John Thomas Graves

John Thomas Graves (* 1806 in Dublin ; † 1870 ) was an Irish mathematician and lawyer. He is known as the discoverer of the octonions .

Life

Graves studied at Trinity College , Dublin, where he befriended William Rowan Hamilton and excelled in mathematics and the classical languages. After graduating in 1827, he went to Oxford University , where he became a member of Oriel College in 1830 . From 1830 he studied law at the King's Inns in Dublin and graduated from Dublin and Oxford in 1831. He then went to the Inner Temple in London as a lawyer . From 1839 to 1843 he was a law professor at University College London and also an examiner (examinator) in law at the University of London. From 1846 he was Assistant Poor Law Inspector and from 1847 Poor Law Inspector for England and Wales.

He was a member of the "Society for the diffusion of useful knowledge" and from 1839 the Royal Society , in whose council he was later. He was a member of the Philological Society and the Royal Society of Literature.

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As early as 1829 he had published a mathematical work on the imaginary logarithm in the Philosophical Transactions of the Royal Society and again in 1834 (supported by Hamilton, since there was no general recognition) in the report of the British Association. During his legal career he corresponded with Hamilton, who was the first to inform him of his discovery of the quaternions in 1843 (and thanked him for his suggestions). Later he worked on the suggestion of Hamilton with the theory of the polyhedron. Today he is best known for his discovery of octaves (or octonions), an 8-dimensional real standardized division algebra , which completes the list of real and complex numbers, quaternions and octaves - which Georg Frobenius proved in 1877. The discovery followed immediately (letter to Hamilton on December 26, 1843) after Hamilton's discovery of the quaternions (October 1843), to which Hamilton had stimulated his friend Graves' interest in algebra in particular. Octonions were first published by Arthur Cayley in Philosophical Magazine in 1845 (as a small supplement to a defense of his work on elliptic functions, "On Jacobi's Elliptic functions- in reply to the Rev.Bronwin, and on Quaternions"). Graves published his discovery an issue later than Cayley in Philosophical Magazine, and had to go back to his friend Hamilton for his priority claims (note in the Transactions of the Royal Irish Academy, June 14, 1847). But his octonions were already called Cayley numbers.

He also wrote articles on Roman and canon law in the Encyclopaedia Metropolitana and articles on ancient Roman jurists in the Dictionary of Greek and Roman Biography and Mythology (3 volumes, London 1844-1849) by William Smith .

Web links

• Biography on pages relating to his estate at University College, London
• John Baez on octonions and their discovery