George Jerrard studied at Trinity College, Dublin. He entered the university in 1821 and seems to have taken rather a long time to complete his B.A. since this was not awarded until the spring of 1827.
His most important work Mathematical Researches (1832-35) is on the theory of equations. Vičte and Cardan had shown how to transform an equation of degree n so that it had no term in xn-1. This method had been generalised by Tschirnhaus to remove terms in xn-1 and xn-2. These methods were, to a large extent, motivated by attempts to solve equations algebraically. Abel and Ruffini showed this was impossible for general equations of degree greater than four.
In 1786 Bring reduced a general quintic to x5+ px + q = 0 while Jerrard generalised this to show that a transformation could be applied to an equation of degree n to remove the terms in xn-1, xn-2 and xn-3.
Hermite used Jerrard's result saying that it was the most important step in studying the quintic equation since Abel's results. Hermite did not know of Bring's result and it is almost certain that Jerrard did not know of Bring's result either.
Jerrard wrote a further two volume work on the algebraic solution of equations An essay on the resolution of equations (1858). He also wrote numerous articles which appear in the Philosophical Magazine and the Royal Society.
He died at his brother's house, the rectory at Long Stratton, Norfolk.