Mathematics: A Tool or Description? Instrumentalistic and Realistic Interpretations of the Applications of Mathematics

In the paper there are presented two proposals of the interpretations of the applications of mathematics in the natural sciences - realistic and instrumentalistic. The realistic conception, in accordance with the successes of science, maintains that there exists some kind of correspondence between the mathematical structures and the internal structure of the world. It is expressed in the thesis of the mathematicality of nature. The instrumentalistic approach separates the cognitive content of the scientific theory from the mathematical means of expression of the content. In this approach the mathematical categories do not represent any aspect of the modelled reality. In the final part of the paper the author undertakes such an attempt of approaching the applications of mathematics which, while combining the advantages of the above discussed conceptions, would be devoid of their disadvantages