**Augustus De Morgan** became the first professor of mathematics at University College London and made important contributions to English mathematics.

- Being a table of numbers consisting of eleven places of figures, corresponding to all Logarithms under 100,000, with an Introduction containing a short account of Logarithms in 1742.
- Augustus lost the sight of his right eye shortly after birth when both eyes were affected with Indian "sore eye".
- They lived at Appledore, then at Bideford, then at Barnstaple, all in Devon.
- John De Morgan returned to Madras in India but in 1816 became ill with a liver problem and died in St Helena on a return voyage to England.
- De Morgan's schooling began in Barnstaple where he was taught reading and writing by Miss Williams, then in Taunton where, 1813-14, Mrs Poole taught him reading, writing and arithmetic and in the next couple of years the Rev J Fenner taught him Greek and Latin.
- Later in Blandford he was taught by the Rev T Keynes, then at Taunton, he was taught Latin, Greek, Euclidean geometry and algebra by the Rev H Barker.
- Finally he attended Mr Parsons' school, at Redland, near Bristol, where he studied from age fourteen to sixteen and a half.
- he did not join in the sports of other boys, and he was even made the victim of cruel practical jokes by some schoolfellows.
- What we have not mentioned when giving details of De Morgan's education is his religious education.
- His schoolmaster, Mr Parsons, put pressure on him to study classics at university, but De Morgan's love was mathematics.
- De Morgan entered Trinity College Cambridge in February 1823 at the age of 16 where he was taught mathematics by George Peacock and William Whewell - the three became lifelong friends.
- His College tutor was J P Higman, and he also attended lectures by George B Airy, Henry Coddington (1798-1845), and Henry Parr Hamilton (1794-1880).
- Although De Morgan's undergraduate career was successful, nevertheless, he did not shine in the way one might expect and there must have been a number of reasons for this.
- He probably devoted too much time to his study of Classics, certainly in his first years, and his health was poor at times.
- Perhaps De Morgan's greatest relaxation while a student was in playing the flute which he did to a high standard.
- Although the three above De Morgan were undoubtedly extremely able, as their subsequent careers showed, nevertheless it seems certain that they lacked De Morgan's mathematical abilities.
- Because a theological test was required for the M.A., something to which De Morgan strongly objected despite being a member of the Church of England, he could go no further at Cambridge being not eligible for a Fellowship without his M.A. In 1826 he returned to his home in London and, despite having doubts that his conscience would make him a poor lawyer, he entered Lincoln's Inn to study for the Bar.
- In 1827 (at the age of 21) he applied for the chair of mathematics in the newly founded London University and, despite having no mathematical publications, he was appointed.
- On 23 February 1828, De Morgan became the first professor of mathematics at the London University; he gave his inaugural lecture On the study of mathematics.
- De Morgan described mathematics as the deductive study of self-evident laws or axioms concerning clear and distinct ideas.
- he praised Locke's 'Essay Concerning Human Understanding' and claimed: "It is notorious that the first ideas which any human being receives are derived either from the figure or number of the objects which surround him.
- It is an essay upon the progress of knowledge, the need of knowledge, the right of everyone to as much knowledge as can be given to him, and the place in mental development which the culture of the reasoning power ought to hold.
- Teaching was, De Morgan said, the best way to learn a subject.
- In 1828 De Morgan published The Elements of Algebra, his English translation of the first three chapters of Élémens d'algèbre by Pierre Louis Marie Bourdon (1779-1854).
- The original work, in the opinion of the translator, is particularly well adapted for elementary instruction, on account of the care which is taken to deduce every rule from first principles, and to distinguish between the results of convention and those of demonstration.
- A translation of the whole would have been attempted, but or the consideration that at present every one who is desirous of attaining a considerable degree of mathematical knowledge must become acquainted with the French language; and it is to such only that the whole book would be necessary.
- The greater of two numbers is equal to half their sum added to half their difference.
- He exchanged several letters with Hachette over the next few years until Hachette's death in 1834.
- In 1830 De Morgan published Elements of Arithmetic.
- In order to avoid the generalities of algebraic language, which the mind of a beginner cannot grasp, it is necessary to confine each demonstration to one particular case; that is, to show, on some particular numbers, those truths which, in Algebra, are asserted of all at once, by means of letters to stand for numbers.
