## Augustus De Morgan

Logician
mathematician
scientist

June 27, 1806
(age 64)
Madura, India

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.