Schizo‐Math1

It is in Anti‐Oedipus that Deleuze coins the phrase “schizophrenic mathematics” (Gilles Deleuze and Félix Guattari, Anti‐Oedipus: Capitalism and Schizophrenia 372), which I have borrowed and shortened to “Schizo‐Math” in order to expand upon some of the themes introduced in the paper “Math Anxiety” by Aden Evens (Angelaki 5:3 (2000): 105).

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Notes

Simon Duffy

Department of Philosophy

Main Quad A14

University of Sydney

Sydney, NSW 2006

Australia

E‐mail: [email protected]

I would like to thank Daniel W. Smith for his generous comments when reviewing an early version of this paper.

It is in Anti‐Oedipus that Deleuze coins the phrase “schizophrenic mathematics” (Gilles Deleuze and Félix Guattari, Anti‐Oedipus: Capitalism and Schizophrenia 372), which I have borrowed and shortened to “Schizo‐Math” in order to expand upon some of the themes introduced in the paper “Math Anxiety” by Aden Evens (Angelaki 5:3 (2000): 105).

Gilles Deleuze, Difference and Repetition 114. Hereafter DR.

Carl Benjamin Boyer, The History of the Calculus and its Conceptual Development 11. Hereafter CB.

Gilles Deleuze, “Sur Spinoza,” 17 Feb. 1981. Hereafter DSS.

Gottfried Wilhelm Leibniz, The Early Mathematical Manuscripts 53.

Leibniz, “Letter to Varignon, with a Note on the ‘Justification of the Infinitesimal Calculus by that of Ordinary Algebra’ ” 545. Hereafter PPL.

George Lakoff and Rafael E. Nafiez, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being 224. Hereafter LN.

For a thorough analysis of this problem with limits in Cauchy, see CB 281.

Deleuze, “Sur Leibniz,” 22 Feb. 1972.

See J.L. Bell, A Primer of Infinitesimal Analysis .

Abraham Robinson, Non‐Standard Analysis 2.

• Given a function, f(x), having derivatives of all orders, the Taylor series of the function is given by

• where f^(k) is the kth derivative of f at a. A function is equal to its Taylor series if and only if its error term R_n can be made arbitrarily small, where

• The Taylor series of a function can be represented in the form of a power series, which is given by

• where each a is a distinct constant. It can be shown that any such series either converges at x=0, or for all real x, or for all x with –R<x<R for some positive real R. The interval (–R, R) is called the circle of convergence, or neighbourhood of the distinctive point. This series should be thought of as a function in x for all x in the circle of convergence. Where defined, this function has derivatives of all orders. See H.J. Reinhardt, Analysis of Approximation Methods for Differential and Integral Equations .

See Morris Kline, Mathematical Thought from Ancient to Modern Times 643–44. Hereafter MK.

Deleuze argues that “It was a great day for philosophy when […] Leibniz proposed […] that there is no reason for you simply to oppose the singular to the universal. It's much more interesting if you listen to what mathematicians say, who for their own reasons think of ‘singular’ not in relation to ‘universal’, but in relation to ‘ordinary’ or ‘regular’ ” (Deleuze, “Sur Leibniz,” 29 Mar. 1980).

Albert Lautman, Essai sur les notions de structure et d'existence en mathématiques 38; my trans. Hereafter ALI.

Höené Wronski, La Philosophie de l'infini: Contenant des contre‐refléxions sur la métaphysique du calcul infinitesimal 35; large sections of this text, translated by M.B. DeBevoise, appear in Michel Blay (ed.), Reasoning with the Infinite: From the Closed World to the Mathematical Universe 158. Hereafter HW. Page references will be given to the French and the English translation respectively.

Jean‐Baptiste Bordas‐Demoulin, Le Cartésianisme ou la véritable rénovation des sciences, suivi de la théorie de la substance et de celle de l'infini 414; my trans. Hereafter BD.

Note: the primitive function f(x)dx, expresses the whole curve f(x).

It was Charles A.A. Briot (1817–82) and Jean‐Claude Bouquet (1819–85) who introduced the term “meromorphic” for a function which possessed just poles in that domain (MK 642).

June Barrow‐Green, Poincaré and the Three Body Problem 32.

Manuel DeLanda, Intensive Science and Virtual Philosophy 15.

Georges Valiron, “The Origin and the Evolution of the Notion of an Analytic Function of One Variable” 171. Hereafter GV.

Benoit B. Mandelbrot, The Fractal Geometry of Nature 414. Mandelbrot qualifies these statements when he says of Poincaré that “nothing I know of his work makes him even a distant precursor of the fractal geometry of the visible facets of Nature” (ibid. 414).

Penelope Maddy, “Believing the Axioms” 488.

Jean‐Michel Salanskis, “Idea and Destination” 71.

Albert Lautman, Essai sur l'unité des sciences mathématiques dans leur développement actuel 58; my trans. Hereafter ALII.

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simon duffy

Simon Duffy Department of Philosophy Main Quad A14 University of Sydney Sydney, NSW 2006 Australia E‐mail: [email protected]