The eminent English mathematician and logician, was born in Madura, in the Madras Presidency, but was educated under Airy at Trinity College, Cambridge, where he graduated as fourth wrangler in 1827. Next year he was appointed first professor of mathematics at University College, London, and the rest of his life was entirely devoted to his science. He became famous as the greatest teacher of mathematics then known, Todhunter and Routh being amongst his pupils. Of his numerous text-books and other treatises, we may here mention:—“The Elements of Arithmetic” (1830), the “Essay on Probabilities” (1838), still the best introduction to the science in our language; “The Elements of Trigonometry” (1837), his celebrated “Treatise on the Differential and Integral Calculus” (1842), “Formal Logic, or the Calculus of Inference,” in which he expounds his and Sir W. Hamilton’s principle of the quantified predicate; and four great treatises on the Syllogism (1850–60). He was also the author of innumerable popular essays and articles, and wrote biographies of Newton and Halley.

Personal

  First as to my eye. When I was in preparation, my mother attended much to a favourite native servant (in India) who had the ophthalmia, which they call the country sore eyes. When I was born it was found I had had it too, and one eye was not destroyed, but never completely formed: it is only a rudiment, with a discoloration in the centre, which shows that nature intended a pupil. The eyelid is of a different size from the other…. This is slightly exaggerated. I have been offered a binocular glass at the opera, &c., scores of times, by people who had known me for years, with recommendation to try if it were not better than my own. So that the thing does not show much, for which no doubt spectacles are partly answerable. Accordingly I have always been strictly unocular. I have seen as much with my right eye as with any one finger—no more, and no less. I am very short-sighted, and more so, I think, as I get older. Without spectacles my reading distance would be less than six inches for moderate type, or my own handwriting. Four inches would be agreeable and convenient. My eye bears any amount of work without fatigue. But on principle I have avoided anything like frequent use of a telescope, which is an insidious foe. Now I am not aware of any use of sight in which I differ from a short-sighted person with two eyes.

  De Morgan’s exposition combined excellences of the most varied kinds. It was clear, vivid, and succinct—rich, too, with abundance of illustration always at the command of enormously wide reading and an astonishingly retentive memory. A voice of sonorous sweetness, a grand forehead, and a profile of classic beauty, intensified the impression of commanding power which an almost equally complete mastery over mathematical truth, and over the forms of language in which he so attractively arrayed it, could not fail to make upon his auditors. Greater, however, than even these eminent qualities were the love of scientific truth for its own sake, and the utter contempt for all counterfeit knowledge, with which he was visibly possessed, and which he had an extraordinary power of arousing and sustaining in his pupils.

  One thing which made his classes lively to men who were up to his mark, was the humorous horror he used to express at our blunders, especially when we took the conventional or book view instead of the logical view. The bland “hush!” with which he would suppress a suggestion which was simply stupid, and the almost grotesque surprise he would feign when a man betrayed that, instead of the classification by logical principles, he was thinking of the old unmeaning classification by rule in the common school-books, were exceedingly humorous, and gave a life to the classes beyond the mere scope of their intellectual interests. I think all my fellow-pupils would agree that never was there a more curious mixture of interests than the prepared discussions of principle in his lectures, and the Johnsonian force and sometimes fun of his part in the short dialogues with his pupils which occurred from time to time.

  Many as were our friends, we had but very little visiting, my husband’s time being so fully filled with his work. The last was done with exceeding order and punctuality…. Not having the means to indulge in the luxuries enjoyed by richer and more affluent writers or experimentalists, he could not furnish his library with all the writing appliances and handsome bindings that ornament rich men’s studies, and his old table and desk, and other cheap contrivances, looked shabby enough. Any one who went into his room would be struck at first by the homeliness of the whole, and the quantity of old and unbound books and packets of papers. But when it was seen how the books were arranged and the papers labelled and put into their proper places according to subjects, the adaptation of means to ends became as apparent as in the clearness and precision with which he laid down principles, and showed what was to be done before making a beginning on his work. His contrivances in the way of inkstand, penholder, and blotting-block, had none of them a new or unused look, but all showed that every contingency had been carefully provided for.

  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.

General

  The second of these is Sir William Hamilton’s; the third is Mr. De Morgan’s. The latter is the more ambitious of the two, and makes more formidable inroads upon the established boundaries of Logic. It is incumbent, therefore, on those who take an interest in the progress of the science, to scrutinize narrowly its pretensions; and if, in endeavouring to fulfil this duty, we find it necessary to express our dissent from the principles of the acute and learned author, we trust that we shall not be considered as feeling anything but the highest respect for the ability which he has in many ways displayed, and which indeed renders the task of opposing him more obligatory, as well as more difficult. Mr. De Morgan’s great eminence as a mathematician makes it necessary for every student of Logic to see that he does not mar its doctrines by spurious importations from his favourite science; while the acuteness and ingenuity of many of his logical details render still more imperative the duty of detecting the unsoundness, if any exists, of his principles. It has been said that, next to him who forms the taste of a country, the greatest genius is he who corrupts. If Mr. De Morgan should rank with posterity as one who corrupted Logic with mathematics, he need not be ashamed of his partners in the offence; for he will find among them Bacon, who corrupted it with physics, and Hegel, who corrupted it with metaphysics.

  As a writer of mathematical text books, he took the highest rank, his books being more suitable, however, for teachers than for pupils. They were characterised by extreme clearness, exhaustiveness, and suggestiveness. Perhaps those best known are his “Elements of Arithmetic,” published 1830; his “Elements of Algebra,” published 1835; and his “Differential and Integral Calculus, with elementary illustrations,” which is a perfect mine of original thought, and in which some of the most important extensions which the subject has since received, are distinctly indicated, and it was published by the Society for the Diffusion of Useful Knowledge. As an actuary he occupied the first place, though he was not directly associated with any particular office, but his opinion was sought for on all sides, by actuaries, on questions connected with the theory of probabilities as applied to life contingencies. In 1838 he wrote his “Essay on Probabilities,” which still retains a high place among the literature of insurance offices.

  He was not only the most successful teacher, but the most learned authority of his time upon the history of Mathematics, and in the practice of his science a most acute pleader for the union of Mathematics with Logic. He wrote books upon every department of Mathematics, and was conspicuous for union of shrewd critical wit with good sense and a wide erudition.

  Few men have ever possessed the scientific faculty more decisively, or have been more strictly bound both by temper and by destiny to the logical exercise of the wits; and few, at the same time, have escaped more completely from any narrow satisfaction with the things known, or have entertained more candidly the possibility of reaching some higher apprehension of realities.

  As a teacher, De Morgan was particularly gifted. A voluminous writer on mathematics, he contributed essentially to those expansions of the fundamental conceptions which have rendered possible the new algebras, such as Quaternions and the Ausdehnungslehre, and have generalized the whole idea of a mathematical algorithm or calculus. But it is his logical work that will give De Morgan his most lasting fame. Here he stands alongside of his immortal contemporary, Boole.

  The mathematical researches of men like Sir William Rowan Hamilton are far too technical, too difficult and too abstruse for popular apprehension. They remain a mere name, and not even their general import is understood. The same remark applies to the mathematical work of Augustus de Morgan, who, by the way, gave valuable hints for Hamilton’s great work on quaternions. But De Morgan was a logician as well, and the author of the “Budget of Parodoxes” is worthy of remembrance in literature.