Skew-symmetric differential forms possess properties that enable one to carry out a qualitative investigation of the equations of mathematical physics and the foundations of field theories. In the paper we call attention to a unique role in field theory of closed exterior skew-symmetric differential forms, which correspond to conservation laws for physical fields (to conservative quantities). At the same time, it was shown that such closed exterior forms can be derived from skew-symmetric differential forms, which follow from the mathematical physics equations describing material media such as thermodynamic, gas-dynamic, cosmic media. This points a connection the field theory equations with the mathematical physics equations. Such connection discloses the properties and specific features of field theory.