Spatial Reckonings: Mapping the Raumproblem in Modern Mathematics and German Modernism, 1890-1933

Abstract

Despite the often-celebrated ascent of 'interdisciplinarity' within academic research, in perhaps every setting, mathematics and the arts are still viewed as unrelated disciplines with divergent origins, influences and aims, thus exemplifying the 'two cultures' described by C.P. Snow in the 1960s. It is precisely this enduring perception that this project seeks to undermine. By placing the transformative era of the late 19th Century to the early 20th Century under the microscope - a period in which both mathematics and the arts underwent significant change - this thesis aims to bring modern mathematics and German-language modernism into a fruitful conversation with one another, showing how label 'modernism' envelops the two realms. To do so, it is proposed in this thesis that both modern mathematics and aesthetic modernism can be tied to a common Raumproblem ['problem of space'], a shifting understanding and representation of space and spatiality. This manifests in particular as a nuanced dynamic between transformation and invariance, which in turn actions and is enveloped by a broader complication of spatial objects and ontology in language - mathematical or otherwise. With this 'spatial reckoning' as a central analytical lens, this dissertation proceeds by uncovering commonalities between the two 'cultures' on two main levels: shared philosophical influences and parity on the level of expression and modes of representation. Firstly, it is argued that the philosophical influences in each field when it comes to a 'modern' re- evaluation of space are by no means as divergent as current scholarship suggests. By working inwards from a wider German context towards Felix Hausdorff, a key proponent of mathematical topology who also published philosophical and creative work, the unexpected influence of Friedrich Nietzsche becomes evident, whose significance in the simultaneous waves of modernist art and literature is perhaps unrivalled. Having traced these philosophical connections, the remaining chapters serve as case studies in 're-reading' key works of literary, filmic and visual modernism in light of their mathematical Doppelgenger. Beginning with the entanglement of transformation and invariance and working progressively outwards towards the level of language and ontology, this thesis interweaves these mathematical developments with Franz Kafka?s prose, F.W. Murnau's innovations in Weimar Cinema, an underrepresented voice of Vienna Modernism in Mela Hartwig, and differing intermedial and programmatic movements like Bauhaus and Dadaism. Taken together, these comparative studies seek to demonstrate that modern mathematics and aesthetic modernism begin to harmonise with one another at this unique moment in time; they begin, in a sense, to 'speak' in a common tongue. In short, by beckoing modern mathematics into the wider modernist arena, this thesis calls for a thorough revision of the divides between these two cultural and academic discourses, and it makes the case for a much more inclusive and cross-disciplinary conception of modernism as a whole.