 A major development in the refounding of the concept of infinitesimal took place in the 1970s with the emergence of synthetic differential geometry, also known as smooth infinitesimal analysis  (SIA).[47]  Based on the ideas of the American mathematician F. W. Lawvere, and employing the methods of category theory, smooth infinitesimal analysis provides an image of the world in which the continuous is an autonomous notion, not explicable in terms of the discrete. It provides a rigorous framework for mathematical analysis in which every function between spaces is smooth (i.e., differentiable arbitrarily many times, and so in particular continuous) and in which the use of limits in defining the basic notions of the calculus is replaced by nilpotent infinitesimals, that is, of quantities so small (but not actually zero) that some power—most usefully, the square—vanishes. Since in SIA all functions are continuous, it embodies in a striking way Leibniz’s principle of continuity Natura non facit saltus.