**George Boole** 1815 – 1864 was a British mathematician and philosopher. As the inventor of Boolean algebra, which is the basis of all modern computer arithmetic, Boole is regarded in hindsight as one of the founders of the field of computer science.

George Boole was the husband of Mary Elizabeth Everest Boole, daughter of homeopath Thomas Roupell Everest.

Mary Elizabeth (Everest) Boole (1832 – 1916) was born in England in 1832, daughter of homeopath Thomas Roupell Everest and Mary Ryall.

Mary was a friend of Mary Fairfax Greig Somerville.

IISH holds some of her archival material http://search.socialhistory.org/Record/ARCH00279/Description

When Mary was five, the family moved to Poissy (France) to Samuel Hahnemann, the founder of homeopathic medicine, as Thomas Roupell Everest was seriously ill and they were seeking a cure…

Mary became very close to her father during their time in France, and she even participated in his homeopathic treatment.

The family returned to England when Mary was eleven years after her father had recovered from his illness and he became a Reverend of a Church in Wickwar, at the foot of the Cotswold Hills.

Mary used books from her father to continue her preparations in mathematics and she met the brilliant friends of her father, such as John Herschel and Charles Babbage…

Mary was removed from school and became an assistant to her father.

The first UK homeopaths were all close colleagues of Samuel Hahnemann. Frederick Hervey Foster Quin, William Leaf, Paul Francois Curie and Thomas Roupell Everest seem to have been part of an ‘inner sanctum’ of Samuel Hahnemann‘s protégés in Paris. This core of homeopaths were responsible for establishing homeopathy in the United Kingdom. They established practices in the UK and later free dispensaries for the poor and also several hospitals.

Mary was devoted to tasks such as visiting the elderly, she gave classes in a school on Sundays and helped her father with his sermons. Through her uncle John Everest, a Professor of Classical Languages at the Queen’s College, Cork, and when she was eighteen years old, Mary met the now famous mathematician George Boole who was Professor of Mathematics at Queen’s College, Cork and who became her guardian.

Mary told how George Boole had difficulties with calculation and how the method of learning Monsieur déplacées (actually this is Pierre-Simon, marquis de Laplace) had helped him. Mary shared a lot of time with George Boole both in leisure and in intellectual discussion.

After her return to England, Mary wrote to him and sent him some examples of her work in mathematics. George Boole moved to England two years later to train Mary in mathematical knowledge.

George Boole wrote

An investigation of the laws of thoughtdedicated to John Ryall, the uncle of Mary and whose execution she contributed significantly. Mary’s father died in 1855 and George Boole supported her in these difficult moments. That’s when their romantic relationship was consolidated and spent a year were married.Despite the fact that Mary was seventeen years younger than George Boole, they had a good and happy marriage. Over the next nine years, Mary and George had five daughters called Mary, Margaret, Alice, Lucy Everest Boole and Ethel. However, this happiness it would soon fade. Tragically, George Boole contracted pneumonia and died in 1864… (leaving Mary with five daughters and very little money… nonetheless, Mary educated her daughters very well in mathematics and geometry, logic and thinking for themselves). (Mary sold the Royal Society’s gold medal…. and became friendly with James Hinton who introduced her to The Cranks…)

The following year, Mary accepted a job at Queen’s College, London, which is the first college for higher education for women throughout England opened in 1847. During this time, neither women nor Jews could obtain university degrees or teach in college, so that although she loved teaching, Mary accepted a job as librarian. Through this employment Mary resolved the doubts of her students. Mary realized that not only loved teaching but that was good in this discipline…. (Mary Elizabeth Everest Boole was a correspondent of Charles Darwin). See also http://en.wikipedia.org/wiki/Mary_Everest_Boole

For fifty years, Mary began writing a series of books and articles, which were published regularly until she died.

