# Gregorio Ricci-Curbastro

**Gregorio Ricci-Curbastro** (Italian: [ɡreˈɡɔːrjo ˈrittʃi kurˈbastro]; 12 January 1853 – 6 August 1925) was an Italian mathematician born in Lugo di Romagna.[1] He is most famous as the inventor of tensor calculus, but also published important works in other fields.

Gregorio Ricci-Curbastro | |
---|---|

Born | |

Died | 6 August 1925 72) | (aged

Nationality | Italian |

Alma mater | Scuola Normale Superiore di Pisa |

Known for | Tensor calculus Ricci calculus |

Scientific career | |

Fields | Mathematics |

Doctoral advisor | Ulisse Dini Enrico Betti |

Doctoral students | Tullio Levi-Civita |

With his former student Tullio Levi-Civita, he wrote his most famous single publication,[2] a pioneering work on the calculus of tensors, signing it as Gregorio Ricci. This appears to be the only time that Ricci-Curbastro used the shortened form of his name in a publication, and continues to cause confusion.

Ricci-Curbastro also published important works in other fields, including a book on higher algebra and infinitesimal analysis,[3] and papers on the theory of real numbers, an area in which he extended the research begun by Richard Dedekind.[4]

## Biography

### Youth

Completing privately his high school studies at only sixteen years of age he enrolled on the course of philosophy-mathematics at Rome University (1869). The following year the Papal State fell and so Gregorio was called by his father to the city of his birth, Lugo. Subsequently he attended courses at Bologna, but after only one year he enrolled at 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 Fuches’s Research Concerning Linear Differential Equations”. During his various travels he was a student of mathematicians of the calibre of Enrico Betti, Eugenio Beltrami, Ulisse Dini and Felix Klein.

### Studies on absolute differential calculus

In 1877 Ricci-Curbastro obtained a scholarship at the Technische Hochschule 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 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.

#### Influences

The advent of tensor calculus in dynamics goes back to Lagrange, who originated the general treatment of a dynamical system, and to Riemann, who was the first to think about geometry in an arbitrary number of dimensions. He was also influenced by the works of Christoffel and of Lipschitz on the quadratic forms. In fact, it was essentially Christoffel’s idea of covariant differentiation[5] that allowed Ricci-Curbastro to make the greatest progress.[6]

### Recognition

Ricci-Curbastro received many honours for his contributions.

He is honoured by mentions in various Academies amongst which are:

- The Veneto Institute of Science - Istituto veneto di scienze - letters and articles (from 1892), of which he was then president from 1916 to 1919.
- The Lincei Academy - Accademia dei Lincei - of which he was a member from 1899.
- The Academy of Padua - Accademia di Padova - from 1905.
- The Science Academy of Turin - Accademia delle Scienze di Torino - from 1918.
- The Galileian Academy of Science - Accademia Galileiana di Scienze, Lettere ed Arti - letters and articles, of which he was then president from 1920 to 1922.
- The Academy of Sciences of the Institute of Bologna - Reale Accademia di Bologna - from 1922.
- The Pontifical Academy of Sciences - Accademia Pontificia delle Scienze - from 1925.

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.

## Publications

- Ricci-Curbastro, Gregorio (1898),
*Lezioni sulla teoria delle superficie*(in Italian), Verona: Drucker[7]

## See also

## Notes

- Levi-Civita, Tullio (1926), "Commemorazione del socio nazionale prof. Gregorio Ricci-Curbastro" [Commemoration of national member Gregorio Ricci-Curbastro read by member T. Levi-Civita at the meeting of 3 January 1926],
*Mem. Accad. Lincei*(in Italian),**1**(8): 555–564 - Ricci, Gregorio; Levi-Civita, Tullio (March 1900). "Méthodes de calcul différentiel absolu et leurs applications" [Methods of the absolute differential calculus and their applications].
*Mathematische Annalen*(in French). Springer.**54**(1–2): 125–201. doi:10.1007/BF01454201. - Ricci-Curbastro, Gregorio (1918),
*Lezioni di Analisi algebrica ed infinitesimale*(1926 ed.), Padova: Tip. Universitaria - Ricci-Curbastro, Gregorio (1897), "Della teoria dei numeri reali secondo il concetto di Dedekind",
*Gior. di Matem.*,**35**: 22–74 - Christoffel, E.B. (1869), "Ueber die Transformation der homogenen Differentialausdrücke zweiten Grades",
*Journal für die reine und angewandte Mathematik*, B. 70: 46–70 - Ricci-Curbastro, Gregorio (1887), "Sulla derivazione covariante ad una forma quadratica differenziale" [On the covariant differentiation with respect to a quadratic differential form],
*Rend. Acc. Lincei*(in Italian),**3**(4): 15–18 - James, George Oscar (1899). "Review:
*Lezioni sulla Teoria delle Superficie*, by Gregorio Ricci" (PDF).*Bull. Amer. Math. Soc*.**7**(8): 359–360. doi:10.1090/s0002-9904-1901-00816-6.

## References

- Tonolo, Angelo (1954), "Commemorazione di Gregorio Ricci-Curbastro nel primo centenario della nascita" (PDF),
*Rendiconti del Seminario Matematico della Università di Padova*(in Italian),**23**: 1–24 - Goodstein, Judith R. (2018).
*Einstein’s Italian mathematicians : Ricci, Levi-Civita, and the birth of general relativity*. American Mathematical Society. ISBN 978-1470428464.