Math(s), Philosophy, History

Math(s), Philosophy, History is an online reading group run by the Free Computing Lab. We read texts at the interface of mathematics, philosophy, and history. See Section B for more info.

We meet on an an approximately bi-weekly basis during the academic semester. This semester (Spring 2026) we are meeting on Fridays at 12pm-1.15pm EST.

To join our mailing list, please email maths@ohrg.org with the subject header ‘JOIN’, and a 1-2 sentence explanation of your interest in the group.

A. Sessions

Upcoming

Past

B. Our history in brief

C. Our focus

As computer science has grown in stature as a discipline in the university, as Moore’s law is pushing computing into all the corners of our life and thought, there is no better time to ask why a more robust rapport between mathematics and critical theory has not emerged. Is it as simple as the fact that, as Sarah Pourciau seems to suggest, humanistic thought is aligned with the apeiron, whereas the sciences by definition rely on ‘carving’ it up into peras (Pourciau, “On the Digital Ocean”)? Or is there an interdisciplinary space where one can test the waters of a common language? We are not imagining an transdisciplinary metalanguage which is so general that noone understands anything at all, but rather a space where thought can actually happen. Can mathematics serve as the ferryman to an epistemological place where disciplinary distinctions become water under the bridge?

More specifically, our readings are designed to help us wrap our heads around the history of modern mathematics. We take modern mathematics to mean the kind that influenced the amorphous era we currently call modernity, an era which bears a relation to capitalism, but is not (we don’t think) reducible to it. (In this characterization we follow the work of (Mehrtens, Moderne Sprache, Mathematik; Siegert; Gray; Hörl; Steingart).) Modernity has been understood as the attempt to be sure of ourselves without any external guarantee, such as God or a feudal order, and as such is broadly related to secular humanism (Ruda). Our group is interested in charting and hypothesizing whether the insights of modern mathematics have anything to do with this modernity, whether set theory represents anything significant in the history of philosophy.

This brand of secular humanism is significant and resonant in contemporary discussions about ‘ethical computer science’, or computing for the social good—as these debates (typically) do not hinge upon explicitly religious notions of morality or social determination, but rather point themselves towards an ambiguously modern notion of freedom and the construction of a society that optimizes for this notion.

