The formation of field theory in the second half of 19th century was a
prominent case of mathematisation processes, but also had
characteristics that made it strikingly different from other such
processes. Not only were Faraday's concepts not formulated in
mathematical terms of his time, but there were no mathematical tools
available that could easily be adjusted to those concepts. At the same
time, however, both Thomson and Maxwell credited Faraday for having
high mathematical qualities. In my talk, I shall analyze in detail how
exactly the mathematical character of Faraday's concepts could be
grasped that made an analytic approach possible in the end. The case
sheds light, finally, on a rather uncommon way of relating experiment
and mathematics.