"Gauss took as the subject for his doctor’s dissertation (1799) a proof of the : an algebraic equation has a root of the form a + bi, a , b real. ...After Girard’s conjecture, there had been attempts at proof, including essays by D’Alembert (1746) and Euler (1749). All were faulty, as were the first and fourth attempts (1799) by Gauss. ...[T]he fundamental theorem in its classic form, as proved in the theory of functions of a complex variable, is no longer regarded as belonging to algebra. It is supplanted in modern algebra by a statement which is almost a triviality. The basic ideas of the modern treatment go back to Galois.., Dedekind.., and Kronecker.., not to Gauss."
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Évariste Galois
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