Murphy, Robert (1806–43), mathematician, was born in Mallow, Co. Cork, fifth son among seven sons and three daughters of John Murphy, shoemaker and Church of Ireland parish clerk in Mallow, and his wife Margaret (maiden name unknown). His father died (1814), leaving the family destitute. In an unfortunate incident Robert was run over by a cart while playing near his home on Beecher's St., Mallow, in 1819, and suffered a badly fractured thighbone, leaving him bed-ridden for a year. During this period of confinement he studied geometry and algebra, showing remarkable precocity in these subjects. His abilities came to the attention of Timothy Mulcahy, a schoolteacher in Cork, through the ingenious solutions he provided for mathematical teasers posed by Mulcahy in a local newspaper. Mulcahy visited Mallow to discover the identity of the mystery mathematician and was astounded to discover that it was a 13-year-old boy. With the assistance of John Dillon Croker, a miller from Quartertown, Mulcahy arranged for Murphy's education to be continued free of charge at a classical school kept by Mr Hopley in Mallow, after which he spent some time at the Rev. Armstrong's diocesan school in Princes St., Cork. (Mulcahy's own son, John Mulcahy (1810?–1853), after an education at TCD, became the first professor of mathematics (1849), and one of two catholics appointed to the faculty of arts at QCG.) In 1823 Mulcahy and Hopley unsuccessfully sponsored Murphy's application to TCD. He was rejected on the basis of his lack of formal education and knowledge of the classics.
His chances of entering university improved when, through his earlier sponsors, he was introduced to a Mr McCarthy, a Cork native and junior fellow at Gonville and Caius College, Cambridge, at home on vacation. McCarthy presented a selection of his work to Robert Woodhouse, Lucasian professor of mathematics at Cambridge, who at first paid little heed to it. It was only after the work of Murphy came to his attention a short time later that he took any interest. In 1824 John Mackey, a young priest from Maynooth, published a pamphlet showing a method of constructing the cube root of two, using only a straight edge and compass. Murphy, who had studied such problems, believed that Mackey's work was fallacious and there was, in fact, no possible solution. He detected an error in Mackey's reasoning and published (1824) a pamphlet refuting Mackey's work. This aroused much interest and came to the attention of Woodhouse, who readily agreed to admit him as a student at a reduced fee of £60. Mulcahy and Hopley duly raised the necessary amount and he entered Gonville and Caius College, Cambridge in October 1825, becoming a scholar and winning the first mathematical prize in 1826.
He graduated BA (1828) as third wrangler, was elected a fellow of his college (1829), and became a deacon of the Church of England (1831); for some fellowships it was necessary to take deacon orders. That same year he was appointed junior dean (1831–3) of Gonville and Caius College. To supplement his modest income he took on the disparate tasks of librarian, lecturer in Hebrew (1830–33), and lecturer in Greek (1832). He graduated MA (1832) and began a steady output of original mathematical work; he published well-received papers on integral equations and the roots of polynomials in the Philosophical Transactions and the Cambridge Philosophical Transactions between 1830 and 1837, and during his short life produced twenty scholarly papers. In 1833 he was commissioned to write a textbook on electricity for Cambridge students, published as Elementary principles of the theories of electricity, heat, and molecular actions. Part 1 – On electricity. His most notable publication was First memoir on the theory of analytical operations (Philosophical Transactions (1837), 179–210), which was a pioneering paper, providing the theoretical background for a great deal of work in differential equations. In one of his papers, he referred to the innovative work of the obscure miller and mathematician George Green (1793–1840). This brought about a general recognition of Green's general mathematical theory of potential, which eventually led to the mathematical theories of electricity of the twentieth century.
Despite the progress of his mathematical career and his recognition as a mathematician, his personal life came under increasing scrutiny from the college authorities, as he fell ‘into dissipation’ (Noel Barry (1998)) and resorted to drinking and gambling. Quite well off for the first time in his life, he repaid his debts to the widow of his college sponsor (Hopley), but appeared unable to handle his new lifestyle. Around 1833 his income was sequestered to repay his debts, and shortly after being elected FRS (1834) he left Cambridge, possibly to avoid his creditors, and returned to Ireland. His mother had died in 1832 and no doubt he also felt a need to return home. He is said to have wandered around west Cork for a while as a cobbler, drinking heavily and eating badly (Mac Cnaimhin (1966)). With the help of his friends he managed to pull himself together; he became an honorary member of the Royal Cork Institution at this time. He returned to Cambridge (1835) before moving to London (1836), where he earned a precarious living working as a private tutor and writing a number of popular accounts of mathematics and science for the Penny Cyclopedia. He was ever hopeful of returning to Cambridge, and had written (1835) to Charles Babbage looking for support for a position as Plumian professor of astronomy. His difficult circumstances thwarted his research, though he did publish some papers and an advanced textbook, Theory of algebraic equations (1839), for the Society for the Diffusion of Useful Knowledge. Through the assistance of his friend and professor of mathematics Augustus De Morgan, he was appointed examiner in mathematics and natural philosophy at the University of London (1838–42) with a salary of £200.
In 1839 he developed tuberculosis, and died 12 March 1843 at 29 East St., Holborn, London. He did not leave a will, but the sum of his estate, approximately £1,000, was granted by probate to his sister, Catherine Murphy. He never married. He was buried in an unmarked grave in Kensal Green cemetery, a common burial place for fellows of the Royal Society. A full bibliography of his published papers can be found in Noel Barry (1998). Some of his letters are held in the archives of the Royal Society of London, University College London, and the British Library.
His brilliant career and early death were seen as a great tragedy. His friend A. de Morgan attested to his true genius for mathematical invention and regretted what he might have been ‘if the promise of his boyhood had not been destroyed by the unfortunate circumstances of his life’ (quoted in Noel Barry (1998)).