Appears in collection : History of mathematics, Philosophy of mathematics, and mathematics: which interactions? / Histoire des mathématiques, Philosophie des mathématiques, et mathématiques: quelles interactions?
Rossana Tazzioli will discuss the case of differential geometry, focusing in particular on Eugenio Beltrami (1835–1900) and his celebrated model of hyperbolic plane geometry. For Beltrami, the material construction of this model was an important factor in the acceptance and dissemination of non-Euclidean geometry. Like other 19th-century mathematicians, he believed that non-Euclidean geometry played a crucial role in understanding physical reality and, more generally—through the application of elasticity theory—in explaining how physical phenomena propagate through space.
With the tensor calculus introduced by Gregorio Ricci Curbastro (1853–1925) and further developed by Tullio Levi-Civita (1873–1941), differential geometry became a powerful framework in which Einstein's gravitational equations could be formulated. Yet these mathematicians approached geometry and its relation to physical reality from a new perspective: they viewed the connections between geometry and physics as more intricate, and chose to remain “agnostic,” leaving direct engagement with physical problems to theoretical physicists.
