222 ABSTRACT ALGEBRA impenetrable (or wrong) to his contemporaries, who weren't prepared for it. (Gauss might have grasped it, but he seems never to have looked at it.) Finally it was clarified by Camille Jordan in his book Traite des substitutions et des equations algebriques around 1870. Two young men who came to Paris in the late 1860s—Felix Klein and Sophus Lie—learned Galois' theory from Jordan and were profoundly influenced by it. Klein was led to articulate his Erlanger Programm describing all geometries in terms of the action of a group of isometries on a space. Lie was motivated to search for a Galois Correspondence for Differential Equations, which led him to the important concepts of a Lie group and a Lie algebra. And so mathematics evolves.
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