Jerrard, George Birch

(1804-1863), mathematician

by R. A. Bryce

© Oxford University Press 2004 All rights reserved

Jerrard, George Birch (1804-1863), mathematician, was born in Cornwall, the son of Joseph Jerrard (d. 1858), who later became a major-general. He entered Trinity College, Dublin, in 1821, graduating in 1827, and is known for his work in the theory of equations. He published two treatises: Mathematical Researches (3 vols., 1832-5) and An Essay on the Resolution of Equations (2 vols., 1858), and about a dozen mathematical articles, almost all in the Philosophical Magazine, between 1835 and 1863.

Much of Jerrard's work related to his attempt to solve one of the most famous unsolved problems in mathematics, the question of a formula solution to equations of the fifth degree. What was sought was a formula analogous to that for second degree (quadratic) equations familiar to generations of schoolchildren, a solution 'by radicals' in mathematical parlance. Such formulae existed for equations of the third and fourth degrees as well, but the quintic, so called, remained elusive until the 1824 proof by the Norwegian Niels Henrik Abel (1802-1829) that no such formula for quintics existed. In Mathematical Researches Jerrard believed he had shown that a solution by radicals for the quintic did exist. Sir William Rowan Hamilton published a rebuttal of this in 1837. Nevertheless, to the end of his life, Jerrard refused to accept Abel's result. His scepticism was shared, in various degrees, by others, notably by James Cockle, though Cockle's opinion was 'not proven' rather than outright disbelief in Abel's result. A long exegesis of Abel by Hamilton in 1839 did nothing to shake Jerrard, and nothing immediately to shake Cockle. Finally, however, in 1862, Cockle published a guarded surrender to Abel and Hamilton which must have been a blow to Jerrard: Cockle had been the best he had had by way of a mathematical supporter. Moreover, by the 1860s, Cockle was being forced to point out in print mistakes of Jerrard, and in this he was joined by Arthur Cayley. The exchange ended unpleasantly, with a good deal of asperity on either side. Jerrard's last rejoinder is a very brief note, in the October 1863 number of the Philosophical Magazine, terminating his part in the correspondence: his exasperation is evident.

Jerrard was not alone in claiming the existence of solutions by radicals for the quintic equation, but he was the most persistent, in the face of the objections of Cayley, Cockle, and Hamilton over more than twenty-five years. The method he proposed in Mathematical Researches was valid up to a point. He showed that the question of solubility or insolubility by radicals could be decided by considering a very specific quintic equation. Using this result the Frenchman Charles Hermite (1802-1901) was able to effect a formula solution of the quintic, but he used functions not encompassed within the meaning of the term 'by radicals'. It is, however, this reduction of the problem to manageable form which is Jerrard's main claim to fame. It is somehow typical of the life of this mathematically tragic figure that his method of reduction had, unknown to him, been discovered in 1786 by the Swede E. S. Bring (1736-1798), though its first publication in England was in 1864, well after Jerrard's Mathematical Researches had appeared.

Jerrard died on 23 November 1863 at the rectory in Long Stratton, Norfolk, the home of his brother, Frederick William Hill Jerrard, the rector, who also had mathematical training: he had attended Gonville and Caius College, Cambridge, and was eighth wrangler in 1833.

R. A. BRYCE

Sources  
J. D. North, 'Jerrard, George Birch', DSB
W. R. Hamilton, 'Inquiry into the validity of a method recently proposed by George B. Jerrard esq.', Report of the British Association for the Advancement of Science (1837), 295-348
J. Cockle, 'Concluding remarks on a recent mathematical controversy', London, Edinburgh, and Dublin Philosophical Magazine, 4th ser., 26 (1863), 223-4
N. H. Abel, Mémoire sur les équations algébriques (Christiania, 1824)
Catalogue of scientific papers, Royal Society, 3 (1869), 547-8
Catalogue of scientific papers, Royal Society, 8 (1879), 25
DNB
Boase, Mod. Eng. biog.
GM, 3rd ser., 16 (1864), 130
D. Bank and A. Esposito, eds., British biographical index, 4 vols. (1990)
Crockford (1859)
C. B. Boyer, A history of mathematics (1968)
CGPLA Eng. & Wales (1863)

Wealth at death  
under £3000: administration, 30 Dec 1863, CGPLA Eng. & Wales


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