Modeling natural phenomena is the ultimate goal of natural sciences. Mathematics too pays the tribute to this noble activity. Actually, practically all mathematical abstractions are rooted in practical problems. On the other hand, novel areas of applications call for developing of new mathematical concepts. In the last (XX-th) century, mathematics penetrate practically all natural and social sciences, from physics to linguistics and correspondingly new branches of mathematics were originated.
How different the modern mathematics would be if Newton paid attention to biology or sociology instead of physics?However, when the intellectual ``math engine'' starts to develop a theory in connection with the need of a natural or engineering problem, this development puts forward its own goals and develops its own means.
Is the situation out of control? Sure it is, and this is wonderful! Actually, mathematical theory may return the favor and become a useful tool for science in the future, or it may not. No one can judge on this matter.
The celebrated example of development of Non-Euclidean geometry illustrates this principle. Here how the story went: