Augustus was recognized as far superior in mathematical ability to any other person there, but his refusal to commit to studying resulted in his finishing only in fourth place in his class.

In 1828 he became professor of mathematics at the newly established University College in London. He taught there until 1806, except for a break of five years from 1831 to 1836. DeMorgan was the first president of London Mathematical Society, which was founded in 1866.

DeMorgan's aim as a mathematician was to place the subject on a more rigorous foundation. As a teacher he was unrivaled, and no topic was too insignificant to receive his careful attention. In 1838 he introduced the term " mathematical induction" to differentiate between the hypothetical induction of empirical science and the rigorous method. Often used in mathematical

His most notable achievements were to lay the foundation for the theory of relations to prepare the way to rise of modern symbolic, or mathematical, logic. His name is commemorated in DeMorgan's Law, which is usually presented in the concise alternative forms ~( pvq ) = ~p & ~q; and ~( p&q ) = `~p v ~q. These read not ( p or q ) equals not p or not q ; and not ( p and q ) equals not p or not q.

He was deeply interested in the history of mathematics. Augustus 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. DeMorgan felt that it was important for the students to know the history of mathematics to understanding the development of the field.

DeMorgan made his greatest contributions to knowledge. The renaissance of logical studies, which began in the first half of the 19th century, was due almost entirely t

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