D. Bibliography

Aaronson, Scott. Why Philosophers Should Care About Computational Complexity. 2013.
Babbage, Charles. On the Economy of Machinery and Manufactures. Charles Knight, 1832.
Berkeley, George. The Analyst; Or, A Discourse Addressed to an Infidel Mathematician: Wherein It Is Examined Whether the Object, Principles, And Inferences of the Modern Analysis Are More Distinctly Conceived, Or More Evidently Deduced, Than Religious Mysteries and Points of Faith. J. and R. Tonson and S. Draper, 1754.
Castelle, Michael. “Contextualizing High-Dimensional Communication: The Relevance of Linguistic Anthropology for Theorizing Large Language Models.” 2025.
Gray, Jeremy. Plato's Ghost: The Modernist Transformation of Mathematics. Princeton University Press, 2008, https://doi.org/10.1515/9781400829040.
Hörl, Erich. “Sacred Channels: The Archaic Illusion of Communication.” Sacred Channels, 2018, pp. 1–342.
Joque, Justin. Revolutionary Mathematics: Artificial Intelligence, Statistics and the Logic of Capitalism. Verso Books, 2022.
Krieger, Martin H. “Convention: How Means and Variances Are Entrenched as Statistics.” Doing Mathematics: Convention, Subject, Calculation, Analogy, World Scientific, 2015. Doing Mathematics: Convention, Subject, Calculation, Analogy.
Marx, George. “The Myth of the Martians and the Golden Age of Hungarian Science.” Science & Education, vol. 5, no. 3, July 1996, pp. 225–34, https://doi.org/10.1007/BF00414313.
Marx, Karl. Mathematical Manuscripts of Karl Marx. New Park Publications, 1983.
Mazzotti, Massimo. Reactionary Mathematics: A Genealogy of Purity. University of Chicago Press, 2023.
Mehrtens, Herbert. Moderne Sprache, Mathematik: Eine Geschichte des Streits um die Grundlagen der Disziplin und des Subjekts formaler Systeme. Suhrkamp, 1990.
Mehrtens, Herbert. “Nationalism and Internationalism.” L'Europe Mathématique/Mathematical Europe: Histoires, Mythes, Identités, edited by Catherine Goldstein et al., Les Editions de la MSH, 1996, pp. 519–29. L'Europe Mathématique/Mathematical Europe: Histoires, Mythes, Identités.
Miller, Jacques-Alain. “Suture (Elements of the Logic of the Signifier).” Screen, vol. 18, no. 4, 1977, pp. 24–34.
Naderi, Reza. “Mark and Lack: Formalism as Fidelity.” Crisis and Critique, vol. 5, 2018.
Peirce, Charles Sanders. Elements of Logic. Harvard University Press, 1974.
Pourciau, Sarah. “A/logos: An Anomalous Episode in the History of Number.” MLN, vol. 134, no. 3, 2019, pp. 616–42, https://doi.org/10.1353/mln.2019.0046.
Pourciau, Sarah. “On the Digital Ocean.” Critical Inquiry, vol. 48, no. 2, Jan. 2022, pp. 233–61, https://doi.org/10.1086/717319.
Rodin, Andrei. “Categorial Logic and Hegelian Dialectics.” Axiomatic Method and Category Theory, vol. 364, Springer Science & Business Media, 2013, pp. 128–36.
Ruda, Frank. Indifference and Repetition: Or, Modern Freedom and Its Discontents. Translated by Heather H. Yeung, Fordham University Press, 2023.
Schmid, Eric. “Diagonal Method and Dialectical Logic: Book Two Revisited.” 2025.
Serres, Michel. “Introduction.” A History of Scientific Thought: Elements of a HIstory of Science, Blackwell, Oct. 1995. A History of Scientific Thought: Elements of a HIstory of Science.
Siegert, Bernhard. Passage des Digitalen. Brinkmann U. Bose, 2003.
Steingart, Alma. Axiomatics: Mathematical Thought and High Modernism. University of Chicago Press, 2023.
Thurston, William P. “On Proof and Progress in Mathematics.” 18 Unconventional Essays on the Nature of Mathematics, edited by Reuben Hersh, Springer-Verlag, 2006, pp. 37–55, https://doi.org/10.1007/0-387-29831-2_3. 18 Unconventional Essays on the Nature of Mathematics.
Turing, Alan. “Can Digital Computers Think? (1951).” The Essential Turing: Seminal Writings in Computing, Logic, Philosophy, Artificial Intelligence, And Artificial Life Plus The Secrets of Enigma, edited by B. Jack Copeland, Clarendon Press, 2004, pp. 476–506. The Essential Turing: Seminal Writings in Computing, Logic, Philosophy, Artificial Intelligence, And Artificial Life Plus The Secrets of Enigma.
Turing, Alan. “Intelligent Machinery, A Heretical Theory (C.1951).” The Essential Turing: Seminal Writings in Computing, Logic, Philosophy, Artificial Intelligence, And Artificial Life Plus The Secrets of Enigma, edited by B. Jack Copeland, Clarendon Press, 2004, pp. 465–75. The Essential Turing: Seminal Writings in Computing, Logic, Philosophy, Artificial Intelligence, And Artificial Life Plus The Secrets of Enigma.
Vasiliev, N. A. “Imaginary (Non-Aristotelian) Logic.” Atti Del V Congresso Internazionale Di Filosofia, special issue of Atti Del V Congresso Internazionale Di Filosofia, 1925, pp. 107–09.
Von Foerster, Heinz. Understanding Understanding: Essays on Cybernetics and Cognition. Springer New York, 2003, https://doi.org/10.1007/0-387-21722-3_10.
Von Neumann, John. “The Mathematician.” The Works of the Mind, vol. 1, no. 1, 1947, pp. 180–96.
Warwick, Andrew. Masters of Theory: Cambridge and the Rise of Mathematical Physics. University of Chicago Press, 2003.
Weatherby. Language Machines: Cultural AI and the End of Remainder Humanism. University of Minnesota Press, 2025.