This paper explores the role of mathematical formalism in physics theories through an analysis of the work of physicists Michael Faraday and James Clerk Maxwell in the field of electromagnetism. After a brief description of the educational backgrounds of each scientist, their views on the nature of physics theory and its relationship to mathematics are contrasted. Faraday sought a mathematics-free theory to describe the results of his experiments, producing a family of concepts that became the roots of electromagnetic field theory. Maxwell built upon these concepts, giving them robust mathematical expression and incorporating them into one unified theoretical picture. An analysis of the resulting electromagnetic field theory is then provided in order to demonstrate the contributions of mathematical formalisms to the theory. This analysis supports the conclusion that mathematical expressions allow for theoretical developments that may not otherwise be discovered.
Israelsen, Shannon P.. "The Scientific Theories of Michael Faraday and James Clerk Maxwell." The Purdue Historian 7, 1 (2014). https://docs.lib.purdue.edu/puhistorian/vol7/iss1/1