(In 1841 Boole published an influential paper in early inv...)
In 1841 Boole published an influential paper in early invariant theory. He received a medal from the Royal Society for his 1844 work, On A General Method of 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. In 1847 Boole published The Mathematical Analysis of Logic, the first of his works on symbolic logic.
(An Investigation of the Laws of Thought on Which are Foun...)
An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic. Boole was a professor of mathematics at what was then Queen's College, Cork, in Ireland.
(The Complete Works of Boole George George Boole was a lar...)
The Complete Works of Boole George George Boole 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 Ireland. This collection includes the following: An Investigation of the Laws of Thought The Mathematical Analysis of Logic Being an Essay Towards a Calculus of Deductive Reasoning.
(George Boole invented Boolean logic, the basis of modern ...)
George Boole invented Boolean logic, the basis of modern digital computer logic, for which he is regarded as a founder of the field of computer science. This authoritative compilation of his papers features his most mature thinking on Boolean logic and includes previously unpublished material. Appropriate for upper-level undergraduates and graduate students, the contents range from The Mathematical Analysis of Logic to Boole's final works, including The Laws of Thought, the most systematic statement of his ideas on logic and probability. Boole had intended to create a follow-up volume but did not survive to fulfill his ambition; this volume features his further studies on the subject.
George Boole was an English mathematician and a founder of the algebraic tradition in logic. He revolutionized logic by applying methods from the then-emerging field of symbolic algebra to logic.
Background
George Boole's parents were Mary Ann Joyce and John Boole. John made shoes but he was interested in science and in particular the application of mathematics to scientific instruments. Mary Ann was a lady's maid and she married John on 14 September 1806. They moved to Lincoln where John opened a cobbler's shop at 34 Silver Street. The family was not well off, partly because John's love of science and mathematics meant that he did not devote the energy to developing his business in the way he might have done. George, their first child, was born after Mary Ann and John had been married for nine years. They had almost given up hope of having children after this time so it was an occasion for great rejoicing. George was christened the day after he was born, an indication that he was a weak child that his parents feared might not live. He was named after John's father who had died in April 1815. Over the next five years, Mary Ann and John had three further children, Mary Ann, William, and Charles.
Education
If George was a weak child after his birth, he certainly soon became strong and healthy. George first attended a school in Lincoln for children of tradesmen run by two Misses Clarke when he was less than two years old. After a year he went to a commercial school run by Mr. Gibson, a friend of John Boole, where he remained until he was seven years old. His early instruction in mathematics, however, was from his father who also gave George a liking for constructing optical instruments. When he was seven George attended a primary school where he was taught by Mr. Reeves. His interests turned to languages and his father arranged that he receive instruction in Latin from a local bookseller.
Having learned Latin from a tutor, George went on to teach himself Greek. By the age of 14, he had become so skilled in Greek that it provoked an argument. He translated a poem by the Greek poet Meleager which his father was so proud of that he had it published. However, the talent was such that a local schoolmaster disputed that any 14 years old could have written with such depth. By this time George was attending Bainbridge's Commercial Academy in Lincoln which he had entered on 10 September 1828. This school did not provide the type of education he would have wished but it was all his parents could afford. However, he was able to teach himself French and German studying for himself academic subjects that a commercial school did not cover.
Boole did not study for an academic degree, but from the age of 16, he was an assistant school teacher at Heigham's School in Doncaster. This was rather forced on him since his father's business collapsed and he found himself having to support financially his parents, brothers, and sister. He maintained his interest in languages, began to study mathematics seriously, and gave up ideas which he had to enter the Church. The first advanced mathematics book he read was Lacroix's Differential and integral calculus. He was later to realize that he had almost wasted five years in trying to teach himself the subject instead of having a skilled teacher. In 1833 he moved to a new teaching position in Liverpool but he only remained there for six months before moving to Hall's Academy in Waddington, four miles from Lincoln.
Career
In 1834 George Boole opened his own school in Lincoln although he was only 19 years old. In 1838 Robert Hall, who had run Hall's Academy in Waddington, died and Boole was invited to take over the school which he did. His parents, brothers, and sister moved to Waddington and together they ran the school which had both boarding and day pupils. At this time Boole was studying the works of Laplace and Lagrange, making notes which would later be the basis for his first mathematics paper. However, he did receive encouragement from Duncan Gregory who at this time was in Cambridge and the editor of the recently founded Cambridge Mathematical Journal. Boole was unable to take Duncan Gregory's advice and study courses at Cambridge as he required the income from his school to look after his parents. In the summer of 1840, he had opened a boarding school in Lincoln and again the whole family had moved with him. He began publishing regularly in the Cambridge Mathematical Journal and his interests were influenced by Duncan Gregory as he began to study algebra.
