How Classical Physics Helps Mathematics

The history of the relations between Physics and Mathematics is a long and romantic story. It begins in the time of Archimedes, and up to the seventeen and eighteen centuries the relations were quite cordial. Mathematics supplied the tools for the solution of physical problems, and in its turn, the necessity to develop proper tools was a very strong factor in stimulating progress in mathematics itself. The problem of the brachistochrone, which was a starting point in the creation of variational calculus, is a classic example. In those times most outstanding mathematicians were also physicists. In the nineteen century the relations were still close, but some tendency to alienation and separation had become visible. Riemann was both mathematician and physicist, while Weierstrass was a pure mathematician and Faraday was a pure physicist. Until the middle of the last century physics was not divided into theoretical and experimental branches. In the second half of the century the efforts of giants like Maxwell and Boltzmann gained for theoretical physics the status of an independent power. What they created was classical theoretical physics. The profession of the theoretical physicist was new for that time. Like mathematicians, theoretical physicists use only paper and pen. However, they did not identify themselves with mathematicians. They were sure that what they study is not a world of abstract mathematical concepts, but real nature. On the other hand, pure mathematicians righteously considered results obtained by theoretical physicists as not rigorously justified. Only a few outstanding mathematicians, like Poincare, were at the same time qualified theoretical physicists. Alienation between physics and mathematics increased after the First World War, which took the lives of a lot of young talents educated by old