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De Morgan, Augustus

Category: Scientist


Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician, who became blind in one eye a month or two after he was born.  He formulated De Morgan's laws and introduced the term mathematical induction. 

Were the writings of De Morgan published in the form of collected works, they would form a small library.

De Morgan had three sons and four daughters, including fairytale author Mary de Morgan. His eldest son was the potter William De Morgan. His second son George acquired distinction in mathematics at University College and the University of London.

He was not a great liker of pomp and titles.  On the occasion of the installation of his friend, Lord Brougham, as Rector of the University of Edinburgh, the Senate offered to confer on him the honorary degree of LL.D.; he declined the honour as a misnomer. 

He never sought to become a Fellow of the Royal Society, and he never attended a meeting of the Society; he said that he had no ideas or sympathies in common with the 'physical philosopher'.

Beyond his great mathematical legacy, the headquarters of the London Mathematical Society is called De Morgan House and the student society of the Mathematics Department of University College London is called the Augustus De Morgan Society.  The crater De Morgan on the Moon is named after him.

De Morgan and Psychic research

De Morgan later in his life became interested in the phenomena of spiritualism. In 1849, he investigated clairvoyance and was impressed by the subject. He later carried out investigations in his own home with the medium Maria Hayden. The result of these investigations was later published by his wife Sophia. De Morgan believed that his career as a scientist might have been affected if he had revealed his interest in the study of spiritualism, so he helped to publish the book anonymously. The book was published in 1863 titled From Matter to Spirit: The Result of Ten Years Experience in Spirit Manifestations.

In the preface of From Matter to Spirit (1863) De Morgan stated:

Thinking it very likely that the universe may contain a few agencies—say half a million—about which no man knows anything, I can not but suspect that a small proportion of these agencies—say five thousand—may be severally competent to the production of all the [spiritualist] phenomena, or may be quite up to the task among them. The physical explanations which I have seen are easy, but miserably insufficient: the spiritualist hypothesis is sufficient, but ponderously difficult. Time and thought will decide, the second asking the first for more results of trial.


It is fascinating to us these days, to realise how man very eminent men of science were investigating this subject, and but for the ‘science as religion’ materialists, might have made some real breakthroughs even then. 

We have been held back by a good two hundred years by ignorant closed minded nincompoops, calling themselves scientists, who were nothing of the sort.


The timidity or apathy of men of science in England on this subject is to be deplored. A remarkable example of the former was seen in the case of the late Sir David Brewster. He was present at two seances of Mr. Home's, where he stated, as is affirmed on the written testimony of persons present, his impression that the phenomena were most striking and startling, and he does not appear then to have expressed any doubt of their genuineness, but he afterwards did so in an offensive manner. …. I mention this circumstance, because, I was so struck with what Sir David Brewster—with whom I was well acquainted—had himself told me, that it materially influenced me in determining to examine thoroughly into the reality of the phenomena. I met him one day on the steps of the Athenaeum; we got upon the subject of table-turning, &c.; he spoke most earnestly, stating that the impression left on his mind from what he had seen, was that the manifestations were to him quite inexplicable by fraud, or by any physical laws with which we were acquainted, and that they ought to be fully and carefully examined into. At present I know of only three eminent men of science in England, who have gone fully into the subject; and in their case the enquiry has resulted in a conviction of the genuineness of the phenomena. I allude to Mr. De Morgan the mathematician, Mr. Varley the electrician [sic], and Mr. Wallace the naturalist, all, as is well known, men of high distinction in widely differing departments of science.


Although De Morgan's observations in the area of psychokinesis, levitation and so on are of great value, he made great strides in areas that help in understanding the spirit realm, -  symbols and set theory.

The spirit realm is essentially a set of atoms/objects which are all the same 'physically' but which exhibit behaviour, making us think there is a physical world with certain properties.  We are actually looking at a sort of pixel box, where each pixel belongs to a class.  Some pixels we can see, some we can't. 

Each pixel is given a name - these are entities [entity types to be more precise - classes of things and thus sets, which is where De Morgan's work comes in] which can be decomposed further into sub-types and which inherit the attributes of their super set.  These are then interrelated [relationship types].  The attributes are used to indicate the state of each entity [occurrence] and thereby as the objects interact whether their state is such that they should respond with that function. 

De Morgan's ideas on sets and how sets interact, as well as his work on symbols and symbolism [with which the spiritual world communicates with us] is thus absolutely key to understanding 'heaven'.  We have provided more details in the observations of his work in this area.


