Augustus De Morgan

Augustus De Morgan . English mathematician and logician. Professor of mathematics at the University College of London between 1828 and 1866 ; first president of the London Mathematical Society. De Morgan was especially interested in algebra . He wrote several works of logic in which the idea of ​​applying mathematical methods in this sphere is found, as well as the first results of such application. In modern mathematical logic, the following fundamental laws of the algebra of logic are named after De Morgan: “the negation of the conjunction is equivalent to the disjunction of the negations (Aœ · Bœ is equivalent to A Ë B)”«The negation of the disjunction is equivalent to the conjunction of the negations. (Aœ Ë Bœ is equivalent to A · B) » . Main work: “Formal logic or the calculation of necessary and probable inferences” ( 1847 ). [1]


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  • 1 Biographical synthesis
    • 1 Studies
    • 2 Trajectory
    • 3 Death
  • 2 References
  • 3 Sources

Biographical synthesis

Augustus De Morgan’s father was a Lieutenant Colonel who served in India . When he was stationed there, his fifth son, Augustus, was born. Very soon after the birth Augustus lost the vision in his right eye, and, when he was seven months old, he returned to England with his family. John de Morgan passed away when Augustus was 10 years old.

At school De Morgan did not stand out and, due to his disability, he did not join in sports with the other children, and was made the victim of cruel teasing by some of his classmates.


De Morgan entered Trinity College, Cambridge in 1823 at the age of 16, where he was tutored by Peacock and Whewell , the three of whom became friends for life. He received a Bachelor’s degree (BA), but, due to the theological tests required for the Master (MA), something that De Morgan strongly disavowed despite being a member of the Church of England, he could not continue in Cambridge being ineligible. for a scholarship without your master’s degree.

In 1826 he returned home to London and entered Lincoln’s Inn to study law . In 1827 (at the age of 21) he applied for the chair of mathematics at the newly founded University College in London, and despite having no mathematical publications he was appointed.


In 1828 De Morgan became the first professor of mathematics at Unversity College. He gave his inaugural class on ‘In the Study of Mathematics’. De Morgan had to resign his post, on principle, in 1831 . He was reappointed in 1836 and held until 1866 when he had to resign a second time, again on principle.

His book Elements of Arithmetic was his second publication and would see multiple editions. In 1838 he defined and introduced the term mathematical induction, giving a rigorous basis to a process that had been used without clarity until then. The term first appeared in De Morgan’s article in the Penny Encyclopedia titled Induction (Mathematics) (Over the years he wrote 712 articles for the Penny Encyclopedia ). The Penny Encyclopedia was published by the Society for the Diffusion of Useful Knowledge, created by the same reformers who founded the University of London; said society also published a famous work by De Morgan entitledThe differential and integral calculus .

In 1849 he published trigonometry and double algebra in which he gave a geometric interpretation to complex numbers.

He recognized the purely symbolic nature of algebra , and was aware of the existence of other algebras different from the ordinary one. He introduced De Morgan’s laws and his great contribution is as a reformer of mathematical logic .

De Morgan corresponded with Charles Babbage and tutored Lady Lovelace who, it is claimed, wrote the first computer program for Babbage.

De Morgan was also written with Hamilton and as he attempted to extend double algebra to the third dimension. In a letter to Hamilton, De Morgan writes of his correspondence with Hamilton and William Hamilton :

Let it be known to you that I have discovered that you and Sir WH are polar reciprocals to me (intellectually and morally, the Scottish baronet is a polar bear, and you, I would say, are a polar knight). When I send some of my research to Edinburgh, that guy’s WH says I copied it from him. When I send something to you, you receive it, generalize it at a glance, present it generalized to society at large, and make me the second discoverer of a known theorem.

In 1866 he co-founded the London Mathematical Society and became its first president. George, De Morgan’s son, a very capable mathematician, was the first secretary. The same year De Morgan was elected a member of the Royal Astronomical Society .

De Morgan was never a member of the Royal Society as he always rejected that his name be placed at the top. He also rejected an honorary post from the University of Edinburgh . It was described by Thomas Hirst as follows:

I am afraid that Mr. De Morgan is a dry and dogmatic pedant, despite his unquestionable ability.

Macfalane remarks that:

… De Morgan considers himself a disengaged Briton, neither English, nor Scottish, nor Welsh, nor Irish.

And he also said:

He disliked the countryside and when his family was enjoying the coast, and the men of science were having a good time at a British Association meeting in the countryside, he stayed in the hot and dusty libraries of the metropolis … he had no ideas or sympathies in common with physical philosophers. His attitude was doubtful due to his physical weakness, which made it impossible for him to be both an observer and an experimenter. He never voted in an election, and he never visited the House of Commons , or the Tower, or Westminster Abbey .

De Morgan was always interested in numerical curiosities and writing in 1864 he emphasized that he had had the distinction of being x years old in the year x2 (He was 43 in 1849 ). Anyone born in 1980 can claim the same distinction.


He died in London , England on March 18 , 1871 .


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