His most famous work Meletemata quaedam mathematematica circa transformationem aequationum algebraicarum (1786) was published at Lund. This work describes Bring's contribution to the algebraic solution of equations.
Bring discovered an important transformation to simplify a quintic equation. It enabled the general quintic equation to be reduced to one of the form
x + px + q = 0.
The transformation was later discovered independently and generalised by Jerrard in 1832-35. By the time Jerrard discovered the transformation, Ruffini's work and Abel's work on the impossibility of solving the quintic and higher order equations had been published. However, at the time of Bring's discovery, there was no hint that the quintic could not be solved by radicals and, although Bring does not claim that he discovered his transformation in an attempt to solve the quintic, it is likely that this is in fact why he was examining quintic equations.
References (2 books/articles)
References elsewhere in this archive:
Tell me about Bring's work on quadratic cubic and quartic equations
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