August De Morgan was an English mathematician and logician who formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous.
Background
August De Morgan was born on June 27, 1806 in Madura, India. He was one of seven children, four of whom survived to adulthood. His father, John De Morgan, was a lieutenant-colonel in the Indian Army; and his mother, Elizabeth Dodson, was the daughter of John Dodson, a pupil and friend of Abraham de Moivre, and granddaughter of James Dodson, author of the Mathematical Canon.
At the age of seven months De Morgan was brought to England, where his family settled first at Worcester and then at Taunton.
Education
De Morgan attended a succession of private schools at which he acquired a mastery of Latin, Greek, and Hebrew and a strong interest in mathematics before the age of fourteen. He also acquired an intense dislike for cramming, examinations, and orthodox theology.
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.
De Morgan entered Trinity College, Cambridge, in February 1823 and placed first in the first-class division in his second year; he was disappointed, however, to graduate only as fourth wrangler in 1827.
Due to his personal views, De Morgan refused his Master of Arts degree, a fellowship at Cambridge, and ordination, and an honorary degree from the University of Edinburgh.
After contemplating a career in either medicine or law, De Morgan successfully applied for the chair of mathematics at the newly formed University College, London, in 1828 on the strong recommendation of his former tutors, who included Airy and Peacock. When, in 1831, the college council dismissed the professor of anatomy without giving reasons, he immediately resigned on principle. He resumed in 1836, on the accidental death of his successor.
He was elected to the council of the Astronomical Society in 1830, serving as secretary (1831-1838; 1848-1854). He also helped found the London Mathematical Society, becoming its first president and giving the inaugural lecture in 1865.
De Morgan’s original contributions to mathematics were mainly in the fields of analysis and logic. In an article written in 1838, he defined and invented the term “mathematical induction” to describe a process that previously had been used - without much clarity - by mathematicians.
Among his other mathematical work is a system that De Morgan described as “double algebra.” This helped to give a complete geometrical interpretation of the properties of complex numbers and, as Sir William Rowan Hamilton acknowledged, suggested the idea of quaternions.
He believed that the traditional method of argument using the Aristotelian syllogism was inadequate in reasoning that involved quantity. As an example De Morgan presented the following argument: "In a particular company of men, most men have coats' most men have waistcoats' some men have both coats and waistcoats." He asserted that it was not possible to demonstrate this true argument by means of any of the normally accepted Aristotelian syllogisms.
The Scottish philosopher Sir William Hamilton worked out a system for quantifying the predicate a short time before De Morgan did and unjustly accused him of plagiarism. He had no shred of evidence to support his charge, and De Morgan’s work was superior to his in both analytical formulation and subsequent development. He was also the first logician to present a logic of relations.
De Morgan was steeped in the history of mathematics. He wrote biographies of Newton and Halley and published an index of the correspondence of scientific men of the seventeenth century. He believed that the work of both minor and major mathematicians was essential for an assessment of mathematical development, a principle shown most clearly in his Arithmetical Books (1847). De Morgan’s book was written at a time when accurate bibliography was in its infancy and was probably the first significant work of scientific bibliography.
De Morgan’s peripheral mathematical interests included a powerful advocacy of decimal coinage; an almanac giving the dates of the new moon from 2000 B.C. to A.D. 2000; a curious work entitled Budget of Paradoxes, which considers, among other things, the work of would-be circle squarers; and a standard work on the theory of probability applied to life contingencies that is highly regarded in insurance literature.
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 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 him a pension of £500, but misfortunes followed. Five years after his resignation from University College De Morgan died of nervous prostration on March 18, 1871.
De Morgan's mother was an active and ardent member of the Church of England, and desired that her son should become a clergyman, but De Morgan showed his non-conforming disposition. While admitting a personal faith in Jesus Christ, he abhorred any suspicion of hypocrisy or sectarianism.
De Morgan later in his life became interested in the phenomena of spiritualism. In 1849 he had investigated clairvoyance and was impressed by the subject. He later carried out paranormal 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.
According to historian Janet Oppenheim, De Morgan's wife Sophia was a convinced spiritualist but De Morgan shared a third way position on spiritualist phenomena which she defined as a "wait-and-see position," he was neither a believer nor a skeptic, instead his viewpoint was that the methodology of the physical sciences does not automatically exclude psychic phenomena and that such phenomena may be explainable in time by the possible existence of natural forces which as yet physicists had not identified.
Views
As De Morgan's father and grandfather had both been born in India, he used to say that he was neither English, nor Scottish, nor Irish, but a Briton "unattached."
Quotations:
"All existing things upon this earth, which have knowledge of their own existence, possess, some in one degree and some in another, the power of thought, accompanied by perception, which is the awakening of thought by the effects of external objects upon the senses."
"The moving power of mathematical invention is not reasoning, but imagination."
"I did not hear what you said, but I absolutely disagree with you."
Membership
In May 1828 De Morgan became a fellow of the Astronomical Society. He was also an influential member and founder of the London Mathematical Society, and member of the Society for the Diffusion of Useful Knowledge from 1826.
The Astronomical Society
,
England
1828
The London Mathematical Society
,
England
The Society for the Diffusion of Useful Knowledge
,
England
1826
Personality
De Morgan was never wealthy; and his researches into all branches of knowledge, together with his prolific output of writing, left little time for social or family life. However, he was well known for his humor, range of knowledge, and sweetness of disposition.
As a teacher he sought to demonstrate principles rather than techniques; and his pupils, who included Todhunter, Routh, and Sylvester, acquired from him a great love of the subject.
Physical Characteristics:
De Morgan lost the sight of his right eye shortly after birth.
Connections
In 1837 De Morgan married Sophia Elizabeth Frend. They had three sons and four daughters.