# Dictionary of National Biography, 1885-1900/Roberts, Michael

​ROBERTS, MICHAEL (1817–1882), mathematician, was born in Peter Street, Cork, on 18 April 1817. He and his twin-brother William were the eldest sons of Michael Roberts of Kilmoney, captain, of a family which had migrated from Kent about 1630. Their mother, Elizabeth Townsend Stewart, was great-great-granddaughter of Colonel Stewart, governor of Edinburgh Castle, who was attainted in 1715 for implication in a plot to deliver that fortress to the Pretender, and fled to The Hague. Michael and William were educated at Middleton school, co. Cork, and entered Trinity College, Dublin, in 1833. Michael, although he obtained a classical scholarship in 1836, studied chiefly under James McCullagh [q. v.], the mathematical professor. He graduated B.A. 1838, and was elected fellow in 1843. In 1862 he was appointed professor of mathematics at Trinity College, and held the post till 1879, when he was co-opted senior fellow. He died on 4 Oct. 1882, having been for some years in failing health. He married, in 1851, Kate, daughter of John Drew Atkin of Merrion Square, Dublin. He had three sons and four daughters. A portrait of Roberts and his twin-brother, at the age of sixteen, by a local artist, is in the possession of the Rev. W. R. W. Roberts, Trinity College, Dublin.
Roberts prepared his professorial lectures with singular thoroughness. His earlier lectures were on the ‘Theory of Invariants and Covariants,’ on which he published several valuable papers. He next turned his attention to hyperelliptic integrals, which, after the publication of Jacobi's papers, had been largely developed by Riemann, Weierstrass, and others. His ‘Tract on the Addition of Elliptic and Hyperelliptic Integrals,’ 1871, was drawn mainly from the notes for his lectures. In it is constructed a trigonometry of hyperelliptic functions analogous to that of elliptic functions.
Roberts was the discoverer of many striking and beautiful properties of geodesic lines and lines of curvature on the ellipsoid, and in particular concerning their relations to umbilics. On these subjects he published six papers in Liouville's ‘Journal de Mathématiques,’ 1845–50; two in the ‘Royal Irish Academy Proceedings,’ 1847; one in the ‘Cambridge and Dublin Mathematical Journal,’ 1848; one in the ‘Nouvelles Annales de Mathématiques,’ 1855; and three in the ‘Annali di Matematica,’ 1868–73. In the international exhibition of 1851 at Hyde Park was exhibited a small model ellipsoid made in Berlin, on which the lines of curvature were traced after a method invented by Roberts. The lines of curvature and asymptotic lines on the surface, at any point of which the sum of the principal curvatures is zero, were also discussed in Liouville's ‘Journal de Mathématiques,’ 1850. Papers by Roberts on the properties and symmetric functions of the roots of algebraic equations, in particular of the third, fourth, and fifth degrees, and on covariants and invariants, appeared in the ‘Nouvelles Annales de Mathématiques,’ 1856–60 (five), in the ‘Annali di Matematica,’ 1859–69 (seven), and in the ‘Quarterly Journal of Mathematics,’ 1861–2 (five). He also published two papers on ‘Abelian Functions’ in ‘Annali di Matematica,’ 1869–71.
W. F. S.