Gregorio Ricci-Curbastro

Gregorio Ricci-Curbastro (1853-1925) was an Italian mathematician and physicist.

In his A Concise History of Mathematics, Dirk J. Struik recounted:

By 1870 [Bernhard] Riemann's ideas became more and more the common good of the younger generation of mathematicians. His theory of quadratic differential forms [See Quadratic form] was made the subject of two papers by the German mathematicians E. B. Christoffel and R. Lipschitz (1870). The first paper introduced the "Christoffel" symbols. These investigations, combined with Beltrami's theory of differential parameters, brought Gregorio Ricci-Curbastro in Padua to his so-called absolute differential calculus (1884). This was a new invariant symbolism originally constructed to deal with the transformation theory of partial differential equations [See Differential equations], but it provided at the same time a symbolism fitted for the transformation theory of quadratic differential forms.

In the hands of Ricci and of some of his pupils, notably of Tullio Levi-Civita, the absolute differential calculus developed into what we now call the theory of tensors. Tensors were able to provide a unification of many invariant symbolisms, and also showed their power in dealing with general theorems in elasticity, hydrodynamics [See Fluid dynamics], and relativity. The name tensor has its origin in elasticity (W. Voigt, 1900).

Beyond his vocabulary of symbols, Ricci-Curbastro "generalised [tensor theory] into a tensor-calculus applicable to transformations in curved space of any number of dimensions...from 1887 onwards: it first became widely known when a celebrated memoir describing it was published in 1900 by Ricci and [Tullio] Levi-Civita (Math. Ann. liv [1900], p. 125....)."