Foreword to the special issue on 'Attempts of a mathematical uprising for restructuring biomedical sciences'

摘要

Mathematical Biology aims to provide a sound mathematical description of biological processes, with the use of tools useful in both theoretical or practical investigations. Reducing to the essential, there are two opposite approaches relevant in building a biomathematical model: either simplifying an inherently complicated biological pattern or being as close as possible to the experimental data. Passing from one extreme to the other, there are a number of different shades which span all of the possible intermediate choices.A crucial role is played by the power of the model of providing reliable forecasts (either qualitative or quantitative) that might not be evident to the experimenter. Viceversa, without any experiment, no model can be capable of giving an evaluable prediction. This is vaguely reminiscent of the ancient folk paradox "Which came first, the chicken or the egg?", becoming, in the present context, "Which came first, Mathematics or Biology?". Circumventing the rules, we support the point of view that the best choice is to take advantage of the complementarity of the two disciplines, with both pros and cons on both sides. On the one hand, Mathematics guide the modeling of many biological processes; on the other hand, Biology has contributed to the development of new mathematical techniques. Examples are provided by a variety of population dynamics, ecology, genetics and epidemics taking advantage of deterministic or probabilistic descriptions. Most of the joint work between biologists, physicists, chemists and engineers involve analysis of mathematical structures and its correspondent computational understanding.