MATHEMATICAL MONOGRAPHS EDITED BY MANSFIELD MERRIMAN and ROBERT S. WOODWARD No. 17 lectures on TEN BRITISH MATHEMATICIANS of the Nineteenth Century BY ALEXANDER MACFARLANE, Late President for the International Association for Promoting the Study of Quaternions 1916

Chapter 2 AUGUSTUS DE MORGAN (1806-1871) - This Lecture was delivered April 13, 1901

Augustus De Morgan was born in the month of June at Madura in the presidency of Madras, India; and the year of his birth may be found by solving a conundrum proposed by himself, “I was x years of age in the year x2." The problem is indeterminate, but it is made strictly determinate by the century of its utterance and the limit to a man's life. His father was Col. De Morgan, who held various appointments in the service of the East India Company.

His mother was descended from James Dodson, who computed a table of anti-logarithms, that is, the numbers corresponding to exact logarithms. It was the time of the Sepoy rebellion in India, and Col. De Morgan removed his family to England when Augustus was seven months old. As his father and grandfather had both been born in India, De Morgan used to say that he was neither English, nor Scottish, nor Irish, but a Briton “unattached," using the technical term applied to an undergraduate of Oxford or Cambridge who is not a member of any one of the Colleges.


When De Morgan was ten years old, his father died.

Mrs. De Morgan resided at various places in the southwest of England, and her son received his elementary education at various schools of no great account.

His mathematical talents were unnoticed till he had reached the age of fourteen. A friend of the family accidentally discovered him making an elaborate drawing of a figure in Euclid with ruler and compasses, and explained to him the aim of Euclid, and gave him an initiation into demonstration.

De Morgan suffered from a physical defect - one of his eyes was rudimentary and useless. As a consequence, he did not join in the sports of the other boys, and he was even made the victim of cruel practical jokes by some schoolfellows. Some psychologists have held that the perception of distance and of solidity depends on the action of two eyes, but De Morgan testified that so far as he could make out he perceived with his one eye distance and solidity just like other people.

He received his secondary education from Mr. Parsons, a Fellow of Oriel College, Oxford, who could appreciate classics much better than mathematics.


His mother was an active and ardent member of the Church of England, and desired that her son should become a clergyman; but by this time De Morgan had begun to show his non-grooving disposition, due no doubt to some extent to his physical infirmity. At the age of sixteen he was entered at Trinity College, Cambridge, where he immediately came under the tutorial influence of Peacock and Whewell. They became his life-long friends; from the former he derived an interest in the renovation of algebra, and from the latter an interest in the renovation of logic - the two subjects of his future life work.

At college the flute, on which he played exquisitely, was his recreation. He took no part in athletics but was prominent in the musical clubs. His love of knowledge for its own sake interfered with training for the great mathematical race; as a consequence he came out fourth wrangler. This entitled him to the degree of Bachelor of Arts; but to take the higher degree of Master of Arts and thereby become eligible for a fellowship it was then necessary to pass a theological test. To the signing of any such test De Morgan felt a strong objection, although he had been brought up in the Church of England. About 1875, theological tests for academic degrees were abolished in the Universities of Oxford and Cambridge.


As no career was open to him at his own university, he decided to go to the Bar, and took up residence in London; but he much preferred teaching mathematics to reading law. About this time the movement for founding the London University took shape. The two ancient universities were so guarded by theological tests that no Jew or Dissenter from the Church of England could enter as a student; still less be appointed to any office. A body of liberal-minded men resolved to meet the difficulty by establishing in London a University on the principle of religious neutrality.

De Morgan, then 22 years of age, was appointed Professor of Mathematics. His introductory lecture “On the study of mathematics" is a discourse upon mental education of permanent value which has been recently reprinted in the United States.

The London University was a new institution, and the relations of the Council of management, the Senate of professors and the body of students were not well defined. A dispute arose between the professor of anatomy and his students, and in consequence of the action taken by the Council, several of the professors resigned, headed by De Morgan. Another professor of mathematics was appointed, who was accidentally drowned a few years later. De Morgan had shown himself a prince of teachers: he was invited to return to his chair, which thereafter became the continuous centre of his labours for thirty years.

The same body of reformers - headed by Lord Brougham, a Scotsman eminent both in science and politics - who had instituted the London University, founded about the same time a Society for the Diffusion of Useful Knowledge.


