Galois's research did not spring ex nihilo from his mind, even if it was the mind of a genius (see the article "Galois's stroke of genius"). Before him, scholars such as Lagrange and Cauchy had already studied what we now call substitution groups; this explains why each of their names is attached to an important theorem in this field. At the time, no one yet spoke of a "group," a term introduced but never properly defined by Galois. The first results were in fact established in the context of substitutions, now called permutations.
The rediscovery of Galois
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Galois's research remained little known until Joseph Liouville (1809–1882) rediscovered it in 1843 and, after filling in a few missing steps, published it three years later in the Revue de mathématiques pures et appliquées. These gaps explain why the subject had been neglected for more than a decade. In 1845, Augustin-Louis Cauchy (1789–1857) resumed his study of substitutions, which he had published in 1815 in the Journal de l’École polytechnique. Was this a coincidence, or had Galois's research inspired him?
