Mathematics, Language, Structure: Hermann Broch, the Sleepwalkers

Chapter 2, focusing on Broch’s The Sleepwalkers, analyses relations between mathematics and turn-of-the-century scepticism of language and investigation of form. The novel trilogy engages with research on the relations of mathematics and language, particularly by Gottlob Frege, and with the new approaches that emerge with it: the formalised language of analytic philosophy and literary formalism’s concentration on language as the basic building block of texts. The chapter also investigates how a competition of methodologies in modern mathematics informs the innovative form of the trilogy: it argues that the stylistically experimental third novel is informed by the central debate in the foundational crisis of mathematics, and traces the trilogy’s visions of total disintegration and valuelessness and, on the other hand, renewal through a counter-movement towards a non-rational element of common intuition to formalist and intuitionist approaches in mathematics. With its main focus on ways in which mathematics features as a structural model in The Sleepwalkers, this chapter shows how the trilogy presents mathematics as deeply implicated in the cultural development and explores the role of its modernist transformation for the form of the trilogy and Broch’s conception of modernist literature.

Conclusion: Modernism, Fiction and Mathematics

The conclusion summarises the varying ways in which the modernist and postmodernist fictions discussed in this book inform the notion of mathematical modernism. Based on the results of the study, the conclusion again argues for the need to account for the unique status of mathematics in the spectrum of the disciplines, particularly when the specific characteristics of mathematics gain attention with its modernist transformation. At the same time, mathematics becomes a necessary and fruitful concern of modernist studies, providing new insights on the roles of reason and imaginary concepts, as well as on modernist experimentation with literary form. This book’s examination of literary engagements with mathematics leads to questioning interpretations of modernism as mainly focused on negative aspects of modernisation and instrumental rationality. Fictions written in and about the period, as well as mathematical prose texts of the time, reconsider the foundations of reason and rediscover neglected aspects of rational domains, including, counter-intuitively, non-rational and imaginary dimensions. The conclusion emphasises that examining the place of mathematics leads to a more nuanced understanding of modernism’s complex engagement with its roots in the Enlightenment and its reassessment in postmodernism.

Mathematics and Fiction: Thomas Pynchon, Gravity’S Rainbow

Chapter 4 sets the engagement with modernist mathematics into broader context when examining the rise, fall and transformation of Enlightenment thinking and science in Pynchon’s Gravity’s Rainbow. This chapter also zeroes in on a topic that runs through all chapters: the interrelations of mathematics and fiction. The analysis focuses on illustrations of fictionality regarding the mathematical concepts of infinitesimals, the calculus, and probability theory and their philosophical and ethical consequences. The examination of interdependent ‘real’ and ‘fictional’ elements in mathematics provides a new perspective on Brian McHale’s identification of ontological uncertainty as the novel’s definitive postmodernist trait: the chapter shows that the novel’s renegotiation of mathematics is a decisive factor in its introduction of postmodernist features. As the title ‘Gravity’s Rainbow’ with its combination of a scientific and a poetical image implies, Pynchon’s novel suggests that the shared use of fictional concepts both in mathematics and in literature connects the seemingly opposed realms.

Mathematics, Epistemology, Ethics: Robert Musil, the Man Without Qualities

Chapter 3 argues that mathematics in Musil’s The Man without Qualities not only exemplifies the side of rationality but also encompasses mystical elements and transitional states between these opposites, tracing the identification of a non-rational element in mathematics to the debate between the logicist/formalist and the intuitionist schools. The chapter thus re-examines notions of the rational and non-rational and attempts at their synthesis from the perspective of the history of mathematics. It also demonstrates that, for Musil, mathematics answers to two major instances of modern crisis: the failing of reason and the loss of trust. Paradoxically combining critical questioning of its foundations and confidence in its usefulness, modern mathematics connects the approaches of analytic philosophy and outcome-focused pragmatism. The chapter thus argues that mathematics becomes a model not only of exactitude but also of vagueness and that in this paradoxical double-function it serves to inspire the critical trust needed to adjust epistemology, ethics and aesthetics in a time of profound change. Not least, in its own form The Man without Qualities translates the model of mathematics into literary aesthetic by reflecting simultaneous examination of its conditions and trust in the credit of fiction.

Mathematics and Politics: Thomas Pynchon, against the Day

Chapter 1 on Pynchon’s Against the Day focuses on interrelations between mathematics and politics as domains that are both shaken by crises of fundamental beliefs. It examines how Pynchon’s novel draws on the history of mathematics and on concrete concepts to explore the crisis of representation, the transformation of anarchism from political to artistic expression, and the possibilities inherent in imaginary domains. Main mathematical concepts and metaphors include imaginary and complex numbers and the ‘foundational crisis of mathematics’, which Against the Day establishes as producing a mathematics that is ‘an-archistic’ in terms of its loss of foundations and that forms part of the exploration of anarchism across the twentieth century. This chapter demonstrates the centrality of mathematics to Against the Day’s renegotiations of possibilities and responsibilities of the political and the literary, and it shows how the novel’s reimagining of modernism illustrates the relevance of mathematics in developing twenty-first-century responses to the crisis of modernity.

Introduction: All that Counts – Modernism, Fiction, Mathematics

The introduction establishes the theoretical grounds for the analysis of mathematics and modernism and situates the book within the critical contexts of modernism and science studies and literature and science studies. It sets out the unique epistemological status of mathematics, key stages in its historical development, and charts the new territory that the book opens up by examining literary engagements with mathematics and modernism. With reference to texts and theories by Herbert Mehrtens, Jeremy Gray, Leo Corry and Moritz Epple, the introduction establishes the concept of modernist mathematics, the role of the so-called ‘foundational crisis of mathematics’, and competing logicist, formalist and intuitionist positions, particularly as represented by David Hilbert and L.E.J. Brower. The introduction also sets out how the issues at stake in mathematics feed into the modernist revaluation of rationality and Enlightenment values and echo the sense of crisis in other areas. A particular focus is on theories that reflect on mathematics as a human construct and deliberately created fiction, including texts by Friedrich Nietzsche, Ernst Cassirer, Oswald Spengler, Hans Vaihinger, Hartry Field and Alain Badiou.