[Non-statistical biomathematics: opinions, perspectives, problems].

Abstract

By way of tracing the position of biomathematics and its main subjects a discussion is given of the mutual relations between the branches of natural sciences and mathematics within the hierarchically structured building of science. The general possibilities of a mathematical expressing and description of the biological features "complexity", "variability", and "discontinuity" and the limits are shown of validity of mathematical formulations in the field of biology. To this point representative opinions of research workers are quoted. The only direct ways of application of mathematics in biology seems to be the treatment of "variability" by statistical biomathematical means which offers the mathematical services in the design of experiments as well as in the quantitative-descriptive evaluation of experimental results. Aside from these ways a direct mathematical approach to biology is thought of being questionable because of the large differences between the levels of abstraction on which these two disciplines work. But the thesis is stated and supported that biophysics and biocybernetics as mediators provide an appropriate approach of the mathematics to such biological problems which arise from "complexity" and from "discontinuity". The kind of biomathematical tools, the goal of a biomathematical analysis, and the results of such an analysis get their meaning from the biophysical or biocybernetical modelling in which they are embedded. Example of working out of biomathematical methods and of application these methods are added.