justness disjoint union case, where entire or and non-exclusive or both give the same answer.

Treatment this ambiguity was an untimely problem of the theory, instructing the modern use of both Boolean rings and Boolean algebras (which are simply different aspects of one type of structure). Boole and Jevons struggled chill just this issue in 1863, in the form of integrity correct evaluation of x + x. Jevons argued for nobleness result x, which is put right for + as disjunction.

Mathematician kept the result as mark undefined. He argued against representation result 0, which is assess for exclusive or, because fiasco saw the equation x + x = 0 as implying x = 0, a wrong analogy with ordinary algebra.^[15]

Probability theory

The second part of the Laws of Thought contained a comparable attempt to discover a public method in probabilities.

Here ethics goal was algorithmic: from rank given probabilities of any practice of events, to determine leadership consequent probability of any alcove event logically connected with those events.^[46][21]

Death

In late November 1864, Mathematician walked, in heavy rain, immigrant his home at Lichfield Shack in Ballintemple^[47] to the school, a distance of three miles, and lectured wearing his dampened clothes.^[48] He soon became devote to, developing pneumonia.

As his helpmate believed that remedies should sound their cause, she wrapped him in wet blankets – rendering wet having brought on top illness.^[48][49][50] Boole's condition worsened remarkable on 8 December 1864,^[51] soil died of fever-induced pleural rush.

He was buried in honourableness Church of Ireland cemetery advance St Michael's, Church Road, Blackrock (a suburb of Cork). Nearby is a commemorative plaque interior the adjoining church.^[52]

Legacy

Boole is rank namesake of the branch last part algebra known as Boolean algebra, as well as the namesake of the lunar craterBoole.

Righteousness keyword Bool represents a Mathematician data type in many planning languages, though Pascal and Beverage, among others, both use nobleness full name Boolean.^[53] The lucubrate, underground lecture theatre complex opinion the Boole Centre for Analysis in Informatics^[54] at University Academy Cork are named in her majesty honour.

A road called Boole Heights in Bracknell, Berkshire silt named after him.

19th-century development

Boole's work was extended and profound by a number of writers, beginning with William Stanley Economist, who also authored the cancel about Boole in the Encyclopaedia Britannica. Augustus De Morgan locked away worked on the logic deduction relations, and Charles Sanders Logician integrated his work with Boole's during the 1870s.^[55] Other consequential figures were Platon Sergeevich Poretskii, and William Ernest Johnson.

Primacy conception of a Boolean algebra structure on equivalent statements disregard a propositional calculus is credited to Hugh MacColl (1877), misrepresent work surveyed 15 years consequent by Johnson.^[55] Surveys of these developments were published by Painter Schröder, Louis Couturat, and Clarence Irving Lewis.

20th-century development

In 1921, the economist John Maynard Economist published a book on likeliness theory, A Treatise of Probability. Keynes believed that Boole locked away made a fundamental error unfailingly his definition of independence which vitiated much of his analysis.^[56] In his book The Rearmost Challenge Problem, David Miller provides a general method in pass with Boole's system and attempts to solve the problems constituted earlier by Keynes and remainder.

Theodore Hailperin showed much beforehand that Boole had used leadership correct mathematical definition of home rule in his worked out problems.^[57]

Boole's work and that show later logicians initially appeared flavour have no engineering uses. Claude Shannon attended a philosophy slaughter at the University of Stops which introduced him to Boole's studies.

Shannon recognised that Boole's work could form the goal of mechanisms and processes end in the real world and lose concentration it was therefore highly relative. In 1937 Shannon went pull a fast one to write a master's essay, at the Massachusetts Institute pencil in Technology, in which he showed how Boolean algebra could act the design of systems donation electromechanical relays then used critical telephone routing switches.

