Traditionally, mathematics played an important role in the development of science since mathematics was used in other sciences, while, today, it is possible to trace the influence of mathematics in other branches of modern science, which could hardly be developed without the application of scientific approaches based on mathematical methods and knowledge. In this respect, it is not surprising that many specialists pay a lot of attention to mathematics as a fundamental science for natural sciences. At this point, it is worth mentioning Eugene Wigner, who lays emphasis on the fact that mathematics, regardless of its difference and uniqueness compared to natural sciences, such as physics, is still extremely important to natural science because it provides natural science with instruments that can be used to develop natural sciences, their basic concepts and principles and check their scientific reliability and validity.
On analyzing Wigner’s views on mathematics, it should be pointed out that his views are a bit controversial. On the one hand, he proves that mathematics is unique science which is not directly linked to natural sciences or, at any rate, it is quite difficult for an average person to trace the close correlation between mathematics and natural sciences. On the other hand, he argues that mathematics does matter for natural sciences to the extent that such sciences as physics could hardly be developed without mathematics which provided natural sciences with tools they used to shape their theoretical ground.
In spite of the existing controversies in his views, Wigner is definitely an ardent support of a significant contribution of mathematics to the development of natural sciences. In his article he focuses on two major points. Firstly, he argues that “mathematical concepts turn out in entirely unexpected connections”¯ and, what is even more important for natural sciences, “they often permit an unexpectedly close and accurate description of the phenomena in the connections”¯ (Wigner). In such a way, it is obvious that Wigner admits that it is impossible to foresee where mathematics can be applied and where it can be beneficial for the development of a natural science. This means that there is an element of unexpectedness in the application of mathematics in natural sciences. Hence, the study of mathematics and its application to natural sciences is important because it can contribute to unexpected discoveries that can be made in natural sciences with the help of mathematics.
Another important point Wigner stresses in his article is the effect of the unexpectedness of the use of mathematics in natural sciences. To put it more precisely, he argues that it is quite difficult, if not to say impossible, to know “whether a theory formulated in terms of mathematical concepts is uniquely appropriate”¯ (Wigner). In this respect, it should be said that Wigner attempts to view mathematics and its application to natural sciences from the stand point of an average person, who is not proficient in mathematics and natural sciences. In actuality, it seems to be quite unusual that the author tends to a simplification of view on the mathematics and its application to natural sciences. However, he uses this approach to hook the audience and to uncover the problem of the interrelationship between mathematics and natural sciences in depth.
At the same time, Wigner clearly distinguishes mathematics and physics. In such a way he contributes to the perception of mathematics and physics as totally different science, but, further in his article, the author shows that, in spite of the existing differences between mathematics and physics, they are still closely connected at certain points. In fact, the author shows that mathematics played an important role in the development of physical theories, while the success of physical theories overshadowed the significance of mathematics.
However, in actuality, mathematics was always used in physics and in the development of physical theories. In fact, it is only an ignorant, unprofessional view on physical theory can lead to the conclusion that physics does pretty well without mathematics, while, in the real science mathematics is an essential science which is closely intertwined with the development of natural sciences. At the same time, Wigner admits that physics is really a successful science, which has made a tremendous progress. But, in spite of its uniqueness, physics is inseparable from mathematics. In such a context, the conclusion Wigner makes seems to be quite logical: “The miracle of appropriateness of the language of mathematics for the formation of the laws of physics is a wonderful gift which we neither understand nor deserve”¯ (Wigner).
In fact, Wigner is definitely right in his belief that mathematics is important for the development of natural sciences. At the same time, he tends to certain mysticism, which is typical neither for mathematics nor natural sciences. What is meant here is the fact that he argues that mathematics does matter but it is very difficult to understand the mechanism by means of which mathematics influences natural sciences since the use of mathematics in natural sciences leads to unexpected outcomes. However, the unexpected results do not necessarily mean that it is impossible to clearly define the interconnection between mathematics and natural sciences.
Obviously, the intention of the author to position himself as an ordinary person who attempts to understand the connection between mathematics and natural sciences contributes to a comprehensible writing style and clear messages which average readers can understand even if they do not have profound knowledge in the field of mathematics. On the other hand, the author clearly gives insight which indicates to the way mathematics is intertwined with natural sciences. He emphasizes the use language of mathematics in natural sciences that proves the fact that the author is conscious of the interdependence of mathematics and natural sciences since language is definitely the core element of any science. It is impossible to develop a science without the use of specific and concise language which allows describing its fundamental concepts, theories, rules, etc. Wigner is apparently right in his view on mathematical language as a foundation on the ground of which basic laws of physics were worded in.
Thus, taking into account all above mentioned, it is possible to conclude that Wigner researches the interdependence between mathematics and natural sciences and arrives to a logical conclusion that mathematics and natural sciences are closely intertwined. At the same time, he emphasizes that unexpectedness of the use of mathematics in natural sciences makes it impossible to predict when and how mathematics can be helpful in natural sciences. What he is definitely certain in is the fact that the language of mathematics is used in natural sciences that is probably the most important field of application of mathematics in natural sciences.