# George Boole

**George Boole** [buːl], (November 2, 1815 Lincoln, Lincolnshire, England – December 8, 1864 Ballintemple, County Cork, Ireland) was a mathematician and philosopher.

As the inventor of Boolean algebra, the basis of all modern computer arithmetic, Boole is regarded in hindsight as one of the founders of the field of computer science, although computers did not exist in his day (see "Legacy" section below).

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## Biography

George Boole's father 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 powers of George Boole did not manifest themselves in early life. At first his favourite subject was classics. Not until the age of seventeen did he attack the higher mathematics, and his progress was much retarded by the want of efficient help. When about sixteen years of age he became assistant-master in a private school at Doncaster, and he maintained himself to the end of his life in one grade or other of the scholastic profession. Few distinguished men, indeed, have had a less eventful life. Almost the only changes which can be called events are his successful establishment of a school at Lincoln, its removal to Waddington, his appointment in 1849 as the first professor of mathematics of then Queen's College, Cork (now University College Cork, where the library is named in his honour) in Ireland, and his marriage in 1855 to Miss Mary Everest (daughter of George Everest), who, as Mrs. Boole, afterwards wrote several useful educational works on her husband's principles.

To the 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 one upon the "Theory of Analytical Transformations," printed in the *Cambridge Mathematical Journal* for
1839, and it led to a friendship between Boole and D.F. 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, will be found in the *Catalogue of Scientific Memoirs* published by the
Royal Society, and in the supplementary volume on
Differential Equations, edited by
Isaac Todhunter. To the *Cambridge Mathematical Journal* and its successor, the *
Cambridge and
Dublin Mathematical Journal*, Boole contributed in all twenty-two articles. In the third and fourth series of the *Philosophical Magazine* will be found sixteen papers. The
Royal Society printed six important memoirs in the *Philosophical Transactions*, and a few other memoirs are to be found in the *Transactions of the
Royal Society of Edinburgh and of the
Royal Irish Academy*, in the *Bulletin de l'Académie de St-Pétersbourg* for
1862 (under the name G Boldt, vol. iv. pp. 198-215), and in *
Crelle's Journal*. To these lists should be added a paper on the mathematical basis of logic, published in the *Mechanic's Magazine* for
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 Equations* appeared in
1859, and was followed, the next year, by a *Treatise 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, and Boole, in composing them, seems to have combined elementary exposition with the profound investigation of the philosophy of the subject in a manner hardly admitting of improvement. To a certain extent these works embody the more important discoveries of their author. In the 16th and 17th chapters of the *Differential Equations* we find, for instance, a lucid 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 the *Philosophical Transactions* for
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 *Differential Equations* 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. Even the manuscripts left at his death were so incomplete that
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 wisely 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 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*, which 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 Laws of Thought contained 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 *Paradiso* to the *Inferno*. 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 Science* and *The 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 the modesty of true genius, 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 the 8th of December 1864, in the full vigour of his intellectual powers, he died of an attack of fever, ending in effusion on the lungs.

The Booles had five daughters:

- Mary, who married the mathematician and author C. Hinton and had three children (Howard, William and Joan)
- Margaret, whose son Jeffrey Tailor became a mathematician and a member of the Russian Academy of Sciences
- Alicia, who became a mathematician
- Lucy, a chemist
- Ethel Lilian, who married the Polish scientist and revolutionary Voynich and is the author of the novel
*The Gadfly*.

## Legacy

Boole's work was extended and refined by William Stanley Jevons, Augustus De Morgan, Charles Peirce, and William Ernest Johnson. This work was summarized by Ernst Schroder, Louis Couturat, and Clarence Irving Lewis.

Boole's work (as well as that of his intellectual progeny) was relatively obscure except among logicians, and seemed to have no practical use. Approximately seventy years after Boole's death, Claude Shannon discovered Boolean algebra while taking a philosophy class at the University of Michigan. Shannon went on to write a master's thesis at the MIT, in which he showed how Boolean algebra could optimize the design of systems of electromechanical relays 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 do logic is the basic concept that underlies all modern electronic digital computers. Hence Boolean algebra became the foundation of practical digital circuit design. Thus Boole, via Shannon, provided the theoretical grounding for the Digital Age.

## Secondary literature

- Ivor Grattan-Guinness, 2000.
*The Search for Mathematical Roots 1870-1940*. Princeton Uni. Press.

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## References

*This article incorporates text from the**1911*Encyclopædia Britannica*, which is in the public domain.*