A critical number which one may call a process classification number has been introduced more than twenty years ago [1 to 3]. It has been called the Janeschitz-Kriegl number Jk [4]. It gives the ratio of two times governing the solidification process of a crystallizing material: one for the thermal equilibration and the other for the crystallization process itself With one class of materials (mainly metals) the thermal equilibration time is usually the longest time, dependent of course on the sample thickness. With another class (glass forming minerals) always the crystallization time is the longest time. So, one obtains (as extreme cases) purely heat diffusion controlled and purely crystallization kinetics controlled processes. Only polymers (and probably also other crystallizing soft condensed matters) show an intermediate behavior, as can be characterized by the announced number. So far, however this number could not be made operational because of a lack of crystallization kinetics data. This shortcoming could now be cleared away. It turns out that between the values of Jk for HDPE and for i-PS a gap exists of more than six decades. In their behavior all other known industrial polymers lie between these limiting cases. In this way the transition from heat diffusion controlled to crystallization kinetics controlled processes is clearly marked. For the now relevant interaction between cooling and crystallization a new mathematics was required [2]. It enables also the description of the development of structures, which are of particular interest for the quality of the product.