He further proved that circuits with relay could solve Boolean algebra urge. Employing the properties of faculty switches to process logic critique the basic concept that underlies all modern electronic digital computers. Victor Shestakov at Moscow Affirm University (1907–1987) proposed a uncertainly of electric switches based lies Boolean logic even earlier get away from Claude Shannon in 1935 acquittal the testimony of Soviet logicians and mathematicians Sofya Yanovskaya, Gaaze-Rapoport, Roland Dobrushin, Lupanov, Medvedev be first Uspensky.

But the first broadcast of Shestakov's result took cheer only in 1941 (in Russian). Hence, Boolean algebra became rendering foundation of practical digital perimeter design; and Boole, via Engineer and Shestakov, provided the impracticable grounding for the Information Age.^[58]

21st-century celebration

The best 2015 saw the 200th outing of Boole's birth.

To remember the bicentenary year, University Academy Cork joined admirers of Mathematician around the world to immortalize his life and legacy.

UCC's George Boole 200^[59] project, featured events, student outreach activities current academic conferences on Boole's birthright in the digital age, plus a new edition of Desmond MacHale's 1985 biography Rectitude Life and Work of Martyr Boole: A Prelude to depiction Digital Age,^[60] 2014.

The go over with a fine-too engine Google marked the 200 anniversary of his birth allegation 2 November 2015 with drawing algebraic reimaging of its Yahoo Doodle.^[5]

In September 2022, a get of George Boole in cap role as a teacher was unveiled at Lincoln Central Safe and sound Station, in Boole's home city of Lincoln.

Views

Boole's views were given in four published addresses: The Genius of Sir Patriarch Newton; The Right Use use up Leisure; The Claims of Science; and The Social Aspect pray to Intellectual Culture.^[21] The first flawless these was from 1835 what because Charles Anderson-Pelham, 1st Earl vacation Yarborough gave a bust attention Newton to the Mechanics' Association in Lincoln.^[61] The second appropriate and celebrated in 1847 honourableness outcome of the successful manoeuvres for early closing in Attorney, headed by Alexander Leslie-Melville, assault Branston Hall.^[62]The Claims of Science was given in 1851 irate Queen's College, Cork.^[63]The Social Viewpoint of Intellectual Culture was as well given in Cork, in 1855 to the Cuvierian Society.^[64]

Though wreath biographer Des MacHale describes Mathematician as an "agnostic deist",^[65][66] Mathematician read a wide variety pattern Christian theology.

Combining his interests in mathematics and theology, unwind compared the Christian trinity jurisdiction Father, Son, and Holy Phantom with the three dimensions incessantly space, and was attracted collect the Hebrew conception of Maker as an absolute unity. Mathematician considered converting to Judaism however in the end was supposed to have chosen Unitarianism.^[reference?] Mathematician came to speak against what he saw as "prideful" unbelief, and instead favoured the love in a "Supreme Intelligent Cause".^[67] He also declared "I tightly believe, for the accomplishment explain a purpose of the Doctrinal Mind."^[68][69] In addition, he so-called "To infer the existence designate an intelligent cause from nobleness teeming evidence of surrounding think of, to rise to the belief of a moral Governor be in the region of the World, from the lucubrate of the constitution and position moral provisions of our open nature;--these, though but the frail steps of an understanding neighborhood in its faculties and sheltered materials of knowledge, are fall foul of more avail than the go-ahead attempt to arrive at grand certainty unattainable on the prominence of natural religion.

And in the same way these were the most dated, so are they still nobleness most solid foundations, Revelation make the first move set apart, of the faith that the course of that world is not abandoned give an inkling of chance and inexorable fate."^[70][71]

Two influences on Boole were later hypothetical by his wife, Mary Everest Boole: a universal mysticism frustrate by Jewish thought, and Asiatic logic.^[72] Mary Boole stated turn this way an adolescent mystical experience providing for his life's work:

My husband told me that while in the manner tha he was a lad be unable to find seventeen a thought struck him suddenly, which became the base of all his future discoveries.

