Mathematical Metaphors in André Bazin’s Neorealism: From Integral to Asymptote and Beyond

This chapter explores the use of mathematical metaphors in André Bazin’s neorealist film criticism, particularly in his writings on Vittorio De Sica’s Bicycle Thieves, Umberto D., and Miracle in Milan. While Bazin did not develop a formal mathematical theory of cinema, he explicitly employed concepts from calculus and analytic geometry—such as the integral and the asymptote—to articulate the ethical and perceptual structure of cinematic realism. Building on these insights, this chapter extends Bazin’s critical vocabulary by introducing additional mathematical concepts—limit, infinitesimal, and singularity—to better articulate the structure of moral attention in neorealist cinema.