John T. Graves

[6] 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.

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.

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.

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".

[11] Shortly before the discovery, Graves wrote in a letter addressed to Hamilton on 26 October 1843, "If with your alchemy you can make three pounds of gold, why should you stop there?

To the same periodical he contributed in September 1838 A New and General Solution of Cubic Equations; in 1839 a paper On the Functional Symmetry exhibited in the Notation of certain Geometrical Porisms, when they are stated merely with reference to the arrangement of points; and in April 1845 a paper on the Connection between the General Theory of Normal Couples and the Theory of Complete Quadratic Functions of Two Variables.

He was also a contributor to William Smith's Dictionary of Greek and Roman Biography and Mythology, with lives of the jurists Cato, Crassus, Drusus, Gaius, and an article on the legislation of Justinian.

[7][13] 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.