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 in October 1843 and then discovering their generalization the octonions himself (he called them octaves) later that same year. He was the brother of both the mathematician and bishop Charles Graves and the writer and clergyman Robert Perceval Graves.
Life
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 sent to school in England, in the parish of Westbury-on-Trym, then a village outside Bristol, under the Rev. Samuel Feild (Field in the Oxford Dictionary of National Biography), later vicar of Hatherleigh. Feild has been described as a "prominent second generation evangelical Anglican"; he was one of two curates in the parish, under Richard Carrow, the parish priest, as perpetual curate.
Graves 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.
Having in 1830 entered the King's Inns, Dublin, Graves was called to the English bar in 1831, as a member of the Inner Temple. For a short time he went the Western circuit. In 1839 he was appointed professor of jurisprudence in London University College in a delayed succession to John Austin. Not long after, he 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 as a Fellow of the Royal Society, and he subsequently sat on 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.
in 1846 Graves married Amelia Tooke, a daughter of William Tooke, and died without issue on 29 March 1870 at Cheltenham.
Mathematical work
In his twentieth year (1826) Graves engaged in researches on the exponential function and the complex logarithm; they were printed in the Philosophical Transactions for 1829 under the title An Attempt to Rectify the Inaccuracy of some Logarithmic Formulæ. Alexandre-Joseph-Hidulphe Vincent claimed to have arrived in 1825 at similar results, which, however, were not published by him till 1832. The conclusions announced by Graves were not at first accepted by George Peacock, who referred to them in his Report on Algebra, nor by Sir John Herschel. Graves communicated to the British Association in 1834 (Report for that year) on his discovery.
In the same report is a supporting paper by Hamilton, On Conjugate Functions or Algebraic Couples, as tending to illustrate generally the Doctrine of Imaginary Quantities, and as confirming the Results of Mr. Graves respecting the existence of Two independent Integers in the complete expression of an Imaginary Logarithm. It was an anticipation, as far as publication was concerned, of an extended memoir, which had been read by Hamilton before the Royal Irish Academy on 24 November 1833, On Conjugate Functions or Algebraic Couples, and subsequently published in the seventeenth volume of the Transactions of the Royal Irish Academy. To this memoir were prefixed A Preliminary and Elementary Essay on Algebra as the Science of Pure Time, and some General Introductory Remarks. In the concluding paragraphs of each of these three papers Hamilton acknowledges that it was "in reflecting on the important symbolical results of Mr. Graves respecting imaginary logarithms, and in attempting to explain to himself the theoretical meaning of those remarkable symbolisms", that he was conducted to "the theory of conjugate functions, which, leading on to a theory of triplets and sets of moments, steps, and numbers" were foundational for his own work, culminating in the discovery of quaternions.