Abstract
This essay juxtaposes a particular a set of novel mathematical ideas from the early nineteenth century with a synchronous development in literary criticism. Important mathematical discoveries of the 1820s, such as non-Euclidean geometries, new impossibility results, and new proof ideals, exhibit structural similarities with notions of Romantic irony expressed by literary critic and philosopher Friedrich Schlegel (1772–1829). The essay shows how both fields—mathematics and literary criticism—were at the time attempting to come to terms with the Kantian divide between the Ding an sich and Ding für uns , and thereby both fields reacted to profound shifts in perspective. By analyzing Schlegel’s notion of Romantic irony in relation to these key mathematical examples the essay presents new insights into the historiographical fields regarding literature and mathematics. This contribution to historiography is twofold: the essay sheds new light on a set of important mathematical developments, while at the same time bringing the historiography of mathematics and literature to bear on each other on a deeper, structural level.
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