Skip to main content

Jerrard, George Birch

Jerrard, George Birch

(b. Cornwell, England, 1804; d. Long Stratton, Norfolk, England, 23 November 1863)


George Jerrard was the son of Major General Joseph Jerrard. Although he entered Trinity College, Dublin, where he was a pupil of T. P. Huddart, on 4 December 1821, he did not take his B. A. until the spring of 1827. Jerrard’s name is remembered for an important theorem in the theory of equations, relating to the reduction of algebraic equations to normal forms. In 1824 Abel had shown that the roots of the general quintic equation cannot be expressed in terms of its coefficients by means of radicals. E. W. Tschirnhausen had previously generalized the technique of Viéte, Cardano, and others of removing terms from a given equation by a rational substitution. Then, in 1786, E. S. Bring reduced the quintic to a trinomial form

x5 + px + q = 0

by a Tschirnhausen-type transformation with coefficients expressible by one cube root and three square roots (that is, the coefficients defined by equations of degree three or less). Jerrard also obtained this result, independently, and in a more general form, reducing any equation of degree n to an equation in which the coefficients of xn-1, xn-2 and xn-3 are all zero.

When Hermite found a solution for quintic equations in terms elliptic modular functions, he cited only Jerrard. Unaware that Bring had found the result for the case n=5, Hermite stated taken Jerrard’ theorem was the most important step taken in the albebracic theory of equations of the fifth degree since Abel. Bring’s partial priority, later brought to light by C. J. D. Hill in 1861, did not entirely detract from the importance of Jerrard’s research.


Apart from his Mathematical Researches, 3 vols.(Bristol-London, 1832-1835), in which his theorem was first given, Jerrard wrote An Essay on the Resolution of Equations, 2vols. (London, 1858). On hisearlier work, see W. R. Hamilton,” Inquiring Into the Validity of a Method Recently Proposed by George B. Jerrard. . .,” in British Association Report, 5 (1837), 295-348. On the question of Bring’s priority, see Felix Klein, Vorlesungen ül die Ikosaeder (Leipzing, 1884), pt. 2, ch. !, see. 2, Eng. trans. (London, 1913), pp. 156-159, English repr. (New York, 1956).

Jerrard wrote extensively in the Philosophical Magazine; references to these articles are in Klein, op. cit.; and the Royal Society, Catalogue of Scientific Papers, 1800-1863, 3 (1869), 547-’548. For a useful bibliography on the therory of equations and its history, see G. Loria, Bibliotheca mathematica, 5 (1891), 107-112. A short obituary is in Gentleman’s Magazine, 1 (1864), 130; sparse personal details are in the registers of Trinity College, Dublin.

J. D. North

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"Jerrard, George Birch." Complete Dictionary of Scientific Biography. . 22 Apr. 2019 <>.

"Jerrard, George Birch." Complete Dictionary of Scientific Biography. . (April 22, 2019).

"Jerrard, George Birch." Complete Dictionary of Scientific Biography. . Retrieved April 22, 2019 from

Learn more about citation styles

Citation styles gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, cannot guarantee each citation it generates. Therefore, it’s best to use citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

The Chicago Manual of Style

American Psychological Association

  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.