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What I did with mathematics March 4, 2008

Posted by Will Thomas in History 174.
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I want to come back to yesterday’s post soon, because I have a few crackpot theories I’d like to share about the relationship between naive positions and the continued preponderance of arcane and disconnected case studies in the history of science, but, before the moment is past, I’d like first to come back to my problem with mathematics in the history of science.

Eventually, I did come across a pretty helpful book, Roger Hahn’s recent biography of Pierre Simon Laplace, which did a very nice job of lucidly placing Laplace within his cultural, institutional, and intellectual context. What more could a historian ask? It leads me to suspect that there is actually a pretty decent French-language literature out there on this (Hahn’s book was originally in French; maybe a post on what areas of the non-English literature need to be read is forthcoming?). I also have my curiosity piqued about a translated book by Johan Christiaan Boudri called What Was Mechanical About Mechanics? The Concept of Force Between Metaphysics and Mechanics from Newton to Lagrange, although I have no idea if it’s any good.

Lamentably, my own approach largely centered on the old W. W. Rouse Ball model of presenting a series of biographies. But I spiced it up with quite a bit of exposition on the growth of methods of approximation, the development of theoretical aids to calculation (Euler’s formula, the Euler-Lagrange equations, etc…), methods of data analysis, all with an eye toward representing physical phenomena in an acceptable mathematical model, which clearly departs from Cartesian/Leibnizian ideas about the justification of mathematics in direct mechanical explanation. Instead, the ability to predict and verify becomes the gold standard of what constitutes knowledge in physics.

More concretely, the development of analyses consistent with each other and with fundamental principles like Newton’s laws becomes the heart of what it means to be a theoretical physicist in the 1700s and after. This shift was made possible through the analytical versatility of the growing mathematical toolkit to support the burden (say, of demonstrating the stability of the solar system), and an agreement to abandon the requirement of clear philosophical interpretation in mathematical formulation (how can you, when you’re doing things like cutting off higher order terms of Taylor series?).

I really tried to drive home the centrality of an analytical toolkit to physics practice and self-identity; and also tried to give some sense of changing institutional venues; from isolated chairs at universities like Cambridge and Basel (the Bernoullis), to dedicated positions in scientific academies (Euler, d’Alembert, etc…), to the proliferation of posts in state-sponsored institutions (Ecole Militaire, Ecole Polytechnique), especially in the aftermath of the French Revolution.

I’m pretty sure it was boring and flew mostly over their heads, but I learned a lot trying to come up with a coherent story to tell about what happened to mathematics and physics in the 1700s.



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