I work in the area of the history and philosophy of mathematical physics
and at present I'm exploring how mathematics was used by those who
followed the Scottish physicist, James Clerk Maxwell (d. 1879), and who
developed electro-magnetism in 19th Britain. I'm interested in issues
such as the ways in which mathematical formulae are given physical meaning
and significance, and in general, used to represent physical phenomena.
In particular I would like to see if I could forge any links between these
issues as they appear in the development of electromagnetic theory and the
discussions on the significance of negative and imaginary numbers (early
19th century, e.g., Woodhouse) and those to do with the meaning of the
abstract or symbolic algebra that emerged in the 1830s in Britain
(Peacock, Babbage, de Morgan).
At least I notice hints of a similarity in the project of the "explanation
of the meaning of the symbolic results of Algebra" (de Morgan, 1939) and
Maxwell's later phrases of interpreting mathematical expressions
physically. William Whewell's a key figure in these issues in bridging
the "mathematical" and "physical worlds." Any suggestions on focusing the
"meaning of mathematics" issue (the phrase is possibly too wide) in the
early to mid part of 19th century Britain welcome.
Regards,
Ron Anderson
Department of Philosophy
Boston College