The role of mathematics in J.C. Maxwell's field theory

Abstract

Phenomenological concepts describing electromagnetic interactions were expressed mathematically by Maxwell in his theory of electromagnetic field. His work was not free of mechanistic influences. It also broke down some elements of inductionistic paradigme. Maxwell's theory cannot be reduced to a simple methodology of solving equations. Physical theories imply a deeper understanding of equations which carry an 'immaterial content'. The 'higher symmetries' hidden in the equations should to use Einstein's expressions be viewed as a 'stuff of the Universe'.