Mathematics is a tool for abstraction, a way to the core of scientific knowledge. Mathematics is not interested in details; for it, life is a kind ofcomplex systems with special relations between elements. For the description of different properties of life, there are various mathematical models. Probably, it is impossible to design a universal model of life; each model has its own field of application and level of approximation. Attractiveness of mathematical models does not consist in their complexity, but in their lucidity and explanatory power. According to Einstein, ''Models should be as simple as possible, but not more so.''
One of the first biological models was the Malthus model of exponential growth (1800). It was developed for the field of population dynamics by the Lotka-Volterra models (1925-31). Models oflife were proposed by J. von Neuman, R. Tom, H. Meinhard, and others; mostly they were differential models. Their use was very productive; in particular, they are a basis for the nonlinear analysis.
Another interesting mathematical tool for life description is the theory of cellular automata. This kind of discrete model has a property to be chaotic at the microlevel and ordered at the global level. In principle, one can imagine the world as a cellular automaton with elements -physical particles. The well-known Game of Life of Conway (1970), which really reflects some features of real life, is also a cellular automaton.
Usually mathematical methods are numerical, but it seems to be a very perspective way to use topological and algebraic approaches also. The above-mentioned topolo-gical theory of ecological niches can be considered as an example of this way.
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