"Although... structural theories of a major division of analysis originated in the late nineteenth century, they are more in the spirit of the general analysis of the twentieth. Their primary objectives are to discover what can be done rather than to do it, and to give criteria for what cannot be done. ...[A]s in Abel’s proof that the general quintic is not solvable by radicals, a demonstration of impossibility definitely disposed of what might seem a reasonable problem. Once more the methodology of Abel and Galois made an outstanding contribution to the development of mathematics. In this connection it is interesting to recall Lie’s opinion that the pattern of nineteenth century mathematics was laid out by four men, Gauss, Cauchy, Abel, and Galois."
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Évariste Galois
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