ABSTRACT
The problem of morphogenesis - broadly understood as the origin and evolution of biological structures - is one of the outstanding questions in present day biology. The differential model offers the ultimate motivation for the introduction of quantitative models in science. Nevertheless, its use is fraught with grave difficulties. Granted that all local morphological or physiological phenomena inside a living being occur according to local biochemical determinism, the problem is to explain the stability and the reproduction of the global spatio–temporal structure in terms of the organization of the structure itself. There appears to be a striking analogy between this fundamental problem of theoretical biology and the main problem considered by the mathematical theory of topology, which is to reconstruct a global form, a topological space, out of all its local properties. A new mathematical theory nearer to the qualitative thinking of the topologist than the quantitative estimates of classical analysis seems particularly relevant.
