A FORGOTTEN EPISODE in French-occupied Naples in the years around 1800âjust after the French Revolutionâillustrates why it makes sense to see mathematics and politics as entangled. The protagonists of this story were gravely concerned about how mainstream mathematical methods were transforming their worldâsomewhat akin to our current-day concerns about how digital algorithms are transforming ours. But a key difference was their straightforward moral and political reading of those mathematical methods. By contrast, in our own era we seem to think that mathematics offers entirely neutral tools for ordering and reordering the worldâwe have, in other words, forgotten something that was obvious to them.
In this essay, Iâll use the case of revolutionary Naples to argue that the rise of a new and allegedly neutral mathematicsâcharacterized by rigor and voluntary restrictionâwas a mathematical response to pressing political problems. Specifically, it was a response to the question of how to stabilize social order after the turbulence of the French Revolution. Mathematics, I argue, provided the logical infrastructure for the return to order. This episode, then, shows how and why mathematical concepts and methods are anything but timeless or neutral; they define what âreasonâ is, and what it is not, and thus the concrete possibilities of political action. The technical and political are two sides of the same coinâand changes in notions like mathematical rigor, provability, and necessity simultaneously constitute changes in our political imagination.
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