Theories (including mathematical models) put forward for a particular phenomenon are unacceptable, if they do not satisfy certain criteria (see, for instance, [1, p. 14; and 2, pp. 190-1961). The objective criterion of correctness demands that the behaviour predicted by the model agrees with the observed data, to the accepted accuracy. There might be several other correct theories, to the given accuracy. In practice, preference is given to the theory which the researcher deems to be the simplest. Courant, in concluding his essay [6, p. 27], emphasizes a fundamental difference between the research formulations and goals of the mathematician and of the scientist solving an applied problem. For the mathematician, the only criterion of the applicability of a theory is its logical consistency. The desire for generality is incompatible with the requirement that the theory should be simple. And since the object of mathematical research is the properties of mathematical relations, even in cases where these relations have arisen in mechanics, for instance, they are usually treated as abstract generalizations, and their correctness (in the above sense) is not discussed. However, if such research claims to have an applied value, it should, of course, satisfy the criteria of correctness and simplicity. In a number of cases, it is found that the mathematical construction cannot be applied in practice. This assertion is demonstrated here on the models of Lindelof and Kozlov.
