As has been shown experimentally in our laboratory, the number of athermal nuclei, as found in unnucleated quiescent melts, increases tremendously with decreasing temperatures of crystallization, down to severe degrees of undercooling. One cannot assume that the presence of heterogeneous nuclei can explain this horrible temperature dependence. Moreover, one can conclude that the number fraction of macromolecules participating in these athermal nuclei is extremely low. Macroscopically, these nuclei seem to form a number of spots in a sea of homogeneous undercooled liquid.In the present paper the proposal is made that this number can be estimated from the probability of the occurrence of local molecular arrangements of varying quality, which preexist by accidence in a so-called living equilibrium in the stable melt, i.e. above the equilibrium melting point. During a rapid quench, realistic for processing conditions, these local arrangements are successively stabilized and serve as precursors for the start of crystallization. Dependent on their quality, this stabilization occurs over a broad range of crystallization temperatures. A selection rule for their effectiveness is derived from thermodynamics. In addition, reasons are discussed for the observed strong influence of flow on the formation of nuclei. From the "short-term" creep experiments, which are successful even at low degrees of undercooling, the impression has been obtained that during flow an unimaginable long-distance mechanical interaction becomes effective between the nuclei of crystallization. However, a more convincing explanation has been found recently: it is described at the end of this paper.