- This reasoning is not strictly logical; but it must be recollected, that the student has it in his power to convince himself of the universal truth of what is stated, by employing different numbers from those used in the text, in every demonstration.
- De Morgan was to resign his chair, on a matter of principle, is 1831.
- Some biographies of De Morgan state that he resigned because a fellow professor was dismissed.
- That the professors could be dismissed without good cause by a governing body which had little academic expertise was something that De Morgan felt strongly about.
- This question is of the highest importance, inasmuch as upon the manner in which it shall be settled depends the order of education and merit which will be found among the Professors in future, and the estimation in which they will be held by the public.
- In order to induce men of character to fill the chairs of the University, these latter must be rendered highly independent and respectable.
- The London University appointed George James Pelly White to succeed De Morgan as Professor of Mathematics.
- White was similar to De Morgan in having been a Trinity man with the same tutors and referees; in fact he stood out as clearly the best candidate.
- Perhaps the most important work that De Morgan undertook during this period was his work for the Royal Astronomical Society.
- this want of rapid publication of results was rendered less harmful by the excellent and fairly detailed summaries of all papers read, which now became a regular feature of the 'Monthly Notices'.
- there can be no doubt that De Morgan, who was Secretary from 1831-39, deserves a considerable share of the credit of this very useful part of the Society's publications.
- Throughout his life De Morgan continued to be warmly interested in the Society and was a regular attendant at the meetings.
- he firmly declined the office of President, which he did not think ought to be held by a man who was not an active worker in astronomy.
- His personal brilliance, his learning, at once extensive and minute, historical and modern, his hold on the best mathematics of the day, much in advance of his contemporaries, have made his name rather increase than diminish with the intervening decades.
- But in his relations to the Council it is his personal side that concerns us, that master passion for principle which was more than any reward or success for him.
- He was appointed to the chair again in 1836, after George White died in a boating accident, and held it until 1866 when he was to resign for a second time, again on a matter of principle.
- In 1838 he defined and introduced the term 'mathematical induction' putting the process that had been used without clarity on a rigorous basis.
- The term first appears in De Morgan's article Induction (Mathematics) in the Penny Cyclopedia.
- (Over the years he was to write 712 articles for the Penny Cyclopedia.) The Penny Cyclopedia was published by the Society for the Diffusion of Useful Knowledge, set up by the same reformers who founded the London University, and that Society also published a famous work by De Morgan The Differential and Integral Calculus (1836).
- endeavoured to make limits the sole foundation of the science, without any aid whatsoever from the theory of series, or algebraical expressions.
- He introduced De Morgan's laws and his greatest contribution is as a reformer of mathematical logic.
- De Morgan corresponded with Charles Babbage and gave private tuition to Ada Lovelace who, it is claimed, wrote the first computer program for Babbage.
- He also corresponded with Hamilton and, like Hamilton attempted to extend double algebra to three dimensions.
- In a letter to Hamilton, De Morgan writes of his correspondence with Hamilton and William Hamilton.
- In 1864 he was a co-founder of the London Mathematical Society, suggesting its name, and became its first president.
- There is in the idea of everyone some particular sequence of propositions, which he has in his own mind, and he imagines that the sequence exists in history; that his own order is the historical order in which the propositions have successively been evolved.
- If he be to have his own researches guided in the way which will best lead him to success, he must have seen the curious ways in which the lower proposition has constantly been evolved from the higher.
- De Morgan was never a Fellow of the Royal Society of London as he refused to let his name be put forward.
- He also refused an honorary degree from the University of Edinburgh.
- De Morgan considered himself a 'Briton unattached' neither English, Scottish, Welsh or Irish.
- he had no ideas or sympathies in common with the physical philosopher.
- His attitude was doubtless due to his physical infirmity, which prevented him from being either an observer or an experimenter.
- Five days after his death, on 23 March 1871, his funeral was held and he was buried at All Souls, Kensal Green, Kensington and Chelsea, London.

Born 27 June 1806, Madura, Madras Presidency, India (now Madurai, Tamil Nadu, India). Died 18 March 1871, London, England.

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Ancient Greek, Geometry, Origin India, Number Theory, Puzzles And Problems, Special Numbers And Numerals, Topology

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive