## 9.7. De Morgan, Augustus (1806-1871)

Augustus De Morgan was an important innovator in the field of logic. In addition, he had many contributions to the field of mathematics and the chronicling of the history of mathematics.Augustus De Morgan was born in Mandura, India, on June 27, 1806. His father was a colonel in the Indian Army. His family soon moved to England where they lived first at Worcester and then at Taunton. His early education was in private schools where he learned Latin, Greek, Hebrew, mathematics and a dislike of exams. He entered Trinity College, Cambridge, in 1823 and graduated four years later.

After graduation, De Morgan reached the point of deciding what to do with the rest of his life. Dubious of competitive fellowships and master degrees, he refused to continue his education. Fearful of hypocrisy and religious bigotry, he also rejected his parents' wish of becoming a priest. After contemplating medicine and law, he finally decided to become a mathematician. In 1828, he was awarded the position of first Professor of Mathematics at University College in London.

His time at the university was far from quiet. In 1831, he resigned on principle after another professor was fired without explanation. He regained his job five years later when his replacement died in an accident. He would resign again in 1861. As a teacher, he was highly praised at making mathematics alive and interesting to his students. In addition, he wrote textbooks on numerous subjects in mathematics and logic.

He was married in 1837 to Sophia Frend, who would later write his biography. During his life, De Morgan was constantly involved in various activities. A member of the Astronomical Society and the Society for the Diffusion of Useful Knowledge, he founded the London Mathematical Society and was its first president. He wrote thousands of books and articles on mathematics, logic, philosophy and many other subjects. In addition, he assembled a large personal library of over 3000 books, a vast feat considering he was never wealthy. Unfortunately with all his work, he had little time for the rest of his life, but he was known as a kind and humorous individual.

Augustus De Morgan died on March 18, 1871, in London, England. His library was later donated to the London University library.

De Morgan contributed many accomplishments to the field of mathematics on many different subjects. He was the first person to define and name "mathematical induction" and developed De Morgan's rule to determine the convergence of a mathematical series. His definition of a limit was the first attempt to define the idea in precise mathematical terms. In addition, he also devised a decimal coinage system, an almanac of all full moons from 2000 B.C. to 2000 A.D. and a theory on the probability of life events which is used by insurance companies.

However, he biggest contribution was in the field of logic. His most important work, *Formal
Logic*, included the concept of the quantification of the predicate, an idea that solved problems that
were impossible under the classic Aristotelian logic. For example, the following is only workable using
De Morgan's method:

- In a particular group of people,
- most people have shirts
- most people have shoes
- therefore, some people have both shirts and shoes.

Of special note to this author, De Morgan was also deeply interested in the history of mathematics. He
wrote biographies of Newton and Halley and produced a dictionary of all the important mathematicians of
the seventeenth century. In 1847, he published the book *Arithmetical Books*, in which he
describes the work of over fifteen hundred mathematicians and discusses subjects such as the history of
the length of a foot. This work is also considered the first scientific bibliography. De Morgan felt that it
was important for students to know the history of mathematics to understanding the development of the
field.

For related information on De Morgan, see: De Morgan's laws.

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Sources

Sources

- Abbott, David Ph.D. ed. "De Morgan, Augustus."
*The Biographical Dictionary of Sciences: Mathematics*. New York: Peter Bedrick Books, 1985. p. 40. - Dubbey, John M. "De Morgan, Augustus."
*Dictionary of Scientific Biography*. New York: Charles Scribner's Sons, 1970. vol. 3, pp. 35-37.

**Paul Golba**