John T. Graves
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.[1] He was the brother of both the mathematician and bishop Charles Graves[2] 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
Graves was an undergraduate at
Having in 1830 entered the
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.[7]
in 1846 Graves married Amelia Tooke, a daughter of
Mathematical work
In his twentieth year (1826) Graves engaged in researches on the
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.[7]
For many years Graves and Hamilton maintained a correspondence on the interpretation of imaginaries. In 1843 Hamilton discovered the quaternions, and it was to Graves that he made on 17 October his first written communication of the discovery. In his preface to the Lectures on Quaternions and in a prefatory letter to a communication to the Philosophical Magazine for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. Immediately after the discovery of quaternions, before the end of 1843, Graves successfully extended to eight squares Euler's four-square identity, and went on to conceive a theory of "octaves" (now called octonions) analogous to Hamilton's theory of quaternions, introducing four imaginaries additional to Hamilton's i, j and k, and conforming to "the law of the modulus".[7] Octonions are a contemporary if abstruse area of contemporary research of the Standard Model of particle physics.[11]
Graves devised also a pure-triplet system founded on the roots of positive unity, simultaneously with his brother Charles Graves, the bishop of Limerick. He afterwards stimulated Hamilton to the study of polyhedra, and was told of the discovery of the icosian calculus.[7]
Graves contributed also to the Philosophical Magazine for April 1836 a paper On the lately proposed Logarithms of Unity in reply to Professor De Morgan, and in the
Academic lawyer
The records of Graves's work as a jurist are twelve lectures on the law of nations, reported in the
Legacy
For many years Graves collected mathematical works. This portion of his library, more than ten thousand books and about five thousand pamphlets he bequeathed to University College London in 1870.[7][12] The library, which is believed to be the largest collection of mathematical works in the UK, contains a first edition of Sir Issac Newton's Philosophiæ Naturalis Principia Mathematica.[13]
References
- ^ The octonions by John C. Baez
- ISBN 0-8176-3316-2.
- doi:10.1093/ref:odnb/11311. (Subscription or UK public library membershiprequired.)
- Alumni Oxonienses: the Members of the University of Oxford, 1715–1886. Oxford: Parker and Co – via Wikisource.
- ^ Lineham, Peter (1986). "The Significance of J.G. Deck 1807-1884" (PDF). bruederbewegung.de. p. 4.
- ^ "A Bristol Miscellany" (PDF). Bristol Record Society's Publications. XXXVII: 62.
- ^ a b c d e f g h i j k Stephen, Leslie; Lee, Sidney, eds. (1890). . Dictionary of National Biography. Vol. 22. London: Smith, Elder & Co.
- ^ Alumni Oxonienses: the Members of the University of Oxford, 1715–1886. Oxford: Parker and Co – via Wikisource.
- ^ The Graves family of Yorkshire and Mickleton Manor, Gloucestershire, England Graves Family Association
- ^ Royal Society, (Great Britain) (1872). Catalogue of Scientific Papers (1800–1863). C. J. Clay. p. 161.
- ^ Wolchover, Natalie (20 July 2018). "The Peculiar Math That Could Underlie the Laws of Nature New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called "octonions."". Quanta Magazine. Retrieved 27 July 2018.
- ^ UCL Special Collections (23 August 2018). "Graves Library". Library Services. Retrieved 5 December 2023.
- ^ Newton, Issac. "Philosophiae naturalis principia mathematica". UCL Explore. Retrieved 5 December 2023.
External links
- Attribution
This article incorporates text from a publication now in the public domain: Stephen, Leslie; Lee, Sidney, eds. (1890). "Graves, John Thomas". Dictionary of National Biography. Vol. 22. London: Smith, Elder & Co.