# De Morgan, Augustus (DNB00)

**DE MORGAN**, AUGUSTUS (1806–1871), mathematician, son of Colonel De Morgan of the Indian army, was born at Madura, in the Madras presidency, in 1806. His mother was daughter of John Dodson of the custom house, and granddaughter of James Dodson [q. v.], author of the ‘Mathematical Canon.’ Seven months after De Morgan's birth his parents sailed for England with their three children. They settled at Worcester. Colonel De Morgan was again in India from 1808 to 1810, when he returned, and satisfactorily proved his innocence of some charges arising from the insubordinate state of the Madras army. He lived with his family in Devonshire, settling at Taunton in 1812. Thence he returned to India, was invalided in 1816, and died at St. Helena on his way to England. The elder De Morgans were of strict evangelical principles. The father began the education of his son and inculcated religious dogmas and practices at a very early age. The mother, who survived till 1856, continued the same discipline. De Morgan was sent to various schools, one of his teachers being J. Fenner, a unitarian minister and an uncle of H. Crabb Robinson. His last schoolmaster was the Rev. J. P. Parson of Redlands, Bristol, to whom he was sent in 1820. He is described as a fine stout boy. He had lost one eye in his early infancy. This exposed him to cruel practical jokes till he gave a ‘sound thrashing’ to his tormentor, and it prevented him from joining in the usual games. He had a gift for drawing caricatures, and read algebra ‘like a novel.’ He pricked out equations on the school-pew, some of which remained after his death, instead of listening to the sermon. In February 1823 he entered Trinity College, Cambridge, as a ‘bye-term man.’ He soon showed his mathematical ability, and in his second year was easily first in the first class. He made many friends at college, including his teachers, Whewell and Peacock. He belonged to a musical society called the ‘Camus’ (i.e. Cambridge Amateur Musical Union Society), and was a skilful flute-player. He had an insatiable appetite for novels, and often sat up reading till the early morning. In 1827 he graduated as fourth wrangler, though far superior in mathematical ability to any man in his year. He was disappointed by the result, which was due to his discursive reading. He retained through life a strong dislike to competitive examinations as tending to give the advantage to docile over original students, and to encourage ‘cram.’ His mind had further been distracted by metaphysical readings, especially in Berkeley's works, and by theological speculation. Even at school he had revolted from the doctrines held by his mother, and at Cambridge he became heterodox. He was through life a strong theist, and preferred the unitarian to other creeds, but never definitely joined any church, calling himself a ‘christian unattached.’ He refused to carry out his mother's wishes by taking orders, and his scruples prevented him from proceeding to the M.A. degree or becoming a candidate for a fellowship. After some thoughts of medicine he resolved to go to the bar, and entered Lincoln's Inn.

The university of London, which afterwards became University College, was just being started. De Morgan found law unpalatable, and on 23 Feb. 1828 was unanimously elected the first professor of mathematics, although the youngest applicant, on the strength of very high testimonials from Peacock, Airy, and other Cambridge authorities. He gave his introductory lecture, ‘On the Study of Mathematics,’ 5 Nov. 1828. Difficulties soon arose in the working of the new institution. The council claimed the right of dismissing a professor without assigning reasons. They acted upon this principle by dismissing the professor of anatomy, and De Morgan immediately resigned his post in a letter dated 24 July 1831. In October 1836 his successor, Mr. White, was accidentally drowned. De Morgan at once offered himself as a temporary substitute. He was then invited to resume the chair, and considering, after consulting Sir Harris Nicolas, that the regulations had been so altered as to give the necessary independence to the professors, he accepted the invitation. He was accordingly reappointed, and was professor for the next thirty years.

