He was Erasmus Smith's Professor of Mathematics at Trinity College Dublin (1843–1862), and was president of the Royal Irish Academy (1861–1866).
He served as dean of the Chapel Royal at Dublin Castle, and later as Bishop of Limerick, Ardfert and Aghadoe.
Educated at Trinity College Dublin, he was elected a Scholar in classics in 1832, and in 1834 graduated BA as Senior Moderator in mathematics, getting his MA in 1838.
[2][3][4] It was intended that he should join the 18th (Royal Irish) Regiment of Foot under his uncle, Major-General James William Graves (1774–1845), and in preparation he had become an expert swordsman and rider.
[5] In 1841, he published the book Two Geometrical Memoirs on the General Properties of Cones of the Second Degree and on the Spherical Conics, a translation of Aperçu historique sur l'origine et le développement des méthodes en géométrie (1837) by Michel Chasles, but including many new results of his own.
His post-TCD mathematical output includes, "On a Theorem Relating to the Binomial Coefficients" (1665), "On the Focal Circles of Plane and Spherical Conics" (1888), "The Focal Circles of Spherical Conics" (1889) and "On the Plane Circular Sections of the Surfaces of the Second Order" (1890) (all published in either the Proceedings or the Transactions of the Royal Irish Academy).
He discovered the key to the ancient Irish Ogham script which appeared as inscriptions on Cromlechs and other stone monuments.
[12] Appointing Eugene O'Curry and John O'Donovan as translators, the Commission created facsimile copies of the original document using the process of anastatic lithography which had been showcased by Samuel Cowell at the Great Exhibition of 1851.