Ricci-Curbastro, Gregorio

Gregorio Ricci-Curbastro, (born January 12, 1853, Lugo, Papal States [Italy]—died August 6, 1925, Bologna), Italian mathematician instrumental in the development of absolute differential calculus, formerly also called the Ricci calculus but now known as tensor analysis.

Ricci was a professor at the University of Padua from 1880 to 1925. His earliest work was in mathematical physics, notably on the laws of electric circuits, and in differential equations. Ricci created the systematic theory of tensor analysis in 1887–96, with significant extensions later contributed by his pupil Tullio Levi-Civita.

Tensor analysis concerns relations that are covariant—i.e., relations that remain valid when changed from one system of coordinates to any other system. The origins of tensor analysis are rooted in the differential geometry of the noted German mathematician Bernhard Riemann. For some time Ricci’s new calculus was regarded as a technical accomplishment rather than a profound innovation. Later, however, Albert Einstein found Ricci’s methods to be indispensable in the mathematical formulation of his theory of general relativity. In applying tensor analysis to the study of surfaces, Ricci encountered several interesting metric properties of hyperspaces. One of them was the Ricci tensor, which occurs in Einstein’s gravitational equations and is often called the Einstein tensor.