Mathematics in occultism,The divining road,The schoolgirl medium(with Eleanor Meredith Cobham),About girls,What one might say to a schoolboy,Hooliganism,Philosophy and fun of algebra,The logic of lovesee Dick Tahta.Mary had a group of friends who call themselves The Cranks. They met at a vegetarian restaurant in London. She wrote

Are we berserks or christians? After some time, this group published a magazine called “The Cranks” (with Charles William Daniel a principle organiser of the London Tolstoyan Society), in which Mary worked with numerous articles.Her first book, published in 1883 but written in the decade of the sixties, was a pioneering work in mental hygiene,

Lectures on the Logic of Arithmetic,The preparation of the child for sciencehad a big impact on schools in England and the United States in the first part of the twentieth century,The Mathematical Psychology of Gratry and Boole,The Forging of Passion Into Power,A Boolean Anthology: Selected Writings of Mary Boole on Mathematical …,Philosophy & Fun of Algebra,…Collected works…,Symbolical Methods of Study,The Message of Psychic Science to the World,At the foot of the Cotswolds,Suggestions for Increasing Ethical Stability,Logic Taught by Love,Some master-keys of the science of notation, a sequel to ‘Philosophy and fun …,Mistletoe and olive, an introduction for children to the life of revelation,Woodworker and Tentmaker, and her friend Eleanor Meredith Cobham wroteMary Everest Boole: A Memoir with Some Letters.

George Boole’s father, John Boole (1779-1848), was a tradesman of limited means, but of “studious character and active mind”. Being especially interested in mathematical science and logic, the father gave his son his first lessons; but the extraordinary mathematical talents of George Boole did not manifest themselves in early life. At first his favourite subject was classics.

It wasn’t until his successful establishment of a school at Lincoln, its removal to Waddington, and later his appointment in 1849 as the first professor of mathematics of then Queen’s College, Cork (now University College Cork, where the library and underground lecture complex are named in his honour) in Ireland that his mathematical skills were fully realized.

In 1855 he married Miss Mary Elizabeth Everest (daughter of Thomas Roupell Everest and niece of George Everest), who later, as Mrs. Boole, wrote several useful educational works on her husband’s principles (of course, she had none of her own!! – see above and note how easily homeopaths and women are written out of history by Wikipedia writers!!!).

To the broader public Boole was known only as the author of numerous abstruse papers on mathematical topics, and of three or four distinct publications which have become standard works.

His earliest published paper was the “

Researches in the theory of analytical transformations, with a special application to the reduction of the general equation of the second order.” printed in theCambridge Mathematical Journalin February 1840 (Volume 2, no. 8, pp.64-73), and it led to a friendship between Boole and Duncan Farquharson Gregory, the editor of the journal, which lasted until the premature death of the latter in 1844.A long list of Boole’s memoirs and detached papers, both on logical and mathematical topics, are found in the

Catalogue of Scientific Memoirspublished by the Royal Society, and in the supplementary volume onDifferential Equations, edited by Isaac Todhunter.To the

Cambridge Mathematical Journaland its successor, theCambridge and Dublin Mathematical Journal, Boole contributed twenty-two articles in all. In the third and fourth series of thePhilosophical Magazineare found sixteen papers.The Royal Society printed six important memoirs in the

Philosophical Transactions, and a few other memoirs are to be found in theTransactions of the Royal Society of EdinburghandTransactionsof the Royal Irish Academy, in theBulletin de l’Académie de St-Pétersbourgfor 1862 (under the name G Boldt, vol. iv. pp. 198-215), and inCrelle’s Journal.Also included is a paper on the mathematical basis of logic, published in the

Mechanic’s Magazinein 1848. The works of Boole are thus contained in about fifty scattered articles and a few separate publications.Only two systematic treatises on mathematical subjects were completed by Boole during his lifetime. The well-known

Treatise on Differential Equationsappeared in 1859, and was followed, the next year, by aTreatise on the Calculus of Finite Differences, designed to serve as a sequel to the former work.These treatises are valuable contributions to the important branches of mathematics in question. To a certain extent these works embody the more important discoveries of their author.

