The emergence of infinitesimal calculus in the 17th century marked the arrival of a powerful problem-solving tool whose abstract language came to have far-reaching applications in the natural sciences. So seemingly limitless was its potential that some wondered whether it might serve as a universal calculator, capable of computing new knowledge even in disciplines beyond the natural sciences such as metaphysics, ethics, and aesthetics. Unlike Kant, who in the Critique of Pure Reason denied that mathematical methods could generate philosophical insight, 18th century writers engaged with the natural sciences probed the ability of mathematics to further human understanding. Friedrich Schlegel creatively employed mathematical formulas in his philosophical speculations, while Novalis brought various methods of calculus to bear on his encyclopedia project. The pleasure that these thinkers took in their mathematical divertissements was accompanied by reflections on the place of mathematics in the order of knowledge. Novalis and Goethe both criticized the dominance of instrumental calculus in apprehending the world. But they also tempered this criticism with poetic imagery that strikes a utopian balance between rational abstraction and aesthetic intuition.
Franziska Bomski is a literary scholar whose work focuses on the intersection of literature and science. Following a degree in German literature and mathematics she earned a PhD from the University of Freiburg with a study on Die Mathematik im Denken und Dichten von Novalis (2014). She has also examined the literary significance of mathematics in the works of Robert Musil and David Forster Wallace. She has held teaching positions at Goethe University Frankfurt, Yale University, and Beihang University. From 2012 to 2018 she served as the research coordinator at the Klassik Stiftung Weimar. She joined the Einstein Forum in 2018. Her recent publications include Genealogien der Natur und des Geistes. Diskurse, Kontexte und Transformationen um 1800 (2018; co-ed. with J. Stolzenberg), and “Equally Possible Cases: Robert Musil and Johannes von Kries” (with A. Albrecht), in The Legacy of Johannes von Kries: A Transdisciplinary Survey (in print 2019, ed. by G. Wagner).