From the first De Morgan was a most energetic worker. In May 1828 he was elected a fellow of the Astronomical Society, and in 1830 was placed on the council. He was secretary from 1831 to 1838, and again from 1848 to 1854, and at other periods held office as vice-president and member of the council. He finally left the council in 1861 from dissatisfaction at the mode of electing a president (his offices are given in {{sc|Mrs. De Morgan's} *Memoirs*, p. 270). He took a keen interest in its proceedings, edited its publications, and made many intimate friends at its meetings, among whom were Sir John Herschel, Admiral Smyth, Francis Baily, Sheepshanks, Bishop, De la Rue, and Professor Airy. A club which had social gatherings after the society's meetings provided him with one of his few opportunities of relaxation. He became a member of the Society for the Diffusion of Useful Knowledge, founded by Brougham and others in 1826. It published some of his early writings, and he contributed a great number of articles to its other publications, the ‘Penny Cyclopædia,’ of which he wrote nearly one-sixth (850 articles), the ‘Quarterly Journal of Education,’ and the unfortunately short-lived ‘Biographical Dictionary.’ He became a member of the committee in 1843. The society was dissolved in 1846. During his absence from the professorship De Morgan took private pupils, besides writing on his favourite topics. In 1831 he contributed the first of a series of twenty-five articles to the ‘Companion to the Almanac,’ and published his ‘Elements of Arithmetic’ (one of the S.D.U.K. tracts). In the autumn of 1831 he moved to 5 Upper Gower Street. Here he was a neighbour of William Frend [q. v.] In the vacation of 1837 De Morgan married Frend's daughter, Sophia Elizabeth, and settled at 69 Gower Street. His eldest daughter, Elizabeth Alice (whose death in 1853 permanently lowered his spirits), was born in 1838; his sons, William Frend, George Campbell, and Edward Lindsey, in 1839, 1841, and 1843. De Morgan was so much absorbed in various kinds of work as to have little leisure for domestic recreation. His lectures permitted him at first to return to his home at midday, though he had to abandon this practice upon moving to Camden Town in 1844. His evenings were always devoted to writing. After 1840 he gave up the practice of taking a holiday with his family in the country. He loved the town, and had a humorous detestation of trees, fields, and birds. He could not even bear Blackheath, calling the heath ‘desolation’ though he liked the steamboats. His lectures at University College attracted many men, afterwards distinguished, such as Sir G. Jessel, afterwards master of the rolls, Bagehot, Stanley Jevons, Jacob Waley, Mr. R. H. Hutton, and Mr. Sedley Taylor. The last two have described their recollections of his teaching (Mrs. De Morgan, pp. 97–101). He had the power of clear exposition, not always combined with learning and original genius, a quaint humour, and a thorough contempt for sham knowledge and low aims in study. He did much work with his pupils beyond the regular time of lecture, and occasionally took private pupils. His income as professor never reached 500*l*., and in later years declined, seldom exceeding 300*l*. Besides his professorial work he served for a short period as actuary; he often gave opinions upon questions of insurance, and contributed to the ‘Insurance Record.’ He took a lively part in scientific proceedings and in controversies such as that upon the rival claims of Adams and Leverrier. He never became a fellow of the Royal Society, and held that it was too much open to social influences to be thoroughly efficient as a working institution. His dislike to honorary titles led him to refuse the offer of the LL.D. degree from Edinburgh. For many years he did his best to promote the adoption of a decimal coinage. He contributed an article upon the subject to the ‘Companion to the Almanac’ for 1841. He gave evidence before commissions, and was on the council of the Decimal Association formed in 1854. A commission finally decided against the measure in 1859, and the agitation dropped.

De Morgan's energy, however, was chiefly absorbed by his voluminous writings upon mathematical, philosophical, and antiquarian points. The most important controversy in which he was engaged arose from a tract ‘On the Structure of the Syllogism,’ read before the Cambridge Philosophical Society 9 Nov. 1846, and his work upon ‘Formal Logic,’ published in 1847. De Morgan had consulted Sir William Hamilton upon the history of the Aristotelian theory. Hamilton gave some information, and afterwards accused De Morgan of unfairly appropriating his doctrine of the ‘quantification of the predicate.’ He returned a copy of the ‘Formal Logic’ presented to him by the author uncut. The value of the doctrine itself may be disputed, but De Morgan's claim to independence is unimpeachable. In 1852 some courtesies were exchanged between the disputants, and Hamilton must have been pacified (Mrs. De Morgan, p. 161). Some of De Morgan's later speculations upon this subject were published in the Transactions of the Cambridge Philosophical Society. His logical writings are not easy reading, and have perhaps attracted less attention than they deserve. They have been in a great degree superseded by the investigations of Boole.

In 1866 the chair of mental philosophy and logic at University College became vacant. A discussion arose as to the true interpretation of the principle of religious neutrality avowedly adopted by the college. One party held that it should include Mr. James Martineau, who, as a unitarian minister, was pledged to maintain the creed of a particular sect. De Morgan, on the other hand, held that any consideration of a candidate's ecclesiastical position or religious creed was inconsistent with the principle. He thought that the refusal to appoint Mr. Martineau was in reality an act of intolerance dictated by a dislike to the candidate's religious philosophy. De Morgan had always been exceedingly sensitive upon this question of religious neutrality, and had thought of resigning his post in 1853, when the college accepted a legacy of books (from Dr. W. G. Peene), which were to be selected by members of the church of England. He now resigned his office in a letter dated 10 Nov. 1866. Some of his old pupils begged him to allow his picture to be taken for the library of ‘our old college.’ He objected on principle to testimonials, and replied that ‘our old college no longer exists.’ It lived only so long as it refused all religious disqualifications. Though no personal bitterness was produced, De Morgan felt the blow so keenly that it injured his health. The last important work which he undertook was a calculation for the Alliance Assurance Company.

