 Nevertheless the proscription of infinitesimals did not succeed in extirpating them; they were, rather, driven further underground. Physicists and engineers, for example, never abandoned their use as a heuristic device for the derivation of correct results in the application of the calculus to physical problems. Differential geometers of the stature of Sophus Lie and Élie Cartan relied on their use in the formulation of concepts which would later be put on a “rigorous” footing. And, in a technical sense, they lived on in the algebraists’ investigations of non-Archimedean fields.