### Demorgan

Augustus ?The Logical One? De Morgan

Augustus De Morgan was born in Mandura, India, on June 27, 1806. His father John was a colonel in the Indian Army. At birth Augustus lost sight in his right eye. After seven months he moved to England with his family. Augustus attended private education where he learned Latin, Greek, Hebrew, and mathematics. He did not excel at school and was made the blunt of all the jokes from his schoolmates.

In 1923, at the age of sixteen, he entered Trinity College in Cambridge. He received his bachelor?s degree at Trinity, but was not eligible for the master?s degree because he refused to take the theological exam. He graduated from Trinity College in 1927.

After graduation, De Morgan had to decide what he was going to do for the rest of his life. ?Fearful of hypocrisy and religious bigotry?, he rejected his parent?s wishes of becoming a priest. After looking at medicine and law, he finally decided on becoming a mathematician. In 1928, De Morgan was awarded the position of the first Professor of Mathematics at University College in London. In 1931, De Morgan resigned on principle after another professor was fired with no explanation.

In 1937, he married Sophia Frend, who would later write De Morgan?s biography. He was also very involved in various associations. He was a member of the Astronomical Society, the Society for the Diffusion of Useful Knowledge, and he also co-founded the London Mathematical Society. He wrote thousands of books and articles on math, logic, and philosophy. De Morgan had a large personal library of over 3,000 books, which was later donated to the London University library after he died on March 18, 1871, in London England.

De Morgan contributed many accomplishments to the field of mathematics. 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. De Morgan also developed a decimal coinage system, an almanac of all the 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.

De Morgan?s main contribution was to the field of logic. His most important development was formal logic. It included the concept of a quantification of the predicate, an idea that solved problems that were impossible under Aristotelian logic. For example, the following can only be workable under De Morgan?s method :

o At a party

o some kids got cake

o some kids got ice-cream

o therefore, all the kids got dessert at the party

He also made two laws corresponding to logic. The two laws are: ~(p @@ q) = ~p || ~q , ~(p || q) = ~p @@ ~q. These laws are called De Morgan?s laws. De Morgan also used these laws to correspond with Charles Babbage, the inventor of the Analytical Engine or the basic computer.

Augustus De Morgan refused many opportunities and awards such as being a member of the Royal Society and refusing an honorary degree from University of Edinburgh. Thomas Hurst, the successor of De Morgan at the Chair of Mathematics at the University College London, commented that ?A dry dogmatic pedant I fear is Mr. De Morgan, notwithstanding his unquestionable ability.? Also Macfarlane remarked that ? De Morgan considered himself a Briton unattached neither English, Scottish, Welsh, or Irish.?

De Morgan was very interested in the history of mathematics. De Morgan felt that his students and other people studying math should learn about the history of the subject to be able to understand the topic more. In 1847, he published a book called Arithmetical Book, in which he describes the work of over fifteen hundred mathematicians. This book is considered the first scientific bibliography.

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