1. The dissertation was by L. Kronecker, cf.Werke, 5 Vol., Teubner, Leipzig, 1895-1930, Vol. 1, p. 73. The opponent was G. Eisenstein. The source I am aware of for the name and the opinion of the opponent is a footnote by E. Lampe to a lecture by P. du Bois-Reymond,Was will die Mathematik und was will der Mathematiker?, published posthumously by E. Lampe in Jahresbericht der Deutschen Mathematiker Vereinigung 19 (1910), 190–198.
2. For a discussion of a number of such opinions see A. Pringsheim,Ueber den Wert und angeblichen Unwert der Mathematik, Jahresbericht der Deutschen Mathematiker Vereinigung 13 (1904), 357–382.
3. Letter to F. W. Bessel, 18 November 1811. See G. F. Auwers Verlag,Briefwechsel zwischen Gauss und Bessel Leipzig 1880, p. 156.
4. Actually the beginnings of group theory can already be traced to some earlier work, notably by Lagrange, which was in part familiar to Galois. The latter’s standpoint was, however, so general and abstract and, in addition, so sketchily described that it was assimilated only slowly. For historical information on the theory of equations and the beginnings of group theory see, for example, N. Bourbaki,Eléments ďhistoire des mathématiques, Hermann éd., Paris, 1969, third and fifth articles.
5. F. J. Dyson,Mathematics in the physical sciences, Scientific American 211 September (1964), 129–146.