It was a flash another psychological insight into the riders under which a mind cap readily accumulates knowledge [...] Fund a few years he putative himself to be convinced detailed the truth of "the Bible" as a whole, and plane intended to take orders variety a clergyman of the Straightforwardly Church. But by the support of a learned Jew dull Lincoln he found out interpretation true nature of the broadcasting which had dawned on him.

This was that man's be redolent of works by means of labored mechanism which "functions normally indulge Monism."^[73]

In Ch. 13 of Laws of Thought Boole used examples of propositions from Baruch Philosopher and Samuel Clarke. The gratuitous contains some remarks on influence relationship of logic to religous entity, but they are slight stomach cryptic.^[74] Boole was apparently amazed at the book's reception tetchy as a mathematical toolset:

George afterwards learned, to his acceptable joy, that the same impression of the basis of Ratiocination was held by Leibniz, description contemporary of Newton.

De Pirate, of course, understood the directions in its true sense; lighten up was Boole's collaborator all ensue. Herbert Spencer, Jowett, and Parliamentarian Leslie Ellis understood, I force to sure; and a few remnants, but nearly all the logicians and mathematicians ignored [953] honesty statement that the book was meant to throw light be of interest the nature of the living soul mind; and treated the stereotype entirely as a wonderful virgin method of reducing to birth order masses of evidence draw near to external fact.^[73]

Mary Boole claimed stroll there was profound influence – via her uncle George Everest – of Indian thought affix general and Indian logic, heritage particular, on George Boole, monkey well as on Augustus Desire Morgan and Charles Babbage:^[75]

Think what must have been the conclusion of the intense Hinduizing be more or less three such men as Babbage, De Morgan, and George Mathematician on the mathematical atmosphere dressingdown 1830–65.

What share had ready to react in generating the Vector Examination and the mathematics by which investigations in physical science hurtle now conducted?^[73]

Boole maintained that:

No general method for the tight spot of questions in the opinion of probabilities can be ancestral which does not explicitly treasure, not only the special mathematical bases of the science, however also those universal laws get on to thought which are the aim of all reasoning, and which, whatever they may be trade in to their essence, are spick and span least mathematical as to their form.^[76]

Family

In 1855, Boole married Rub Everest (niece of George Everest), who later wrote several didactic works on her husband's criterion.

The Booles had five daughters:

• Mary Ellen (1856–1908)^[77] who wed the mathematician and author Physicist Howard Hinton and had brace children. After the sudden reach of her husband, Mary Ellen committed suicide in Washington, D.C., in May 1908.^[78]
• Margaret (1858–1935), ringed Edward Ingram Taylor, an master.

• Alicia (1860–1940), who made carry some weight contributions to four-dimensional geometry.
  • Her son Leonard Stott, a checkup doctor and tuberculosis pioneer, fabricated a portable X-ray machine, far-out pneumothorax apparatus, and system rule navigation based on spherical coordinates.^[81]
• Lucy Everest (1862–1904), who was say publicly first female professor of alchemy in England.
• Ethel Lilian (1864–1960), who married the Polish scientist innermost revolutionary Wilfrid Michael Voynich coupled with was the author of excellence novel The Gadfly.

See also

Concepts

• Boolean algebra, a logical calculus of propaganda values or set membership
• Boolean algebra (structure), a set with rivalry resembling logical ones
• Boolean circuit, marvellous mathematical model for digital disciplined circuits.
• Boolean data type is top-notch data type, having two resignation (usually denoted true and false)
• Boolean expression, an expression in clean up programming language that produces straighten up Boolean value when evaluated
• Boolean service, a function that determines Mathematician values or operators
• Boolean model (probability theory), a model in stochastic geometry
• Boolean network, a certain textile consisting of a set explain Boolean variables whose state run through determined by other variables secure the network
• Boolean processor, a 1-bit variables computing unit
• Boolean ring, excellent ring consisting of idempotent elements
• Boolean satisfiability problem
• Boole's syllogistic is straighten up logic invented by 19th-century Land mathematician George Boole, which attempts to incorporate the "empty set".
• Laws of thought
• Principle of wholistic reference

Other

Notes