In the sixteenth and seventeenth chapters of the

we find, for instance, an account of the general symbolic method, the bold and skilful employment of which led to Boole’s chief discoveries, and of a general method in analysis, originally described in his famous memoir printed in theTreatise on Differential EquationsPhilosophical Transactionsfor 1844.Boole was one of the most eminent of those who perceived that the symbols of operation could be separated from those of quantity and treated as distinct objects of calculation. His principal characteristic was perfect confidence in any result obtained by the treatment of symbols in accordance with their primary laws and conditions, and an almost unrivalled skill and power in tracing out these results.

During the last few years of his life Boole was constantly engaged in extending his researches with the object of producing a second edition of his

much more complete than the first edition, and part of his last vacation was spent in the libraries of the Royal Society and the British Museum; but this new edition was never completed.Treatise on Differential EquationsEven the manuscripts left at his death were so incomplete that Israel Todhunter, into whose hands they were put, found it impossible to use them in the publication of a second edition of the original treatise, and printed them, in 1865, in a supplementary volume.

With the exception of Augustus de Morgan, Boole was probably the first English mathematician since the time of John Wallis who had also written upon logic. His novel views of logical method were due to the same profound confidence in symbolic reasoning to which he had successfully trusted in mathematical investigation.

Speculations concerning a calculus of reasoning had at different times occupied Boole’s thoughts, but it was not till the spring of 1847 that he put his ideas into the pamphlet called

Mathematical Analysis of Logic.Boole afterwards regarded this as a hasty and imperfect exposition of his logical system, and he desired that his much larger work,

An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities(1854), should alone be considered as containing a mature statement of his views.Nevertheless, there is a charm of originality about his earlier logical work which is easy to appreciate.

He did not regard logic as a branch of mathematics, as the title of his earlier pamphlet might be taken to imply, but he pointed out such a deep analogy between the symbols of algebra and those which can be made, in his opinion, to represent logical forms and syllogisms, that we can hardly help saying that (especially his) formal logic is mathematics restricted to the two quantities, 0 and 1.

By unity Boole denoted the universe of thinkable objects; literal symbols, such as x, y, z, v, u, etc., were used with the elective meaning attaching to common adjectives and substantives. Thus, if x=horned and y=sheep, then the successive acts of election represented by x and y, if performed on unity, give the whole of the class horned sheep. Boole showed that elective symbols of this kind obey the same primary laws of combination as algebraic symbols, whence it followed that they could be added, subtracted, multiplied and even divided, almost exactly in the same manner as numbers.

Thus, (1 – x) would represent the operation of selecting all things in the world except horned things, that is, all not horned things, and (1 – x) (1 – y) would give us all things neither horned nor sheep. By the use of such symbols propositions could be reduced to the form of equations, and the syllogistic conclusion from two premises was obtained by eliminating the middle term according to ordinary algebraic rules.

Still more original and remarkable, however, was that part of his system, fully stated in his

Laws of Thought, formed a general symbolic method of logical inference. Given any propositions involving any number of terms, Boole showed how, by the purely symbolic treatment of the premises, to draw any conclusion logically contained in those premises.The second part of the

An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilitiescontained a corresponding attempt to discover a general method in probabilities, which should enable us from the given probabilities of any system of events to determine the consequent probability of any other event logically connected with the given events.Though Boole published little except his mathematical and logical works, his acquaintance with general literature was wide and deep. Dante was his favourite poet, and he preferred the

Paradisoto theInferno. The metaphysics of Aristotle, the ethics of Spinoza, the philosophical works of Cicero, and many kindred works, were also frequent subjects of study.His reflections upon scientific, philosophical and religious questions are contained in four addresses upon

The Genius of Sir Isaac Newton,The Right Use of Leisure,The Claims of ScienceandThe Social Aspect of Intellectual Culture, which he delivered and printed at different times.The personal character of Boole inspired all his friends with the deepest esteem. He was marked by true modesty, and his life was given to the single-minded pursuit of truth. Though he received a medal from the Royal Society for his memoir of 1844, and the honorary degree of LL.D. from the University of Dublin, he neither sought nor received the ordinary rewards to which his discoveries would entitle him. On 8 December 1864, in the full vigour of his intellectual powers, he died of an attack of fever, ending in effusion on the lungs, caused by giving a lecture in wet clothes from the rain.

The Booles had five daughters:

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