[maths:24-06-21]

    Pourciau on number and the digital ocean

    Session
    Date
    21 June 2024
    Reading
    Pourciau, A/Logos (2019)
    Pourciau, On the Digital Ocean (2022)
    Authors
    Sarah Pourciau
      [maths:24-07-12]

      Aaronson on computational complexity

      Session
      Date
      12 July 2024
      Reading
      Aaronson, Why Philosophers Should Care about Computational Complexity (2013)
      Authors
      Scott Aaronson
        [maths:24-07-26]

        Thurston on proof and progress

        Session
        Date
        26 July 2024
        Reading
        Thurston, On Proof and Progress in Mathematics (2006)
        Authors
        William P. Thurston
          [maths:24-08-09]

          Von Neumann on the mathematician

          Session
          Date
          9 August 2024
          Reading
          Von Neumann, The Mathematician (1947)
          Authors
          John von Neumann
            [maths:24-08-30]

            Gray on the modernist transformation of mathematics

            Session
            Date
            30 August 2024
            Reading
            Gray, Plato's Ghost (2008), pp.18-38
            Authors
            Jeremy Gray
                [maths:24-10-04]

                Peirce on the elements of logic

                Session
                Date
                4 October 2024
                Reading
                Peirce, Elements of Logic (1974), pp.134-173
                Authors
                Charles Peirce
                  [maths:24-10-17]

                  Babbage on the economy of machinery

                  Session
                  Date
                  17 October 2024
                  Reading
                  Babbage, On the Economy of Machinery and Manufactures (1832), pp.i-50
                  Authors
                  Charles Babbage
                    [maths:24-11-15]

                    Joque on revolutionary mathematics (cancelled)

                    Session
                    Date
                    15 November 2024
                    Reading
                    Joque, Revolutionary Mathematics (2022)
                    Authors
                    Justin Joque
                      [maths:25-01-24]

                      Serres on the history of scientific thought

                      Session
                      Date
                      24 January 2025
                      Reading
                      Serres, Introduction (1995)
                      Authors
                      Michel Serres
                        [maths:25-02-06]

                        Hörl on sacred channels

                        Session
                        Date
                        6 February 2025
                        Reading
                        Hörl, Sacred Channels (2018), pp.89-108
                        Authors
                        Erich Hörl
                          [maths:25-02-20]

                          Krieger on convention in statistics

                          Session
                          Date
                          20 February 2025
                          Reading
                          Krieger, Convention: How Means and Variances Are Entrenched as Statistics (2015)
                          Authors
                          Martin Krieger
                            [maths:25-03-07]

                            Vasiliev on imaginary logic

                            Session
                            Date
                            7 March 2025
                            Reading
                            Vasiliev, Imaginary (Non-Aristotelian) Logic (1925)
                            Authors
                            N. A. Vasiliev
                              [maths:25-04-03]

                              Marx’s mathematical manuscripts

                              Session
                              Date
                              3 April 2025
                              Reading
                              Marx, Mathematical Manuscripts of Karl Marx (1983), pp.109-119
                              Authors
                              Karl Marx
                                [maths:25-04-17]

                                Warwick on Cambridge mathematical physics

                                Session
                                Date
                                17 April 2025
                                Reading
                                Warwick, Masters of Theory (2003), pp.ix-xi, 212-226
                                Authors
                                Andrew Warwick
                                  [maths:25-05-01]

                                  Rodin on categorial logic and Hegelian dialectics

                                  Session
                                  Date
                                  1 May 2025
                                  Reading
                                  Rodin, Categorial Logic and Hegelian Dialectics (2013)
                                  Authors
                                  Andrei Rodin
                                      [maths:25-06-12]

                                      Steingart on axiomatics and high modernism

                                      Session
                                      Date
                                      12 June 2025
                                      Reading
                                      Steingart, Axiomatics (2023), pp.1-24
                                      Authors
                                      Alma Steingart
                                        [maths:25-07-03]

                                        Mazzotti on reactionary mathematics

                                        Session
                                        Date
                                        3 July 2025
                                        Reading
                                        Mazzotti, Reactionary Mathematics (2023), pp.128-146
                                        Authors
                                        Massimo Mazzotti
                                            [maths:25-08-01]

                                            Mehrtens on nationalism and internationalism

                                            Session
                                            Date
                                            1 August 2025
                                            Reading
                                            Mehrtens, Nationalism and Internationalism (1996)
                                            Authors
                                            Herbert Mehrtens
                                              [maths:25-09-22]

                                              Weatherby on language machines

                                              Session
                                              Date
                                              22 September 2025
                                              Reading
                                              Weatherby, Language Machines (2025), pp.1-40
                                              Authors
                                              Leif Weatherby

                                              We were lucky to have Leif Weatherby present.

                                              Introduced by William Stewart.

