Mathematics as Power: Massimo Mazzotti on the Politics of Numbers

January 21, 2025

Massimo Mazzotti, L&S history professor, speaks about his book, Reactionary Mathematics: A Genealogy of Purity.

In this interview, Massimo Mazzotti discusses the inspirations behind Reactionary Mathematics: A Genealogy of Purity, a thought-provoking exploration of the relationship between mathematics and politics. Drawing from historical contexts, the book examines how mathematics has been mobilized to support revolutionary transformations and resist social upheaval, ultimately shaping its modern image as a politically neutral discipline. Mazzotti offers readers a fresh perspective on the historical roots of our algorithmic society and the inherently political nature of mathematics, inviting critical engagement with its role in ordering the world.

Through mathematics, we order and reorder the world, we impose structures on it and, therefore, we open up certain possibilities while closing others down.

Massimo Mazzotti

What inspired you to write Reactionary Mathematics: A Genealogy of Purity, and how does it build on or diverge from your previous work, particularly The World of Maria Gaetana Agnesi: Mathematician of God?

The book addresses a fundamental question in the history of science: what is the relation between mathematics and politics? Does it even make sense to talk of a mathematics that is reactionary rather than, say, revolutionary? My answer is that, yes, it makes sense.

The inspiration for this book was certainly our present condition. We live in a world that is pervaded by mathematics, and yet its presence and workings are largely invisible to most of us. There has been, in the last few years, a growing awareness that processes of quantification and mathematical procedures shape our social life—think about the recent popularity of an obscure technical term like “algorithm.” A historical perspective can help us see the long-term process that brought about the conditions for the algorithmic society we now live in.

The book offers a genealogy of how we came to see certain mathematical techniques as neutral tools that we could use to represent and control both nature and society. This neutrality is grounded on an idea of mathematics as a pure body of knowledge, part of which can be used to model aspects of the empirical world. This is a relatively modern idea, which dates to the period that we now call the age of revolutions. It’s not a coincidence that such a profound change in the meaning of mathematics should take place during a period of major social and political upheaval.

My previous book on the mathematician Maria Gaetana Agnesi (1718-1799) explored an earlier moment. One in which Agnesi, the first female mathematician to publish a book of mathematics (1748), became fascinated by mathematical reasoning in itself, and tried to get to the significance of its purest forms. Which for her was, above all, a spiritual significance.

We live in a world that is pervaded by mathematics, and yet its presence and workings are largely invisible to most of us.

Massimo Mazzotti

Your work ties mathematical development to broader social, political, and economic orders. Could you elaborate on how pure mathematics became a tool for reasserting authority during the Restoration?

The first half of the book reconstructs the emergence of a new mathematics that, by the end of the eighteenth century, was closely associated with administrative reform, the necessities of the modern centralized state, and the increasingly pervasive practices of capitalism. By the 1790s, at the opening of the revolutionary period, this operative mathematics was mobilized by militant groups, like the Jacobins, to support a radical transformation of political order. The analytic logic of calculus and statistics was, in their eyes, the very logic of revolution. At this point, mathematics was perceived as intrinsically political, something very distant from our contemporary views.

As revolution, and French troops, spread across Europe, something very interesting started to happen. Resistance to the revolutionary principles and to the form of the modern state assumed also a mathematical dimension. By this, I refer to the unprecedented concerns with the foundations of mathematics: why should we trust its results? Expressed through the language of mathematics and philosophy, these foundational doubts were in fact undermining the legitimacy of the new social and political projects. Centering pure mathematics as the core of the discipline was a response to these concerns, and a way to argue that applications of mathematical techniques to social issues had only limited epistemological validity. This shift in the understanding of the meaning and scope of mathematics had thus produced, I argue, a reactionary mathematics.

The modern liberal state that consolidated its forms during the Restoration certainly mobilized mathematics and other kinds of technical knowledge to support its action. But it was a mathematics that has been politically neutralized: a tool to be deployed by new technical elites for specific and limited purposes. A mathematics that did not reveal the hidden structures of reality and could not guide political transformations. This was the dawn of the world of modern mathematics: a world of mathematical self-restriction, in which technical knowledge cannot be the engine of social change.

How did you go about uncovering the historical and political context that shaped the mathematical resistance in Naples? Were there specific sources that were particularly illuminating?

The Neapolitan case is not exceptional, but it’s interesting because the experience of these political and cognitive transformations was more extreme there than in other parts of Europe. The sources from Naples are more explicit and radical when it comes to expressing these views for or against revolutionary mathematics. In particular, I have found instructive to dig archival evidence on the life and work of Nicola Fergola (1753-1824), the most prominent Neapolitan mathematician of his generation. What emerges is the portrait of a tormented man, whose obsession with mathematical purity was matched only by his relentless pursuit of spiritual perfection and by his hatred of revolutionary principles. Thanks to his manuscripts, I began to realize how mathematics, religion, and politics came seamlessly together in the lived experience of the protagonists of my book.

How do you hope modern readers, especially those with interests in the history of mathematics, politics, or science, will engage with the ideas presented in your book?

I argue that the image of the neutrality of mathematics and, by extension, of highly technical knowledge, is a modern construct, with a precise genealogy. In reality, mathematics is always political, and not just because it can be deployed to achieve political goals. I’m gesturing toward something more fundamental. Through mathematics, we order and reorder the world, we impose structures on it and, therefore, we open up certain possibilities while closing others down. I’d like readers to engage with my suggestion that the mathematical always and necessarily entails the political.

Are you working on any other research or projects?

I’m writing up a history of Olivetti, an Italian company that made typewriters, calculators, and computers. I focus on its mid-century moment (1930-1960) and argue that its innovative industrial design and progressive agenda were part of a broader project for the reconstruction of Italy and Europe along the lines of a new democratic socialism. Central to this project was the notion of technology for community, as community was to become the key actor of of a more just political life. It’s the story of a failure, to be sure, but a failure that can be very instructive when seen for today’s Silicon Valley.

What’s currently on your nightstand?

Rebecca Solnit Orwell’s Roses. I’m always up for beautifully written essays, and for stories that weave together what, at first, seem distant and unrelated.