This thesis argues that beauty served as a critical epistemic tool in late nineteenth-century mathematics: an intuitive compass that trained mathematicians to choose between competing claims to truth in an era where it became clear that formal systems could not guarantee completeness or certainty. Across three chapters, I trace how aesthetic judgment functioned not only as a personal sensibility but as a shared heuristic for navigating this foundational ambiguity. The through-line, thus, is found in the transformation of beauty from a source of internal discomfort, such as in Euclidean geometry, to a logic of mathematical discovery, as seen in Henri Poincaré’s own breakthroughs, to a cultural medium through which abstract ideas entered artistic modernism.