Boole had begun to correspond with De Morgan in 1842 and when in the following year he wrote a paper On a general method of analysis applying algebraic methods to the solution of differential equations he sent it to De Morgan for comments. It was published by Boole in the Transactions of the Royal Society in 1844 and for this work, he received the Society's Royal Medal in November 1844. His mathematical work was beginning to bring him fame.
Boole was appointed to the chair of mathematics at Queens College, Cork in 1849. In fact, he made an application for a chair in any of the new Queen's Colleges of Ireland in 1846, and in September of that year De Morgan, Kelland, Cayley, and Thomson were among those writing testimonials in support.
Boole's father died in December 1848 before the decision had been made concerning the Irish chairs but an announcement came in August 1849 that Boole was to become the first Professor of Mathematics at Queen's College, Cork, and he took up the position in November. He taught there for the rest of his life, gaining a reputation as an outstanding and dedicated teacher. However, the position was not without difficulty as the College became embroiled in religious disputes.
In May 1851 Boole was elected as Dean of Science, a role he carried out conscientiously.
In 1854 George Boole published An investigation into the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities. Boole approached logic in a new way reducing it to a simple algebra, incorporating logic into mathematics. He pointed out the analogy between algebraic symbols and those that represent logical forms. It began the algebra of logic called Boolean algebra which now finds application in computer construction, switching circuits, etc. Boole himself understood the importance of the work. He wrote in a letter to Thomson dated 2 January 185: "I am now about to set seriously to work upon preparing for the press an account of my theory of Logic and Probabilities which in its present state I look upon as the most valuable if not the only valuable contribution that I have made or am likely to make to Science and the thing by which I would desire if at all to be remembered hereafter."
Boole also worked on differential equations, the influential Treatise on Differential Equations appeared in 1859, the calculus of finite differences, Treatise on the Calculus of Finite Differences (1860), and general methods in probability.
Towards the end of the 1850s, Boole had spread his academic net wide. He was still working on probability, logic, and operator theory but his first love, in terms of mathematics, had been differential calculus. In fact, this discipline had influenced several of his key discoveries. At this time he felt a need to produce a textbook on differential equations. As his work progressed on this volume he also produced important original research on this and other related topics. The resulting book was entitled A Treatise on Differential Equations and was published in 1859. Boole was very happy when he received the news that the University of Cambridge had adopted this work as a college textbook. Indeed this book is as relevant today as it was over a century-and-a-half ago.
Taking into account the impact of his mathematical work of the previous 20 years, Boole now re-examined his published output and realized that many of his methods and techniques in relation to calculus problems needed to be reassessed, because of their potentially wider range of applications. Difference equations began to occupy his mind and he set to work on his fourth and final book, a textbook called A Treatise on the Calculus of Finite Difference. The purpose of this new work was to shine a light on the connections between difference equations and differential equations while bringing into focus the power of abstract operator methods as applied to a new area of mathematics. Students today widely use this book, which like his Laws of Thought of 1854 was acknowledged as a masterpiece.
Through the publication of this book, it could be said that George Boole had anticipated developments during the twentieth century, as computers and calculating machines are based on the discrete difference equation rather than on the continuous differential equation.
However, his career, which was started rather late, came to an unfortunately early end when he died at the age of 49.
(In 1841 Boole published an influential paper in early inv...)
1847
Views
As his thinking developed, Boole came to regard mathematics as abstract, the manipulation of symbols to which no particular meaning is attached. Freeing algebra from arithmetic, he used algebraic symbols to represent logical statements and established an algebra of symbols that can be added or multiplied. This powerful abstract approach caused a paradigm shift, giving modern mathematics an enormous scope and potency.
While in his teens, Boole had become fascinated by the work of Sir Isaac Newton (a fellow-native of Lincolnshire). His first love was differential calculus, which inspired and motivated many of his later discoveries.
From 1840, he published papers in the Cambridge Mathematical Journal on a range of topics, stressing repeatedly the importance of manipulation of symbolic operators in various areas of mathematics. His 1841 paper An Exposition of a General Theory of Linear Transformations, introduced a new branch of mathematics - now called Invariant Theory - which later became part of the inspiration for Einstein’s Theory of Relativity.
