De Morgan was a noted teacher who stressed principles over techniques. His students included many famous mathematicians, including Ada Augusta, Countess of Lovelace, who was Charles Babbage's collaborator in his work on computing machines. (De Morgan cautioned the countess against studying too much mathematics, since it might interfere with her childbearing abilities!)

De Morgan was an extremely prolific writer. He wrote more than 1000 articles for more than 15 periodicals. De Morgan also wrote textbooks on many subjects, including logic, probability, calculus, and algebra. In 1838 he presented the first clear explaination of the proof technique known as mathematical induction (a term he coined). In the 1840s De Morgan made fundamental contributions to the development of symbolic logic. He invented notations that helped him prove propositional equivalences, such as the laws that are named after him. In 1842 De Morgan presented the first precise definition of a limit and developed some tests for convergence of infinite series. De Morgan was also interested in the history of mathematics and wrote biographies of Sir Issac Newton and Edmond Halley.

Sources: MacTutor History of Mathematics Archive, Encyclopedia Britannica, __Discrete Math and Its Applications__