## Maxwell’s choice

What was Maxwell’s conception of Faraday’s methodology? Maxwell considered Faraday a mathematician—this was a bold move. No one else in the community (including Faraday himself!) had this understanding of what it meant to be a mathematical physicist. Maxwell had a unique view of mathematics, namely, it need not be expressed in equations or other formal structures. Faraday’s “speculations” were in fact mathematical and only had to be put in terms of standard formalism for this to be obvious to others. The “geometry of position” offered Maxwell an example of a mathematical domain that did not involve calculations. Faraday’s lines of force occupy the same position in electromagnetic science as a pencil of lines do in the “geometry of position.” They furnish a method of constructing an exact mental image of the thing we are reasoning about. Maxwell realized the advantages of Faraday’s methodology that remained hidden to others and then proceeded to develop successive theories of electromagnetism in which he sought to maintain the core concepts he inherited from Faraday. At the same time, Maxwell had been consistent throughout the years in respecting the achievements of Ampère, but Maxwell was critical of Ampère’s approach. Maxwell thought that the origin of this approach was rooted in mathematics and astronomy from which Faraday departed. Essentially, Ampère—in contrast to Faraday—accepted the application of the Newtonian concept of action at a distance to electromagnetism. Maxwell recorded the importance of Ampère’s achievements in electromagnetism, but then distanced himself from Ampère’s methodology.