UC Berkeley

While mathematics is often associated with quantification, this dissertation aims to show that it can also offer powerful ways of thinking qualitatively about literary form. In particular, it tracks the development of different modes of formal thinking that are flexible enough to work across differences in medium, scale, and temporality, and which can unify forms undergoing change. In my first chapter, "Mathematical Ekphrasis," I show how nineteenth-century approaches to algebra and geometry - which conceptualize these fields as the sciences of time and space - align them with the mediums of poetry and painting respectively, arguing that coordinate geometry can be read as a kind of ekphrasis, in ways which not only illuminate mathematical aesthetics, but also Pre-Raphaelite art and literature. Chapter 2, "Vanishing Points," is centered around a personal connection between Christina Rossetti and Arthur Cayley, and explores how both poet and mathematician conceptualize space in a projective or "perspectival" fashion. Chapter 3, "Topological Poetics," argues that Gerard Manley Hopkins's poetry manifests a fundamentally topological approach to form, in which forms are defined not by their metrical properties, but by invariant features that persist throughout continuous transformations. Chapter 4 builds upon the association between algebra and temporality first broached in Chapter 1 to argue that number theory can offer a new vocabulary for discussing the form of poetic temporality, especially as expressed in Elizabeth Barrett Browning's Sonnets from the Portuguese and Aurora Leigh. Finally, the coda turns to methodological questions, using the debates surrounding computational proof in mathematics (arising out of the computer-based solution to the four-color theorem), and the digital humanities, in order to interrogate the values and methods upon which scholars in both fields base their work.