Mathematics plays a central role in the description, explanation and manipulation of natural phenomena. To what extent, and how and why mathematics applies to nature is a problem that has long occupied philosophers. Descartes, Leibniz, Kant, Mach and Poincaré, to mention some of the most distinguished names, offer global solutions to this problem that are based on deep-lying metaphysical assumptions. In this essay, I would like to suggest an alternative approach, which is piecemeal rather than global, and historical before it is metaphysical.
I want to propose, first, that the question of applied mathematics be recast as a question about how mathematics and physics, a physics “always already” mathematized, are partially unified at various points in history, in such a way that they can share certain items, problems and methods while nonetheless remaining quite distinct. And, second, I suggest that these unifications may be quite heterogeneous and variable over time.