Augustus Demorgan Essay, Research Paper

Augustus DeMorgan was an English mathematician, logician, and bibliographer. He was born in June 1806 at Madura, Madras presidency, India and educated at Trinity College, Cambridge in 1823. Augustus DeMorgan had passed away on March 18, 1871, in London.

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 proof, for advancing from n to n+I.

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 to the writings of the two British mathematicians, DeMorgan and G. Boole. He always laid much stress upon the importance of logical training. His importance in the history of logic s, however, primarily due to his realization that the subject as it had come down from Aristole was unnecessarily restricted scope. By reflecting on the processes of mathematics, he was led like Boole, to the conviction that a far larger number of valid inference were possible that had hitherto been recognized.

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.

These statements assert that the negative ( or contradictory) of an alternative proposition is a conjunction which the conjuncts are the contradictions of the corresponding alternants. That the negative of a conjunctive is an alternative proposition in which the alternants are the contradictories of the corresponding conjuncts.

DeMorgan s most important work was Formal Logic. It included the concept of the quantification of the predicate, an idea that solved problems that were impossible under the classic Aristotelian logic. His work included a system of notations for symbolic logic that could denote converses and contradictions and the famous DeMorgan s laws.

DeMorgan published first-rate elementary texts on arithmetic, algebra, trigonometry, calculus, and important treaties on the theory of probability and formal logic. Many of these papers dealt with the possibility of establishing a logical calculus and the fundamental problem of expressing thought by means of symbols. He pointed out that every science that was thrived, has thrived upon it s own symbols and that logic had not developed any symbols. This was the set out to remedy. DeMorgan realized that close relationships between logic and pure mathematics. He also believed that these disciplines should be treated jointly. His studies in logic were the highest value in both illuminating new areas and in encouraging others.

DeMorgan contributed many accomplishments to the field of mathematics on many different subjects. He also devised a decimal coinage system, an almanac of all full moons from 2000 B.C and 2000 A.D. and a theory on the probability of life events which is used by insurance companies.

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.