                                                  [maths:25-10-19]

                                                  Schmid on diagonal method and dialectical logic

                                                  Session
                                                  Date
                                                  19 October 2025
                                                  Reading
                                                  Schmid, Diagonal Method and Dialectical Logic (2025)
                                                  Authors
                                                  Eric Schmid
                                                    [maths:25-11-24]

                                                    Miller on suture

                                                    Session
                                                    Date
                                                    24 November 2025
                                                    Reading
                                                    Miller, Suture (1977)
                                                    Authors
                                                    Jacques Miller
                                                      [maths:25-12-08]

                                                      Naderi on mark and lack

                                                      Session
                                                      Date
                                                      8 December 2025
                                                      Reading
                                                      Naderi, Mark and Lack (2018)
                                                      Authors
                                                      Reza Naderi
                                                        [maths:26-01-23]

                                                        Von Foerster on understanding understanding

                                                        Session
                                                        Date
                                                        23 January 2026
                                                        Reading
                                                        Von Foerster, Understanding Understanding: Essays on Cybernetics and Cognition (2003), pp.1-20, 247-261
                                                        Authors
                                                        Heinz Von Foerster
                                                          [maths:26-02-10]

                                                          Longo on the constructed objectivity of mathematics

                                                          Session
                                                          Date
                                                          10 February 2026
                                                          Reading
                                                          Longo, The Constructed Objectivity of Mathematics and the Cognitive Subject (2003)
                                                          Authors
                                                          Giuseppe Longo
                                                            [maths:26-03-06]

                                                            Husserl on the origin of geometry

                                                            Session
                                                            Date
                                                            6 March 2026
                                                            Reading
                                                            Husserl, The Origin of Geometry (1970)
                                                            Authors
                                                            Edmund Husserl
                                                              [maths:26-03-27]

                                                              Benacerraf on what numbers could not be

                                                              Session
                                                              Date
                                                              27 March 2026
                                                              Reading
                                                              Benacerraf, What Numbers Could Not Be (1965)
                                                              Authors
                                                              Paul Benacerraf
                                                                [maths:26-04-10]

                                                                Avigad on mathematicians in the age of AI

                                                                Session
                                                                Date
                                                                10 April 2026
                                                                Reading
                                                                Avigad, Mathematicians in the Age of AI (2026)
                                                                Authors
                                                                Jeremy Avigad
                                                                  [maths:26-05-01]

                                                                  Henkle on the ontology of number

                                                                  Session
                                                                  Date
                                                                  1 May 2026
                                                                  Reading
                                                                  Henkle, On the Ontology of Number, or the Limits of Structuralism (2026)
                                                                  Authors
                                                                  Jonah Henkle
                                                                    [maths:26-06-08]

                                                                    Atiyah on mathematics in the 20th century

                                                                    Session
                                                                    Date
                                                                    8 June 2026
                                                                    Reading
                                                                    Atiyah, Mathematics in the 20th Century (2002)
                                                                    Authors
                                                                    Michael Atiyah
                                                                      [maths:26-06-22]

                                                                      Meli on Newton versus Leibniz

                                                                      Session
                                                                      Date
                                                                      22 June 2026
                                                                      Reading
                                                                      Meli, Equivalence and Priority (1993)
                                                                      Authors
                                                                      Domenico Meli
                                                                          [maths:26-07-20]

                                                                          Deringer on political calculations

                                                                          Session
                                                                          Date
                                                                          20 July 2026
                                                                          Reading
                                                                          Deringer, Introduction: Political Calculations (2018)
                                                                          Authors
                                                                          William Deringer
                                                                              [maths:26-08-31]

                                                                              Jing on algorithm

                                                                              Session
                                                                              Date
                                                                              31 August 2026
                                                                              Reading
                                                                              Jing, Algorithm (2026)
                                                                              Authors
                                                                              Felicia Jing

                                                                              We were lucky to have Felicia Jing as a participant.

                                                                              Introduced by Lachlan Kermode.

                                                                              [maths:algorithmic-materiality]Algorithmic Materiality

                                                                              I’m delighted to kick off the Autumn/Fall with Felicia Jing’s essay here in the Math(s), Philosophy, History reading group.

                                                                              Felicia Jing just completed a PhD in Political Theory at Johns Hopkins University, is a visiting fellow at NYU’s Remarque Institute this Fall, and will be joining Brown University in the Spring 2027 for a postdoc in the Program of Science, Technology, and Society. The essay we read today is a condensed version of her dissertation’s first chapter that is forthcoming in Political Concepts: A Critical Lexicon.