Its object was to spread scientific and other knowledge by means of cheap and clearly written treatises by the best writers of the time. One of its most voluminous and effective writers was De Morgan. He wrote a great work on The Differential and Integral Calculus which was published by the Society; and he wrote one-sixth of the articles in the Penny Cyclopedia, published by the Society, and issued in penny numbers. When De Morgan came to reside in London he found a congenial friend in William Frend, notwithstanding his mathematical heresy about negative quantities. Both were arithmeticians and actuaries, and their religious views were somewhat similar. Frend lived in what was then a suburb of London, in a country-house formerly occupied by Daniel Defoe and Isaac Watts. De Morgan with his flute was a welcome visitor; and in 1837 he married Sophia Elizabeth, one of Frend's daughters.

The London University of which De Morgan was a professor was a different institution from the University of London. The University of London was founded about ten years later by the Government for the purpose of granting degrees after examination, without any qualification as to residence. The London University was affiliated as a teaching college with the University of London, and its name was changed to University College. The University of London was not a success as an examining body; a teaching University was demanded. De Morgan was a highly successful teacher of mathematics.


It was his plan to lecture for an hour, and at the close of each lecture to give out a number of problems and examples illustrative of the subject lectured on; his students were required to sit down to them and bring him the results, which he looked over and returned revised before the next lecture. In De Morgan's opinion, a thorough comprehension and mental assimilation of great principles far outweighed in importance any merely analytical dexterity in the application of half-understood principles to particular cases.

De Morgan had a son George, who acquired great distinction in mathematics both at University College and the University of London. He and another like-minded alumnus conceived the idea of founding a Mathematical Society in London, where mathematical papers would be not only received (as by the Royal Society) but actually read and discussed. The first meeting was held in University College; De Morgan was the first president, his son the first secretary. It was the beginning of the London Mathematical Society.

In the year 1866 the chair of mental philosophy in University College fell vacant. Dr. Martineau, a Unitarian clergyman and professor of mental philosophy, was recommended formally by the Senate to the Council; but in the Council there were some who objected to a Unitarian clergyman, and others who objected to theistic philosophy. A layman of the school of Bain and Spencer was appointed. De Morgan considered that the old standard of religious neutrality had been hauled down, and forthwith resigned. He was now 60 years of age. His pupils secured a pension of $500 for him, but misfortunes followed. Two years later his son George- the younger Bernoulli, as he loved to hear him called, in allusion to the two eminent mathematicians of that name, related as father and son - died. This blow was followed by the death of a daughter. Five years after his resignation from University College De Morgan died of nervous prostration on March 18, 1871, in the 65th year of his age.


Note that De Morgan’s double algebra is analytical plane trigonometry, and although he never got this far; he appears to have been considering it as a candidate for defining the spirit realm.


Mainly through the efforts of Peacock and Whewell, a Philosophical Society was inaugurated at Cambridge; and to its Transactions De Morgan contributed four memoirs on the foundations of algebra, and an equal number on formal logic. The best presentation of his view of algebra is found in a volume, entitled Trigonometry and Double Algebra, published in 1849; and his earlier view of formal logic is found in a volume published in 1847. His most unique work is styled a Budget of Paradoxes; it originally appeared as letters in the columns of the Athenium journal; it was revised and extended by De Morgan in the last years of his life, and was published posthumously by his widow.

Selected writings

  • An Explanation of the Gnomonic Projection of the Sphere. London: Baldwin. 1836.
  • Elements of Trigonometry, and Trigonometrical Analysis. London: Taylor & Walton. 1837.
  • The Elements of Algebra. London: Taylor & Walton. 1837.
  • An Essay on Probabilities, and Their Application to Life Contingencies and Insurance Offices. London: Longman, Orme, Brown, Green & Longmans. 1838.
  • The Elements of Arithmetic]. London: Taylor & Walton. 1840.
  • First Notions of Logic, Preparatory to the Study of Geometry. London: Taylor & Walton. 1840.
  • The Differential and Integral Calculus. London: Baldwin. 1842.
  • 1845. The Globes, Celestial and Terrestrial. London: Malby & Co.
  • 1847. Formal Logic or The Calculus of Inference, Necessary and Probable. London: Taylor & Walton.
  • Trigonometry and Double Algebra. London: Taylor, Walton & Malbery. 1849.
  • 1860. Syllabus of a Proposed System of Logic. London: Walton & Malbery.
  • 1872. A Budget of Paradoxes. London: Longmans, Green


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