Gregorio Ricci-Curbastro

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Lore & Background

Ricci-Curbastro completed his high school studies privately at only 16 years of age, enrolling on the course of philosophy-mathematics at Rome University in 1869. The following year, the Papal State fell, and so Gregorio was called by his father to the city of his birth, Lugo di Romagna. Subsequently, he attended courses at University of Bologna during the year 1872–1873, then transferred to the Scuola Normale Superiore di Pisa. In 1875, he graduated in Pisa in physical sciences and mathematics with a thesis on differential equations, entitled 'On Fuchs's Research Concerning Linear Differential Equations'. During his various travels, he was a student of the mathematicians Enrico Betti, Eugenio Beltrami, Ulisse Dini and Felix Klein. In 1877 Ricci-Curbastro obtained a scholarship at the Technical University of Munich, Bavaria, and he later worked as an assistant of Ulisse Dini, his teacher. In 1880, he became a lecturer of mathematics at the University of Padua, where he dealt with Riemannian geometry and differential quadratic forms. He formed a research group in which Tullio Levi-Civita worked, with whom he wrote the fundamental treatise on absolute differential calculus (also known as Ricci calculus) with coordinates or tensor calculus on Riemannian manifold, which then became the lingua franca of the subsequent theory of Albert Einstein's general relativity. In fact, absolute differential calculus had a crucial role in developing the theory, as is shown in a letter written by Albert Einstein to Ricci-Curbastro's nephew. In this context, Ricci-Curbastro identified the so-called Ricci tensor, which would have a crucial role within that theory. Ricci-Curbastro also published important works in other fields, including a book on higher algebra and infinitesimal analysis, and papers on the theory of real numbers, an area in which he extended the research begun by Richard Dedekind. He participated actively in political life, both in his native town and in Padua, and contributed with his projects to the Ravenna-area land drainage and the Lugo aqueduct. An asteroid, 13642 Ricci, is named after him.

Reader's Guide

Gregorio Ricci-Curbastro's primary legacy is the discovery and development of tensor calculus. The advent of tensor calculus in dynamics goes back to Lagrange, who originated the general treatment of a dynamical system, and to Bernhard Riemann, who was the first to think about geometry in an arbitrary number of dimensions. He was also influenced by the works of Elwin Bruno Christoffel and of Rudolf Lipschitz on the quadratic forms. In fact, it was essentially Christoffel's idea of covariant differentiation that allowed Ricci-Curbastro to make the greatest progress. The Ricci tensor, named after him, became a central component of Einstein's field equations. Beyond tensor calculus, Ricci-Curbastro contributed to real number theory, extending Richard Dedekind's work, and wrote a book on higher algebra and infinitesimal analysis. His honors include membership in several academies, such as the Lincei Academy (from 1899) and the Pontifical Academy of Sciences (from 1925), and he served as president of the Veneto Institute of Science (1916 to 1919) and the Galileian Academy (1920 to 1922). His work remains essential in differential geometry and theoretical physics.

Did You Know?

• Ricci-Curbastro completed his high school studies privately at only 16 years of age.
• He signed his most famous publication with Tullio Levi-Civita as 'Gregorio Ricci' — the only time he used the shortened form of his name in a publication.
• Albert Einstein wrote a letter to Ricci-Curbastro's nephew confirming the crucial role of absolute differential calculus in developing general relativity.
• An asteroid, 13642 Ricci, is named after him.
• He contributed to the Ravenna-area land drainage and the Lugo aqueduct projects.