                                                                              This essay offers us a new and more materialist angle on the history and politics of computer science. The materiality of the algorithm is, following Marx, not only the economy of the hardware on which it runs, but also the socio-political logic that structures developments in hardware, software, and programming. The substitution of software for hardware when it comes to questions of its economy—a substition spirited in no small part in media studies by Friedrich Kittler’s infamous claim that “there is no software”—displaces rather than addressses the question of the politics and historicity of computing.

                                                                              Jing shows that there is something about the logic of algorithms—and therefore of software, given code is treated as the materialization of algorithmic logic—that walks hand-in-hand with capital. Indeed, Jing’s gesture to this intimate contact between capital and computation builds on Alfred Sohn-Rethel’s chief insight, namely that one of the most conseqential results of capital’s perceptual physics [Best] on the division of labour is to conceptually separate the head from the hand, and therefore to valorize the labor that issues from the ‘intellect’ in a way that undermines the conscious and egalitarian contract of capital and the wage, that is, that all labour is exchangeable under the aegis of fair compensation.

                                                                              Jing narrates the courting of these two concepts first by touching on the algorithm as an Althusserian ‘absent concept’, and then by firming it up as a Robinsonnade with reference to the Marxian critique of prehistory:

                                                                              In a vanishing act of ‘hiding the machine’, algorithms are sanitized not only from the material development of hardware, its dirty industrial history, its dependency on the labor of earlier ‘human computers’ but also—importantly–from the state machine. That is, the centralized bureaucratic state, class antogonisms, and the legal forms of coercion were, at every moment, a site of struggle over and against the political form of an alorithm. Jing - Algorithm, pp.8-9

                                                                              Jing goes on to show how the conceptual constitution of the ‘algorithm’ as prehistorical flattens the history of computer science into a crude, teleological account, geared towards a narrative of ever-advancing progress. This flattened conception squeezes the possibility of criticality, politicality, and thus an emancipatory politics from the entire enterprise of computing, readying it to be cast, like a ketchup wrapper, into the dustbins of history as a bone that could never stick in the throat of capital’s voracious appetite.

                                                                              What I love about this essay is how Jing takes on Donald Knuth just as Marx did Adam Smith, i.e. as the originator of a mythology with real consequences. I think Knuth is the right figure to take on for a number of reasons, not least because it is also Knuth who establishes the idea of ‘literate programming’ as its idea, which is to say that Knuth argues that a program should be conceptualized as a work of art such a a novel, an artefact by analogy of literature chiefly, and not of industry. Jing’s argument shows how the Knuth’s analogical insistence in literate programming might hide another absent concept in the computer program. In its prehistorical guise as architected by a single and singular genius, the computer program becomes—like the novel—a form of expression distinctly fathered by modernity, and therefore by capital.

                                                                              To mark the genealogical relation between computing and capital in this way is not the same, critically, as consigning computing and computer science to the collection of practices with which we must not dare to engage should we seek an emancipated future. On the contrary, following Marx’s engagement with the political economy of his day, it is to insist that we must read figures such as Donald Knuth again, symptomatically, to articulate more concretely how capital and computing are entangled as logical structures, what power one does and does not have over the other.

                                                                              It is Jing’s keen engagement with this materiality of computing, a materiality truer than that which results from holding one’s eye up to the end of a fiber optic cable—as friend-of-the-pod Tung-Hui Hu once reported himself doing—that makes her essay an opportune way out of our group’s summer focus on the 19th century, our 19th century summer.

                                                                              One of our group’s recurring themes is how we should think the materiality of mathematics in general, and the materiality of pure mathematics in particular, the algebraic turn that authors we have read such as Jeremy Gray and Erich Hörl have referred to variably as mathematics’ modernism or modernization. Algorithmic materiality, it seems to me, skips hand-in-hand with the materiality of calculus, at least when the song of capital is playing over the speakers. The conceptual divisions we have tracked in previous sessions, between applied and pure mathematics, between pure mathematics and mathematic physics, and between algebra and geometry: all these divisions should be thought in the light of capital’s surreptitously enforced division between head and hand, between intellectual-qua-immaterial and manual-qua-material labour. This is what Jing’s essay illuminates for us, and I’ll now turn over to her to say a few words about it before we open up for any and all questions and comments as usual.

                                                                              References

                                                                              • Jing, Felicia. “Algorithm.” July 2026.
                                                                                [maths:26-09-30]

                                                                                Handelman on the mathematical imagination

                                                                                Session
                                                                                Date
                                                                                30 September 2026
                                                                                Reading
                                                                                The Mathematical Imagination: On the Origins and Promise of Critical Theory
                                                                                Authors
                                                                                Matthew Handelman
                                                                                  [maths:26-09-16]

                                                                                  James on vectors from Leibniz to Einstein

                                                                                  Session
                                                                                  Date
                                                                                  16 September 2026
                                                                                  Reading
                                                                                  Vectors from Leibniz to Einstein
                                                                                  Authors
                                                                                  James Propp