# Augustus De Morgan 1806 – 1871

February 05, 2010

{::}** Augustus De Morgan** (1806 – 1871) was a British mathematician and logician. He formulated De Morgan’s laws and introduced the term mathematical induction, and made its idea rigorous. The crater De Morgan on the Moon is named after him.

De Morgan was a patient and friend of James John Garth Wilkinson, and he was also a friend of John Ashburner, William and Mary Howitt, Robert Masters Theobald, Henry Peter Brougham 1st Baron Brougham and Vaux. De Morgan was also a correspondent of John Rutherford Russell (* see Of Interest Section below).

De Morgan was a member of the Society for the Diffusion of Useful Knowledge, and he was very interested in spiritualism, (writing a book about this with his wife), and Emanuel Swedenborg,

Augustus De Morgan was born in 1806. His father was Col. De Morgan, who held various appointments in the service of the East India Company. His mother descended from James Dodson, who computed a table of anti-logarithms, that is, the numbers corresponding to exact logarithms.

Augustus De Morgan became blind in one eye a month or two after he was born. The family moved 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 went unnoticed until he was fourteen, when a family friend discovered him making an elaborate drawing of a figure in Euclid with ruler and compasses. She explained the aim of Euclid to Augustus, and gave him an initiation into demonstration.

He received his secondary education from Mr. Parsons, a Fellow of Oriel College, Oxford, who appreciated classics 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-conforming disposition.

In 1823, at the age of sixteen, he entered Trinity College, Cambridge, where he came under the influence of George Peacock and William Whewell, who 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. His Cambridge tutor was John Philips Higman.

At college the flute, on which he played exquisitely, was his recreation. He 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. In 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 London University (now University College London) took shape. The two ancient universities of Oxford and Cambridge were so guarded by theological tests that no Jew or Dissenter outside 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 mathematicsis 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 professors resigned, headed by De Morgan.

Another professor of mathematics was appointed, who then 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 Henry Peter Brougham 1st Baron Brougham and Vaux, 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 Calculuswhich was published by the Society; and he wrote one-sixth of the articles in thePenny 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. William 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 William 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.

During this period, he also promoted the work of self-taught Indian mathematician Ramchundra, who has been called De Morgan’s Ramanujam. He supervised the publication in London of Ramchundra’s book on

Maxima and Minimain 1859. In the introduction to this book, he acknowledged being aware of the Indian tradition of logic, although we don’t know if this had any influence on his own work.

De Morgan had three sons and four daughters. His eldest son was the potter William De Morgan. His second son George 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 1866 the chair of mental philosophy in University College fell vacant.

James 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 Alexander Bain and Herbert 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 him a pension of £500p.a., but misfortunes followed. Two years later his son George – the “younger Bernoulli”, as Augustus loved to hear him called, in allusion to the eminent father and son mathematicians of that name – 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 18 March 1871.

Of Interest:

* From
http://www.ebay.co.uk/itm/1858-HOMEOPATHY-ALS-Augustus-de-Morgan-to-Rutherford-Russell-SML-HAHNEMANN-/311190181736?pt=LH_DefaultDomain_0&hash=item4874615768 Letter
dated 18.8.1858 from Augustus de
Morgan
to John Rutherford
Russell
‘… *7 Camden Street NW. August 18, 1858. Dear Sir, I have deferred the
pleasure of thanking you for the copy of your ‘Contribution to Medical
Literature; till I could say that I had looked into it, which I have
done and with great satisfaction. I hope the perusal will satisfy a
large number of prejudiced persons that a homoeopathist can observe,
reason, and do justice to the observation and reasoning of
opponents. And the articles in Homoeopathic Journal will never do for
the simple reason that they will not be seen by the parties whom I
allude to. There is the phrase to which I call your attention, in care
of a second edition. It is on page 9 “M. Comte is one of the first of
living mathematicians.” I respect your fellow, Mr. John Mill, who has an
idiosyncratic respect for Comte. I never heard Comte’s name mentioned by
a mathematician as a mathematician - nor did I ever hear that he wrote
an original paper on any mathematical subject. His mathematical
elementary work on Algebraic Geometry is of a very ordinary character as
to mathematics, and verbose beyond all readability. I believe he once
was employed to teach in the polytechnic school, and that he was not
educated there: which was a compliment. But if he has any celebrity
whatever as a mathematician, it has certainly not reached my ear. I
never had any reason to suppose that Comte was mathematician enough to
read the work of Laplace at which he sneers in the last paragraph of
your quotation. Unquestionably with a sufficient number of
well ascertained cases, nerological [?] tables could be made as useful
as fables of mortality. The difficulty is, that dead or alive is a fact
which can be ascertained, while this or that disorder is very frequently
a question which must be settled by something else than mathematics
before the tabular entry can be made. I remain Dear Sir, Yours
faithfully, A De Morgan*…’