Remarkable for their technical elegance and originality, Cauchy's two papers on permutations (see the article "Substituting to count") laid the foundations of substitution theory and, consequently, group theory. Cauchy studied permutations in their own right, whereas Waring, Vandermonde, Lagrange and Ruffini had regarded them merely as a tool for solving algebraic equations. In developing his ideas, Cauchy introduced the notions of a cyclic group and of partitioning a group into cosets of a subgroup. His work nevertheless went unnoticed by his contemporaries, with the brilliant exceptions of Abel and Galois, who knew how to put it to use. Galois read Cauchy's papers in the Journal de l’École polytechnique and drew from them his definitions of permutation and substitution.
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Henri d’Artois, son of Charles X, around 1833,
when Cauchy was his tutor in Prague.