In 1843, Boole began applying algebraic methods to the solution of differential equations. He wrote a lengthy paper On a General Method in Analysis, published in 1844 in Philosophical Transactions, the prestigious scientific journal of the Royal Society in London.
The paper investigates differentiation and differential equations from an operator point of view and introduces Boole’s new "algebra of classes." This "boolean algebra" contributed to freeing mathematics from number systems, and pushed mathematics a step further towards abstraction. For this paper, Boole received the Royal Society’s Gold Medal, the first-ever awarded for mathematics. It was a turning point in Boole’s career and brought his name to the attention of leading mathematicians and scientists.
After being appointed Professor of Mathematics at Queen’s College Cork, Boole re-wrote and expanded his 1847 book. In 1854 he published An Investigation of the Laws of Thought, regarded as his magnum opus.
In this work, Boole demonstrates that logical propositions can be expressed as mathematical equations and that the algebraic manipulation of symbols in those equations offers a fail-safe method of logical deduction. The Laws of Thought extends his exploration of logic and introduces another ground-breaking concept, mathematical probability. In the 20th century, Boolean algebra was taken up most effectively by the American engineer Claude Shannon, whose 1938 paper A Symbolic Analysis of Relay and Switching Circuits builds on Boole’s Analysis of Logic.
Today, Boole’s legacy is associated principally with Shannon and circuit theory, leading to the construction of modern computers. Less well-recognized but equally significant is the impact of Boole’s mathematical logic on computer programming, and how computers handle data.
Quotations:
"No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful."
"I presume that few who have paid any attention to the history of the Mathematical Analysis will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary - being determined, either by steps of logical deduction or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived."
"Of the many forms of false culture, a premature converse with abstractions is perhaps the most likely to prove fatal to the growth of a masculine vigor of intellect."
"Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave nether room nor demand for a theory of probabilities."
"To unfold the secret laws and relations of those high faculties of thought by which all beyond the merely perceptive knowledge of the world and of ourselves is attained or matured is an object which does not stand in need of commendation to a rational mind."
"t is not of the essence of mathematics to be conversant with the ideas of number and quantity."
Membership
The Royal Society
,
United Kingdom
1857
Personality
Living in early nineteenth-century Lincoln, the young George Boole was acutely aware of the various social evils present within his local community. When he had reached a certain foothold in life through self-education and hard work, he hoped to improve the social and educational conditions for those less fortunate than himself.
In George Boole, we find a remarkable combination of high creativity with firm rigour. An independent thinker who explored the diversity of mathematics, he marched intently into the unknown while more orthodox figures chose a slower path.
Physical Characteristics:
Boole had never enjoyed the most robust of health. In relation to his delicate constitution, Mary Boole is quoted as saying that he suffered from "hereditary disease of the lungs, aggravated by residence in a damp climate, with a nervous system sensitive to the highest degree."
Quotes from others about the person
"Boole's system of logic is but one of many proofs of genius and patience combined. ... That the symbolic processes of algebra, invented as tools of numerical calculation, should be competent to express every act of thought and to furnish the grammar and dictionary of an all - containing system of logic, would not have been believed until it was proved. When Hobbes ... published his "Computation or Logique" he had a remote glimpse of some of the points which are placed in the light of day by Mr. Boole." - Augustus De Morgan.
Interests
history, biography, travel, science, poetry, classical languages, literature
Philosophers & Thinkers
Joseph-Louis Lagrange, Pierre-Simon Laplace
Writers
Walter Scott
Connections
George Boole met Mary Everest (a niece of Sir George Everest, after whom the mountain is named) whose uncle was the professor of Greek at Cork and a friend of Boole. They met first in 1850 when Mary visited her uncle in Cork and again in July 1852 when Boole visited the Everest family in Wickwar, Gloucestershire, England. Boole began to give Mary informal mathematics lessons on the differential calculus. At this time he was 37 years old while Mary was only 20. In 1855 Mary's father died leaving her without means of support and Boole proposed marriage. They married on 11 September 1855 at a small ceremony in Wickwar. It proved a very happy marriage with five daughters: Mary Ellen born in 1856, Margaret born in 1858, Alicia (later Alicia Stott) born in 1860, Lucy Everest born in 1862, and Ethel Lilian born in 1864. MacHale wrote:
"The large gap in their ages seemed to count for nothing because they were kindred spirits with almost complete unity of purpose."