# De Morgan, Augustus

De Morgan, Augustus

▪ English mathematician and logician
born , June 27, 1806, Madura, India
died March 18, 1871, London, Eng.

English mathematician and logician whose major contributions to the study of logic include the formulation of De Morgan's laws and work leading to the development of the theory of relations and the rise of modern symbolic, or mathematical, logic.

De Morgan was educated at Trinity College, Cambridge. In 1828 he became professor of mathematics at the newly established University College in London, where, except for a period of five years (1831–36), he taught until 1866, when he helped found and became the first president of the London Mathematical Society. One of his earliest works, Elements of Arithmetic (1830), was distinguished by a simple yet thorough philosophical treatment of the ideas of number and magnitude. In 1838 he introduced and defined the term mathematical induction to describe the process that until then had been used with little clarity in mathematical proofs.

De Morgan was among the Cambridge mathematicians who recognized the purely symbolic nature of algebra, and he was aware of the possibility of algebras that differ from ordinary algebra. In his Trigonometry and Double Algebra (1849) he gave a geometric interpretation of the properties of complex numbers (complex number) (numbers involving a term with a factor of the square root of minus one) that suggested the idea of quaternions. He made a useful contribution to mathematical symbolism by proposing the use of the solidus (oblique stroke) for the printing of fractions.

The laws that bear De Morgan's name are a pair of dually related theorems that make possible the transformation of statements and formulas into alternate, and often more convenient, forms. Known verbally by William of Ockham in the 14th century, the laws were investigated thoroughly and expressed mathematically by De Morgan. The laws are: (1) the negation (or contradictory) of a disjunction is equal to the conjunction of the negation of the alternates—that is, not (p or q) equals not p and not q, or symbolically ∼(pq) ≡ ∼p·∼q; and (2) the negation of a conjunction is equal to the disjunction of the negation of the original conjuncts—that is, not (p and q) equals not p or not q, or symbolically ∼(p·q) ≡ ∼p ∨ ∼q.

Asserting that logic (logic, history of) as it had come down from Aristotle was unnecessarily restricted in scope, De Morgan made his greatest contributions as a reformer of logic. The renaissance of logic studies, which began in the first half of the 19th century, came about almost entirely because of the writings of De Morgan and another British mathematician, George Boole. Alternate forms and generalizations of De Morgan laws exist in various branches of mathematics.

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Universalium. 2010.

### Look at other dictionaries:

• De Morgan, Augustus — (1806–1871) English mathematician and logician. De Morgan was born in India and educated at Cambridge, and became first professor of mathematics at the university of London. He wrote widely on mathematics and astronomy. His Essay on Probabilities …   Philosophy dictionary

• De Morgan,Augustus — De Mor·gan (dĭ môrʹgən), Augustus. 1806 1871. British mathematician and logician who wrote important works on calculus and with George Boole laid the foundation for modern symbolic logic. * * * …   Universalium

• Augustus De Morgan — (1806 1871) Born 27 June 1806( …   Wikipedia

• Augustus de Morgan — (* 27. Juni 1806 in Madurai, Indien; † 18. März 1871 in London) war ein englischer Mathematiker. Er war Mitbegründer und erster Präsident der London Mathematical Society …   Deutsch Wikipedia

• Augustus De Morgan — (* 27. Juni 1806 in Madurai, Indien; † 18. März 1871 in London) war ein englischer Mathematiker. Er war Mitbegründer und erster Präsident der London Mathematical Society …   Deutsch Wikipedia

• Augustus De Morgan — Saltar a navegación, búsqueda Augustus De Morgan Augustus De Morgan (27 de junio de 1806 18 de marzo de 1871) fue un matemático y lógico inglés nacido en la India. Profesor de matemáticas en el Colegio Universitario de Londres entre 1828 y 1866;… …   Wikipedia Español

• DE MORGAN, AUGUSTUS —    an eminent mathematician, born in Madura, S. India; was professor of Mathematics in London University from 1828 till his death, though he resigned the appointment for a time in consequence of the rejection of a candidate, James Martineau, for… …   The Nuttall Encyclopaedia

• De Morgan, Augustus — (1806 1871)    Mathematician, b. in India, and ed. at Camb., was one of the most brilliant of English mathematicians. He is mentioned here in virtue of his Budget of Paradoxes, a series of papers originally pub. in The Athenæum, in which… …   Short biographical dictionary of English literature

• Morgan — I Morgan,   Duron. II Morgan   [ mɔːgən] der, (s), älteste, seit Beginn des 19. Jahrhunderts typtreu gezüchtete nordamerikanische Pferderasse; kompaktes, vielseitig verwendbares Reit und Wagenpferd, Stockmaß zwischen 155 und 160 cm;… …   Universal-Lexikon

• Augustus Edward Hough Love — Naissance 17 avril 1863 Weston super Mare (Angleterre) Décès 5 juin 1940 (à 77 ans) Oxford (Angleterre) Nationalité …   Wikipédia en Français

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