Ricci-Curbastro, Gregorio (1853–1925)

Italian mathematician whose systematization of absolute differential calculus (the Ricci calculus) enabled Albert Einstein to derive the theory of relativity.

Ricci-Curbastro was born in Lugo, Romagna, and studied at several Italian universities and in Germany at Munich. From 1880 he was professor of mathematical physics at Padua. He was also a magistrate and local councillor.

By introducing an invariant element – an element that can also be used in other systems – Ricci-Curbastro was able to modify differential calculus so that the formulas and results retained the same form regardless of the system of variables used. In 1896, he applied the absolute calculus to the congruencies of lines on an arbitrary Riemann variety; later, he used the Riemann symbols to find the contract tensor, now known as the Ricci tensor (which plays a fundamental role in the theory of relativity). He also discovered the invariants that occur in the theory of the curvature of varieties.

With a former pupil, Tullio Levi-Civita, he published Méthodes de calcul différentiel absolu et leurs applications, describing the use of intrinsic geometry as an instrument of computation dealing with normal congruencies, geodetic laws, and isothermal families of surfaces. The work also shows the possibilities of the analytical, geometric, mechanical, and physical applications of the new calculus.