**Robert Murphy** was an Irish mathematician who worked on the theory of equations and was among the first to consider algebras of operators.

- John Murphy clearly had a reasonable education since he served as the parish clerk.
- It is often the case that misfortune has its positive side and this appears to be true for Murphy for it was during the time that he was confined to bed that he discovered that he had a talent for mathematics.
- He then made strenuous efforts to arrange for Murphy to get an education.
- He persuaded Croker to help finance Murphy's education and he also spoke to Mr Hopley, the headmaster of the local school, who agreed to cover Murphy's fees and the cost of books at his school.
- Murphy spent three years between 1819 and 1823 at Mr Hopley's school where he was taught by a Mr Armstrong.
- In 1823 Murphy, supported by Mulcahy, Hopley and Croker, applied to enter Trinity College, Dublin.
- Such setbacks were not going to stop Murphy doing mathematics.
- Murphy had amused himself by studying the classical Greek problems and believed that they were insoluble.
- Murphy began his account by looking briefly at the history of duplication the cube and trisecting the angle.
- Murphy then goes on to correctly point out the errors in the Reverend John Mackey's arguments using only Euclid's Elements and Cardan's Ars Magna Ⓣ(The great art) (more precisely the Cardan-Tartaglia formula for solving cubic equations).
- Now Murphy had a stroke of luck.
- McCarthy was a junior fellow of Gonville and Caius College, Cambridge, who lived in Cork and when he returned home for a vacation he met Murphy.
- Collecting together some of Murphy's mathematics he returned to Cambridge and showed them to Robert Woodhouse.
- Woodhouse glanced at Murphy's work and at first did not rate it highly but, on a second reading, he saw its potential.
- He wrote to McCarthy saying that he would accept Murphy as a student at Gonville and Caius College, Cambridge, for a fee of £60 if his sponsors could raise that amount.
- He assured them that this would cover all of Murphy's expenses for the duration of his undergraduate course.
- Mulcahy, with the help of several friends in Mallow, was able to put together the £60 and Murphy was admitted as a pensioner to Gonville and Caius College, Cambridge, on 7 July 1825.
- Murphy won the 1st Mathematics Prize in 1826 and went on to graduate with a B.A. in 1829.
- This excellent performance, quite remarkable for someone with Murphy's minimal formal education before beginning his undergraduate studies, led to Murphy being awarded a Perse Fellowship.
- Already as an undergraduate there is considerable evidence that Murphy could not handle his finances.
- In December of the following year, at the meeting of the Senior Fellows when Murphy's degree was confirmed, it was "agreed to advance Mr Murphy a loan of fifty pounds".
- Also the same meeting of the Senior Fellows in December 1832 it was agreed that "sixty pounds be allowed to Mr Murphy for the present year".
- In the two months, October and November 1832, ten Common Room wagers by Murphy are recorded in the College Wager Book and, in 1833, 21 of the total of 60 bets recorded involve Murphy.
- What sort of bets did Murphy make?
- Many of the bets involved bottles of wine and there is a suggestion that Murphy had problems with alcohol as well as with betting.
- Although Murphy lost his position as a junior dean in charge of discipline in 1833, he continued to hold other posts at Gonville and Caius College, being a Hebrew lecturer in 1833, 1834 and 1835.
- Murphy published On the General Properties of Definite Integrals (1830), On the Resolution of Algebraical Equations (1831), First Memoir on the Inverse Method of Definite Integrals, with Physical Applications (1830) and On Elimination between an Indefinite Number of Unknown Quantities (1832) in the Transactions of the Cambridge Philosophical Society.
- We can already see the two main areas on which Murphy was working, namely on integral equations and algebraic equations.
- It is unlikely that Murphy would know of it until Green became an undergraduate at Caius College in October 1833.
- Murphy's book was certainly completed by June 1833 (this is the date on the Introduction) so it is completely understandable that Green's ideas did not get included in Murphy's book.
- On the theory of equations Murphy wrote papers such as On the Existence of Real or Imaginary Root to Any Equation (1833), Further Development of the Existence of a Real or Imaginary Root to Any Equation (1833), Analysis of the Roots of Equations (1837) and the results from these papers were all contained in Murphy's 1839 book A Treatise on the Theory of Algebraical Equations.
- Perhaps Murphy's most remarkable paper was First Memoir on the Theory of Analytic Operations published in 1837 in the Philosophical Transactions of the Royal Society of London.
- In this paper Murphy looks at linear operators on functions.
- Looking at examples of such operators was not new but Murphy looked at these operators as an algebraic system.
- Let us continue to describe the events of Murphy's life.
- Murphy's hope for this chair were not realised since, even before he reached London, De Morgan had been appointed to fill the vacant chair.
- De Morgan, who fully understood Murphy's genius, tried to help him over the next few years.
- Murphy lived cheaply in London and made some money tutoring privately.
- Today Murphy is little known but, had he been more able to organise his life, his health may have been better and he may have had the time to produce results of lasting importance of which his genius showed him to be capable.

Born 1806, Mallow, Cork County, Ireland. Died 12 March 1843, London, England.

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Origin Ireland

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