In October 1867 he was saddened by the loss of his son George Campbell, a youth of great promise, who had been a founder and secretary of the Mathematical Society. His father was the first president, and gave an inaugural lecture on 16 Jan. 1865. The son became mathematical master in University College school in 1866, and at the time of his death was vice-principal of University Hall, Gordon Square. In 1868 De Morgan had himself a sharp attack of congestion of the brain. He afterwards was able to arrange his own books on moving to a new house. He read the Greek testament carefully, and was interested in a proposed ‘Free Christian Union.’ The death of his daughter Helen Christiana in August 1870 gave a fresh shock to his nerves, and he afterwards sank gradually and died 18 March 1871. A year before his death an annuity of 100*l*. was obtained from the government and accepted with some reluctance.

De Morgan's library consisted at the end of his life of about three thousand volumes. He was a genuine book-hunter, though his means compelled him to limit himself to occasional treasures from bookstalls. He made many quaint marginal and learned annotations, and turned his bibliographical researches to good account in his writings. His library was bought after his death by Lord Overstone and presented to the university of London.

De Morgan was a man of great simplicity and vivacity of character, of affectionate disposition, and entire freedom from all sordid self-interest. He had a love of puns, and all ingenious puzzles and paradoxes, which makes some of his books, especially his ‘Budget of Paradoxes’ (1872, reprinted from the ‘Athenæum’), as amusing as they are learned. He held to his principles with a certain mathematical rigidity which excluded all possibility of compromise and gave ground for the charge of crotchetiness on some important occasions. But this was at worst the excess of a lofty sense of honour. His mathematical writings include valuable text-books, and many speculations of great interest upon the logic of mathematical reasoning. ‘His “double algebra” was the forerunner of quaternions, and contained the complete geometrical interpretation of the √-1’ (*Monthly Notices*). Sir W. Rowan Hamilton acknowledged the suggestions which he had received from De Morgan in this respect.

A list of De Morgan's writings is given in Mrs. De Morgan's memoir (pp. 401–15). His separate works are: 1. ‘Elements of Arithmetic,’ 1831 (16th thousand, 1857). 2. ‘Algebra,’ 1835. 3. ‘Connection of Numbers and Magnitude,’ 1836. 4. ‘Essay on Probabilities,’ 1838. 5. ‘First Notions of Logic,’ 1839. 6. ‘Differential and Integral Calculus,’ 1842. 7. ‘Arithmetical Books … from actual inspection,’ 1847. 8. ‘Formal Logic,’ 1847. 9. ‘Trigonometry and Double Algebra,’ 1849. 10. ‘The Book of Almanacs,’ 1850. 11. ‘Syllabus of a proposed System of Logic,’ 1860. He contributed articles to the following between the dates given:—‘Quarterly Journal of Education’ (1831–3), ‘Cambridge Philosophical Transactions’ (1830–68), ‘Philosophical Magazine’ (1835–52), ‘Cambridge Mathematical Journal’ (1841–5), ‘Cambridge and Dublin Mathematical Journal’ (1846–53), ‘Quarterly Journal of Mathematics’ (1857–1858), ‘Central Society of Education’ (1837–1839), ‘The Mathematician’ (1850), ‘British Almanac and Companion’ (1831–57), ‘Smith's Classical Dictionary,’ ‘Dublin Review,’ ‘Encyclopædia Metropolitana’ (including important articles upon the calculus of functions and the theory of probabilities), ‘Penny Cyclopædia.’ Besides these, he wrote prefaces and introductions to many works, including Mrs. De Morgan's ‘From Matter to Spirit’ (1863), obituary notices in the ‘Transactions of the Astronomical Society’ and the ‘Insurance Record,’ and contributed innumerable articles to the ‘Athenæum’ and ‘Notes and Queries.’

[Memoir by (his widow) Sophia Elizabeth De Morgan, 1882; Monthly Notices of Royal Astron. Soc. for February 1872; Stanley Jevons in Encycl. Brit.]