John Thomas Graves (4 December 1806 – 29 March 1870) was an Irish jurist and mathematician. He was a friend of William Rowan Hamilton, and is credited both with inspiring Hamilton to discover the quaternions and with personally discovering the octonions, which he called the octaves. He was the brother of both the mathematician Charles Graves and the writer and clergyman Robert Perceval Graves.
Born in Dublin 4 December 1806, he was son of John Crosbie Graves, barrister, grandnephew of Richard Graves, D.D., and cousin of Robert James Graves, M.D. He was an undergraduate at Trinity College, Dublin, where he distinguished himself in both science and classics, and was a class-fellow and friend of William Rowan Hamilton, graduating B.A. in 1827. He then moved to Oxford, where he became an incorporated member of Oriel College, 11 November 1830. Graves proceeded M.A. at Oxford in 1831, and at Dublin in 1832.
He was called to the English bar in 1831 as a member of the Inner Temple, having previously (1830) entered the King's Inns, Dublin. For a short time he went the western circuit, and in 1839 he was appointed professor of jurisprudence in London University College in succession to John Austin, who finally retired in 1835. Not long after Graves was elected an examiner in laws in the University of London.
Graves was one of the committee of the Society for the Diffusion of Useful Knowledge. In 1839 he was elected a member of the Royal Society, and he subsequently sat upon its council. He was also a member of the Philological Society and of the Royal Society of Literature. In 1846 Graves was appointed an assistant poor-law commissioner, and in the next year, under the new Poor Law Act, one of the poor-law inspectors of England and Wales.